(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 147708, 3618]*) (*NotebookOutlinePosition[ 148352, 3640]*) (* CellTagsIndexPosition[ 148308, 3636]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Application of the Boltzmann transformation\nand the method of \ successive approximations \nto solve a heat conduction problem", "Subsubtitle", FontSize->18, FontVariations->{"CompatibilityType"->0}], StyleBox["\n", FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}], StyleBox["Author's Data", FontSize->14, FontWeight->"Bold"], StyleBox[": ", FontSize->14], StyleBox["Housam BINOUS\nDepartment of Chemical Engineering\nNational \ Institute of Applied Sciences and Technology\nTunis, TUNISIA\nEmail: \ binoushousam@yahoo.com ", FontSize->14, FontWeight->"Plain"] }], "Title", TextAlignment->Center, Background->RGBColor[0.605478, 0.996109, 0.605478]], Cell[OLEData["\<\ d00003T0003noooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooe80K`1_07@0801506h0M01b07T00000000000000000 0000000000000000000000000000000000000000000F00D0ooooooooool40000 48f1I9]?ca66jP2Z0;TYj0000000000000000>0WA4QVnlH10`000<0B00000000 0@1?06`0I@000000000000000000000000000000000000000000000000000000 0000000000000000000000X00P7oooooooooooooool000000000000000000000 0000000000000000000000000000000050000000001@06T0H`1d07D0LP1U07<0 0000000000000000000000000000000000000000000000000000000000000000 4P020Oooooooooooooooo`000000000000000000000000000000000000000000 000000D0002j0`0000000500K`1g06D0LP1@06l0J@1^07@0801406l0H`1e06d0 I@1^07@000000000000000000000000000000000000X0080oooooooooooooooo 0000000000000000000000000000000000000000000000003`000?dI00000000 o_ooookoooonoooo10000?koool600001`0000P0000900002P0000/0000<0000 3@0000h0000?000040000140000B00004`000?kooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooolo0000@000044000120000o_oood@000150000AP0004L000180000 B@0004X000010000oooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooooooooooooooooooooooooooooooooooool100020000000000000000 0000000000000000000000000000000000000000000000000000000000000000 Kg9`Kg;YL`0300000@0001h0000H0000E6UdLVEc86AULb1TJF5`Kg=YM6UfIG<0 0`000040000?0?8350400000mPlN0000500005o0TN?I6@001P3d0`<0Z01RJFi_ MG<80000HP1Y06h0K`1e07<000000000M=@C07CD4`010?ko0`X00?ooool@SH5T Vdo?4HKZ0:X0^BWX8P00051bjG=UKWAQM6U_KR1=JF=bKg=_IW@PD6mgIG9@KfU^ M00?0000CE=@LVEcIFidHGAYKfh04P00051_MfEbD6mYKW@^DfQ_Mbhh0?@i/W40 0000000000000000;@43060Q6o2b0`00=5Tj0aRL19?7UmXc4IQ7eG`900000000 0000060I00203`00:5HW0?0660200`000?ihfZFFBfSD@1S7IbHk^mTdBN^feUHl A8/_e59kDL@GB3giMPm5Y=S:5YNjY[B;KCa8`H=B?5@_?T0lf0DA4KDP1LG7AM23 ]8RT7Sb8F4D@Gj2eB]O<=lTh/k@X^Y1UOS?OmimoI[in9cK_Jk;jHkb_bMYSLDm>4Ogf Q9RWM3JGjGJfIGZLGFj^mM2?=injKn KMkB]ARe^n;b_:?fTASSUB4G[3k2eb[R>>Ik`SU[V;=TWeVSgfJlG?14G=K;6VN1 j`F?DCWOdO?U:UlaICe7oeRVS^mEm1gm9iGe7Gf]X^oCoKK:;l]TOIl^;U?7VjR/ ki6F6WWL8l>ciGb?C5E=_doh_nYSe3h?_]9RWlhJS=/4KmKElKH4hmJ@KiXkH;a3 k6<_U^<;eQXTSfL=6oHQ;oPZc=L[V<0Ae9Z?^1kZQInC5:adYc_=bE=jZUlnAj`HMQ_@^2[l4CLTg`cIRJcb/n6WOdKG0B30UnKC84CobgT9mZ W2M2_X@iOaGaLJR_=b:Nle/AcgULn7U1ECm32QNd=5;72b5?La:F_[g_cU`gYOGZ TFM@=ef^4GjW6?0]0bm2a>NZ@0VP>o3eP`UI/=_[cVMbZ8kYXR1S?^Z71?Hgn3J5 BV]DPoaO_`F8l`40000mQTD02@00038:Y0Ae0`40000mQTD02@00038:1PG:0P40 002fQSd02@00038:E@Bl0P40002fQSd02@00038:D`=A2040000nQTD02@00038: D`L1040002fQSd0 2@00038:10>61040002fQSd02@00038:D`>S0`40000mQTD02@00038:]@?50P40 002fQSd02@00038:10>l0P40002fQSd070000?/2Pol00000002@0@0000070P0@ E6U]IGa2040000`QSl02@00038: D`?C1`40000/QQl02@00038:D`00L05T0>00Q03d0>01I03P08@0K03P0>00K01`08@0m02L0F@0m01`0 >00Q01`0?@0m01`0?@0Q01`08@0m03L0700m02L0?@0m01/0>01H00@0000^0@00 100002d11P040000l04400<0000000000000000000000000000004i1CTT00000 0000``/800000P0000L1Z040o_l32P00oooooa2=PFBKCllAQ^X0ZP2i:NPR0000 D7;YLfE^M65dJFm^84eYHg9_LfmVM21@KgMULU1_JFid00l0001=De1bIG=UKWAQ M6U_KP0B0000D6mgIG9@KfU^M2iCJ6mg;SP0m3VbL@0000000000000000401@20 H24Kl943001k`l3/c_k]mGl4afV3ZF@IUf:b19TKfFDNc2: d6:GA;LEGM;Y40/M2ToVXCn7j90;4B:Q41h2ja;D8IB8/D>7R4b2B0_B;=cVoMk< hke=:G9PU]oWoGjoko^m=kmi>`X:8:CNl3ToJ2^R5g7^0?H/[2R^YN1R/@QF_E;U SPEiG0SWXngELLOJXDGA5UBT`BSVl1?7VW9^/aZQ`e4Wahd9XJHMSV^aTePUCWF]4;[o8W9jW^87:85HQm6/EH[LcKKkOPdhfCE QcRJ75W/On[LI/>goTYo>/4d5DCWfV_dhn/ZCJe1Om>K8TKMnWXHJUd@M0VQ4[Fl m[_4Zof:ga_k5?;6GTKHF28lj6=SRO1mWMFDGdE^CEBAeYC/c:Cjc9ID_gTRVnVh />hJFDgH[FTV<^bW2TVGad=;D6>GbhG`P2;j2n43B?Ag6Y4XiAcWDH?b06L<;M>A lkPNmSK9NC/BfMB?Q26OlmL0j7=>jj:NZ@mS>EoF/dTZ9>KKi8L^j]_TV5oD/hV/ Ia=Icl;]5J:NQJOSC2oPlU1:NgNilIWV;OCWBN_7iOh3Hk3C_MTenS@ d[O`e;Fin3mgJ1[FglgGnaXjX_N?NMIh>gN_?doYnVHRKM3iMMhnQ]]POHeI[e?W X=IfnBicOeUPSU2Lh_337Ne2]lB2fPCjSgPO[XI4]_0MGMBkSBOP95UbnIG:N=WUN`[S kcaNPkkmb>lW[M4[VM2hX:JA;:oh?8JOK:Q4o/NgRMiZ;>F/`Kk G<>ONfPCi@K>Po3LMg5NeTBmC^3T:QWjP]1fGmJdSOeGdCD =oF3T[i=cTETOQLDmFfbWh/0U07N_FP0_`4B0180o`4000P010<90000?`<1 0040403`1b00003oool000000820P0000000^n3S030020@<0003oooooooooo`000000000000000000000000000000000000000000 000004<0000h0P00000004<0M@1b0780I@1^07@0801E07<0I@1b000000000000 0000000000000000000000000000000000000000000J0080oooooooooooooooo 0000000000000000000000000000000000000000000000000P00038000000000 0@1306l0K@1`04l0HP1Z00000000000000000000000000000000000000000000 0000000000000000000001800P0100000P000?ooool000000000000000000000 00000000000000000000000000030000N`000000000?0000j0000080003T1000 7P0000h00014JF5`Kg=YM6UfIB0a06l07P0000L0001RJFi_MG<0M1h000070000 HVU^KgEc07@N00000P0003D0KVlN00005@0004eYHg9_LfmVM21@KgMULU1_JFid 001@0400001@;XFP0@000400002PMJjP4^g60D000010XD98I__60@<000060000 00000000000000000000000000110780J@1Q06`0803no`001@42000000000000 00000000000100000]G=eI`^6a2CU`P0:bci[S0000080P004000004000280000 0`000900000?0000[00000@0002l00001P000<@000070000c00000P0003D0000 2@000=`0000:0000i00001L0003/00002`000?@0000@0000o00001<000040@00 5P0000`1000=0000504000`0001Y0@000P000>@4000N00005000045VIVUSJ65W IB3P86`WjF=bHFh07P0000P0001dMFiYKF5b00<0002g7@000`00004000030000 0@0000<0000000000`00000000030000000000<000112PX02`000000000;0000 000000/0000000002`000000000N4000100000H00011LVUQK00B0000CFmTj6aU 871QLR1TjFIQMG@05`0004eYHg9_LfmVM215LGEQM6U_KR0c;S003P0004AYHG1_ LfUdJGIU8340310000P0000N00004P00051_K6USIGP3S`@00040j@0@003P4000P1H000D0000:0000000000000001000000000@l02@B/0000 000:10@0000700003`3<3iP000000Q2S06/Z1<0U:PC01KW1c08000000000:bX4`1jF`T`Y:PC000010000:@? 20000800@0000?oo002U3``000000008;P0000L000000:T?2P0000L0000200`4 00100:`mP3:VS^]1iC70`41000?0?X3 I`000000oP<300000040003m0c@0000S0000I00002<0001T0000200000000034 Z1<0NU/9<00000000000o?goo`00000101<0L03k0`P000000000L0P00700n`<8 00000@00040;000O01<4?0000000o@X3000000l0n0??2@000P3_0aP0000100000@872@P000000000000000004`1P 0?0780000?ooo`000000P8200000002kh><0I002IV@2Ic000H03`1b00003o ool0000009JFUP000000nmmC0?nIIP3<<`00VFH00600l0LP0000oooo00000020 P800000009W RQ0?017`40000000``/800000`0000T2Z00?00g`@0000000W`l4000010000000 X0l20000:P000:4?5P0000800000000800010080000000803P000?X?10000000 000?00C`^00001802_0800001P@0000:002300_`<00007l00@050800_82X0841 100028<100002;l10@0A0<010@002?l10@0900420P0020004?080000GPlP460E RQ0?017`40000000``/80000100000P2Z00?00g`@0000000W`l4000010000000 X0l20000:P000:4?5P0000800000000800020080000000803P000=P?10000000 000?00C`@P0001802_0800000@@0000<001c00_`:P000841oiWo09<1SYn;09@1 g[eX0;l14P0B0?l1000800@32@0003l30@010100l0LP0000oooo00000020P800 00000;_Ph`0c00000l0RQ<`0000002j3a00001O05l0 G`1@0500E00a0300002;4a0000000>/^200001;]aP40D8RP802j3b80001=06l0 I03X06`0I@0P0700H@1b0200I03Y06H0H@1e07@03`3^0j<200020>l360000000 000?400000000000080000000`0C00l030@C0P003`02l0/2000P00S`200000<0 000520003`03l8<1000?00C`:00000402O0@0000000000000000000000000080 2_08000000P000D0000?00C`IP000;842_08000010P0010:001c00_`:P0000A1 0@0000/11`0003l10001084110002;l1400@0?l1000803l2000200004?080000 @0E70c0Cn@h?017`30000000`@/400001`0000l01?3M0000XP`:l0P000052000 00X00:<02o0l0000P01/BjP0Q@020000Q`060000_`020080P@440008P`400008 _`400100`0410008o`4000P00@820008000@l0P0001=0kl2AQ=]10l03O1a0000 002O3`@000040000002X3b/0001DJ6DPKF5dJ6E]HGAYHf5/86I_LVeeK65dJFm^ 86mV87AXIB1`LVmRK6E]002Q3aH0000/000000000000;00000400P0101P0002Z 3``0000/00001P0000T4000?00C`J00001802_0800000@P0000<002c00_`@P00 08011`000841oiWo08<1l05f48`1c_oooi<1SYn;09@1g[eX09`12`00@;l17P0O 0?l1000800@32@0003l30@0101<08_460000_`400600403`1b00003oool00000 0820P0000000^n3S03eIOFaDEAHokkiiVRbbAXSOPF] ^U6AgJWWg7_OiKjQHjNE24Q_Lo[^kgjLLmmmmicg>fn>_EgeWfOgco/@2/Y:<24o D@In[Le0HBjX1?39]_c4a0@eVBPC/nFB:Q/PSGlIL206gGS]QFcQDOSIDP^FN^Id 7]QKhX@L4Me[mK57k5>=7FMN3iHbgE>R j1T6 i7^N8M9Gj[c3IM<`e;kBck f_CReaSQCXU7c@QogP=YNX^LHHjdn2Q_mC6XS:NjTWe>Fk;OfI3^BWC3f7=Omam5 LEZokOmkX6<1AIUVPo5XiQgkN8oAWHg I[_Jde/0eYGIcnlj6BeRei1fVKA[H>@`KK67QMb5h]:je0>mjKidAlIiHglO3[S_f/T:g@f3YhoN;?U0 iLYJ^?Z36Uhg3L>dKIn15`bi1Q]V3N9oM6R0Mf=SM:SC[LAAdn==:1Pce@CN[4dj >h@=[`2fljS9m[0_XT=[`:``X1cEm51@]bMET:7iNb`LgP7AXCA:;f;O5jBJ3Jl4 ]Z/Ef<>;IE]6]HWETD6j2T>l7@gaINaJ8_DVPUMX>]VD>Z=3:DdWcF/YXS_S dBe/9A]d_B?cBm9[J9m4IU8V^NNAnFchbPJa;^omMZ;U9Wjok>65o0khHn9W@=mD /0fn_>55>7FYg;Z4_@GE@H]EIHJf7bT6_kJ>]i? mOLJa__59P__OOfEJUhoM;PJMQ^R7N2iCj=@j>=VTEe_nf?KWdD];/F?Dfk4hOOQ mFeCJ7cmm8^[o[5fojYK/>dMfGI[PBHgkZk7NV8Lh1^lKT3Y<@BG8XhDdP1[[`nZgO?U6i]ij?^DiK _l_m38WM0gdJBE/]WZHMIMB7olc3?V::Eo1N^[/bi]H42j2J`NPeA;DFXdjfUJ]a 8CIH/JVN62>MVGVB;W1EQF2L=2H4ja:I_lBc?IR>_FSBjO^ARATP emd/mgX>ZfN[NJdJJlL5KV>m9bFoQ`[OQ =I7mo2fk=2]`=6aa;fnEn4Iog1AhT[O`;gSk7hodnWFkab45b_lPeoGUk;gL=bRl0U;Wnl4[doblIZm?UIUYlcnG4gi9hTN< O4S7FOIdd=3d?LT>1PQo;o4kY/0oB?a?@n3_e7PoSo2OZ?42Oj[62gaB[NOOUWLm 1cehe8b3]gmDHVm4_5Sb_aY9^/KFcNIo/oWOnL[oXPe/il^VD1fOe7iYc6e^X2F=DCiNY:BbIF[Z0ZBT/VI[2TZTY;9VJ`Y:YY@^HV/:BZBT/VI[2mg[d:jJV l7:?O/GD59ImkCY?IM2AQd=koG[MQEcWdVn 7R3>djMoZZO^>295nXQkkM_L;1n07?miI^8:A:C;3go[o_b/Adm V=_B_E2>NcOZ5b`DX0_[VkOc3N6onE6TY_U=/TiLMcKoWc[oGjcbolMoDoWo6Kmm Ef6n[TNjP_`OY];gZVDg5mMG=?n7VNOoc`NWb^nV6le7>2^;Bg`Pm3eOHbNhdGc0 d?]7`cN3gYnb8c`JIaCNJo=O2aAVoWJ2]g;F>J3`=oakA4KQ SZ2^c`V><>ml[kjLU@cYlg?FjJ2^?fOM5]3eiBb__YcUeIMUVfYeOEUf;2[dUDWl J2EiEdNjemdaldMnAaW5BlLh?_]kbeMlamHX7_/4Sn<3J_b_nG]=lMm l9k2klhoMd8kn?e_DOO[OXNNjWLQmgl>HhZ_8ocPWd:7o1ii`]?fZMhAa_W6@LEO]?Fac_1FYlGolg@LLiJ4MKGTk<< fm^oa^O5H_kd_PlNScc5kbZ^_]?]hEKJ5EhKm?JglgRBb;[aI3g_keCOlF@lDES6 4oEMC/HCQFDlDORbSBO9la=?STMflaeHY;0hmh]nhnOnL_o^hLKQW`391GLI001b 5a@000010400000009L4001^3P006A400000m@lL0000000003l:00<00000_AT0 004000040000000Yj53]h8PEH3OC>X5kfDek/L3GC5UNa7ZFhEZ1A`fIgoHURUCl lh0/coJ=5JSdAaGi]^mOQRcOmZe@i8lHS`MEo6J1;7o4Z2Y@j@f6;3m97Y/Wdi=T /4cVCi;a>I`nTa_Oi;ZTgoQ2QLMV /FkHbBHBk/O^O`^o[n]lQ:mN7eSme?[DjWEHMm6YBkl=^7kgHB`gS`5lR=o=V=^M =dTJ8g^UmZNMdl9;IaNB674U<>j:IYVgjJE1=RoHKi`7gk4:>8Sc/`W;3gS;P[Rc:o o`kTN?n]8>hKKPFiX76[=/Koc5[No2Ih`kBn?^l_XJ`W7MliWNAY]W>Z8INl_F_Ae`jlh7NEe3HJocW]e@n3?OC=jYYc[=neQD 5WK`RL37[8lk`3g=^cBIO[C`:b3C8eJ@WLH9PHnamjd^PHUOOTn>F;Fjo7hL/MCg JM^gXE1n;kIm7b[_gKJ_cBO;/gemA>EGiHdH[@6IOlBhkY?USaP?NFEi8hHZKlA@ iBG9eW9IGY9L275iOPLO;ZJkZbgNhLjHoPTKDD;4YH<nVhR3/JFIaaD^3G;;VmkB_gZ=Si3h:8>eHF b_dI3P00;A400000 m@lL0000000003l:00<000000Q/0004000040000002a<00000000000001T0;D0 F@2[1`0@001011D0@0@E00000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000003ooooo0`0000@000010000 ooooo`8000000000W34003DU003J=P000@090003KA/000P0B0000000100000<1 200500002`8000001@0000`2b`Ri2`<0000N00P0003j0PD000000?ooo`040000 ;@4000L0003l0P00MTMf0000100002d10@040000;@4000`000102B40l0000000 000N0;P;000000@0000]0@001`000?`2003oool000040000;@4200@0003`0@40 1`000?`2001hB7P000040000;@4100@0000]0@00300004098@3`0000000001/0 ^0/N0000100002d100040000;@4200@0003`0@401`000?`2001jBGX000040000 ;@4100@0000]0@00300004098@3`0000000001X0^0/i0000100002d100040000 ;@4200@0003`0@401`000?`2001lBW`000040000;@4100@0000]0@0030000409 8@3`0000000001X0^0]C0000100002d100040000;@4200@0003`0@401`000?`2 001nC7h000040000;@4100@0000]0@00300004098@3`000000000180^0]]0000 100002d100040000;@4200@0003`0@401`000?`20020CH0000040000;@4100@0 000]0@00300004098@3`0000000001X0^0]o0000100002d100040000;@4200@0 003`0@401`000?`20022CX8000040000;@4100@0000]0@00300004098@3`0000 00000180^0^I0000100002d100040000;@4200@0003`0@401`000?`20024D8@0 00040000;@4100@0000]0@00300004098@3`0000000000l0^0^[0000100002d1 00040000;@4200@0003`0@401`000?`20026D8H000040000;@4100@0000]0@00 300004098@3`0000000000/0^0^j0000100002d100040000;@4200@0003`0@40 1`000?`20028DHP000040000;@4100@0000]0@00300004098@3`000000000180 ^0_50000100002d100040000;@4200@0003`0@401`000?`2002:DhX000040000 ;@4100@0000]0@00300004098@3`0000000000l0^0_G0000100002d100040000 ;@4200@0003`0@401`000?`2002EHh000040000;@4100@0000]0@00300004098@3`000000000100^0_a0000 100002d100040000;@4200@0003`0@401`000?`2002@EY0000040000;@4100@0 000]0@00300004098@3`0000000000/0^0/10@00100002d100040000;@4200@0 003`0@401`000?`2002BF98000040000;@4100@0000]0@00300004098@3`0000 000000/0^0/<0@00100002d100040000;@4200@0003`0@401`000?`2002DFI@0 00040000;@4100@0000]0@00300004098@3`0000000000l0^0/G0@00100002d1 00040000;@4200@0003`0@401`000?`2002FFYH000040000;@4100@0000]0@00 300004098@3`0000000000/0^0/V0@00100002d100040000;@4200@0003`0@40 1`000?`2002HFiP000040000;@4100@0000]0@00300004098@3`0000000000T0 ^0/a0@00100002d100040000;@4200@0003`0@401`000?`2002JG9X000040000 ;@4100@0000]0@00300004098@3`0000000000d0^0/j0@00100002d100040000 ;@4200@0003`0@401`000?`2002LGI`000040000;@4100@0000]0@0030000409 8@3`0000000000/0^0]70@00100002d100040000;@4200@0003`0@401`000?`2 002NGih000040000;@4100@0000]0@00300004098@3`0000000000/0^0]B0@00 100002d100040000;@4200@0003`0@401`000?`2002PH:0000040000;@4100@0 000]0@00300004098@3`0000000000T0^0]M0@00100002d100040000;@4200@0 003`0@401`000?`2002RHJ8000040000;@4100@0000]0@00300004098@3`0000 000000d0^0]V0@00100002d100040000;@4200@0003`0@401`000?`2002THZ@0 00040000;@4100@0000]0@00300004098@3`0000000000T0^0]c0@00100002d1 00040000;@4200@0003`0@401`000?`2002VHjH000040000;@4100@0000]0@00 300004098@3`0000000000/0^0]l0@00100002d100040000;@4200@0003`0@40 1`000?`2002XIJP000040000;@4100@0000]0@00300004098@3`0000000000/0 ^0^70@00100002d100040000;@4200@0003`0@401`000?`2002ZIZX000040000 ;@4100@0000]0@00300004098@3`0000000000P0^0^B0@00100002d100040000 ;@4200@0003`0@401`000?`2002/Ij`000040000;@4100@0000]0@0030000409 8@3`0000000000h0^0^J0@00100002d100040000;@4200@0003`0@401`000?`2 002^J:h000040000;@4100@0000]0@00300004098@3`0000000000P0^0^X0@00 100002d100040000;@4200@0003`0@401`000?`2002`JK0000040000;@4100@0 000]0@00300004098@3`0000000000T0^0^`0@00100002d100040000;@4200@0 003`0@401`000?`2002bJ[8000040000;@4100@0000]0@00300004098@3`0000 000000/0^0^i0@00100002d100040000;@4200@0003`0@401`000?`2002dK;@0 00040000;@4100@0000]0@00300004098@3`0000000000/0^0_40@00100002d1 00040000;@4200@0003`0@401`000?`2002fKKH000040000;@4100@0000]0@00 300004098@3`0000000000T0^0_?0@00100002d100040000;@4200@0003`0@40 1`000?`2002hK[P000040000;@4100@0000]0@00300004098@3`0000000000T0 ^0_H0@00100002d100040000;@4200@0003`0@401`000?`2002jL;X000040000 ;@4100@0000]0@00300004098@3`0000000000d0^0_Q0@00100002d100040000 ;@4200@0003`0@401`000?`2002lL;`000040000;@4100@0000]0@0030000409 8@3`0000000000T0^0_^0@00100002d100040000;@4200@0003`0@401`000?`2 002nL[h000040000;@4100@0000]0@00300004098@3`0000000000/0^0_g0@00 100002d100040000;@4200@0003`0@401`000?`20030Ll0000040000;@4100@0 000]0@00300004098@3`0000000000/0^0/20P00100002d100040000;@4200@0 003`0@401`000?`20032ML8000040000;@4100@0000]0@00300004098@3`0000 000000P0^0/=0P00100002d100040000;@4200@0003`0@401`000?`20034ML@0 00040000;@4100@0000]0@00300004098@3`0000000000T0^0/E0P00100002d1 00040000;@4200@0003`0@401`000?`20036MlH000040000;@4100@0000]0@00 300004098@3`0000000000d0^0/N0P00100002d100040000;@4200@0003`0@40 1`000?`20038NOX000040000 ;@4100@0000]0@00300004098@3`000000000180^0/00`00100002d100040000 ;@4200@0003`0@401`000?`2003/S^`000040000;@4100@0000]0@0030000409 8@3`000000000180^0/B0`00100002d100040000;@4200@0003`0@401`000?`2 003^Snh000040000;@4100@0000]0@00300004098@3`0000000001X0^0/T0`00 100002d100040000;@4200@0003`0@401`000?`2003`T?0000040000;@4100@0 000]0@00300004098@3`000000000180^0/n0`00100002d100040000;@4200@0 003`0@401`000?`2003bTO8000040000;@4100@0000]0@00300004098@3`0000 000001X0^0]@0`00100002d100040000;@4200@0003`0@401`000?`2003dT_@0 00040000;@4100@0000]0@00300004098@3`0000000001X0^0]Z0`00100002d1 00040000;@4200@0003`0@401`000?`2003fU?H000040000;@4100@0000]0@00 300004098@3`0000000001/0^0^40`00100002d100040000;@4200@0003`0@40 1`000?`2003hUOP000040000;@4100@0000]0@00300004098@3`0000000002<0 ^0^O0`00100002d100040000;@4200@0003`0@401`000?`2003jU_X000040000 ;@4100@0000]0@00300004098@3`0000000002`0^0_20`00100002d100040000 ;@4200@0003`0@401`000?`2003lUo`000040000;@4100@0000]0@0030000409 8@3`0000000003D0^0_^0`00100002d100040000;@4200@0003`0@401`000?`2 003nV?h000040000;@4100@0000]0@00300004098@3`0000000009h0^0/S1000 100002d100040000;@4200@0003`0@401`000?`2003lUo`000040000;@4100@0 000]0@00300004098@3`0000000003@0^0_11000100002d100040000;@4200@0 003`0@401`000?`2003jU_X000040000;@4100@0000]0@00300004098@3`0000 000002@0^0_e1000100002d100040000;@4200@0003`0@401`000?`2003hUOP0 00040000;@4100@0000]0@00300004098@3`0000000002<0^0/I1@00100002d1 00040000;@4200@0003`0@401`000?`2003fU?H000040000;@4100@0000]0@00 300004098@3`0000000001X0^0/l1@00100002d100040000;@4200@0003`0@40 1`000?`2003dT_@000040000;@4100@0000]0@00300004098@3`0000000001/0 ^0]F1@00100002d100040000;@4200@0003`0@401`000?`2003bTO8000040000 ;@4100@0000]0@00300004098@3`000000000140^0]a1@00100002d100040000 ;@4200@0003`0@401`000?`2003`T?0000040000;@4100@0000]0@0030000409 8@3`000000000180^0^21@00100002d100040000;@4200@0003`0@401`000?`2 003^Snh000040000;@4100@0000]0@00300004098@3`0000000001X0^0^D1@00 100002d100040000;@4200@0003`0@401`000?`2003/S^`000040000;@4100@0 000]0@00300004098@3`000000000180^0^^1@00100002d100040000;@4200@0 003`0@401`000?`2003ZS>X000040000;@4100@0000]0@00300004098@3`0000 00000140^0_01@00100002d100040000;@4200@0003`0@401`000?`2003XRnP0 00040000;@4100@0000]0@00300004098@3`0000000000/0^0_A1@00100002d1 00040000;@4200@0003`0@401`000?`2003VR^H000040000;@4100@0000]0@00 300004098@3`000000000100^0_L1@00100002d100040000;@4200@0003`0@40 1`000?`2003TRN@000040000;@4100@0000]0@00300004098@3`000000000140 ^0_/1@00100002d100040000;@4200@0003`0@401`000?`2003RQn8000040000 ;@4100@0000]0@00300004098@3`000000000100^0_m1@00100002d100040000 ;@4200@0003`0@401`000?`2003PQn0000040000;@4100@0000]0@0030000409 8@3`0000000000X0^0/=1P00100002d100040000;@4200@0003`0@401`000?`2 003NQMh000040000;@4100@0000]0@00300004098@3`000000000100^0/G1P00 100002d100040000;@4200@0003`0@401`000?`2003LQ=`000040000;@4100@0 000]0@00300004098@3`0000000000/0^0/W1P00100002d100040000;@4200@0 003`0@401`000?`2003JPmX000040000;@4100@0000]0@00300004098@3`0000 000000/0^0/b1P00100002d100040000;@4200@0003`0@401`000?`2003HP]P0 00040000;@4100@0000]0@00300004098@3`0000000000d0^0/m1P00100002d1 00040000;@4200@0003`0@401`000?`2003FPMH000040000;@4100@0000]0@00 300004098@3`0000000000/0^0]:1P00100002d100040000;@4200@0003`0@40 1`000?`2003DOm@000040000;@4100@0000]0@00300004098@3`0000000000/0 ^0]E1P00100002d100040000;@4200@0003`0@401`000?`2003BO]8000040000 ;@4100@0000]0@00300004098@3`0000000000d0^0]P1P00100002d100040000 ;@4200@0003`0@401`000?`2003@OM0000040000;@4100@0000]0@0030000409 8@3`0000000000/0^0]]1P00100002d100040000;@4200@0003`0@401`000?`2 003>O1P00 100002d100040000;@4200@0003`0@401`000?`2002lLK`000040000;@4100@0 000]0@00300004098@3`0000000000/0^0_G1P00100002d100040000;@4200@0 003`0@401`000?`2002jL;X000040000;@4100@0000]0@00300004098@3`0000 000000/0^0_R1P00100002d100040000;@4200@0003`0@401`000?`2002hK[P0 00040000;@4100@0000]0@00300004098@3`0000000000P0^0_]1P00100002d1 00040000;@4200@0003`0@401`000?`2002fKKH000040000;@4100@0000]0@00 300004098@3`0000000000T0^0_e1P00100002d100040000;@4200@0003`0@40 1`000?`2002dK;@000040000;@4100@0000]0@00300004098@3`0000000000d0 ^0_n1P00100002d100040000;@4200@0003`0@401`000?`2002bJk8000040000 ;@4100@0000]0@00300004098@3`0000000000T0^0/;1`00100002d100040000 ;@4200@0003`0@401`000?`2002`J[0000040000;@4100@0000]0@0030000409 8@3`0000000000T0^0/D1`00100002d100040000;@4200@0003`0@401`000?`2 002^JJh000040000;@4100@0000]0@00300004098@3`0000000000/0^0/M1`00 100002d100040000;@4200@0003`0@401`000?`2002/Ij`000040000;@4100@0 000]0@00300004098@3`0000000000/0^0/X1`00100002d100040000;@4200@0 003`0@401`000?`2002ZIZX000040000;@4100@0000]0@00300004098@3`0000 000000T0^0/c1`00100002d100040000;@4200@0003`0@401`000?`2002XIJP0 00040000;@4100@0000]0@00300004098@3`0000000000d0^0/l1`00100002d1 00040000;@4200@0003`0@401`000?`2002VI:H000040000;@4100@0000]0@00 300004098@3`0000000000T0^0]91`00100002d100040000;@4200@0003`0@40 1`000?`2002THj@000040000;@4100@0000]0@00300004098@3`0000000000/0 ^0]B1`00100002d100040000;@4200@0003`0@401`000?`2002RHJ8000040000 ;@4100@0000]0@00300004098@3`0000000000/0^0]M1`00100002d100040000 ;@4200@0003`0@401`000?`2002PH:0000040000;@4100@0000]0@0030000409 8@3`0000000000P0^0]X1`00100002d100040000;@4200@0003`0@401`000?`2 002NGih000040000;@4100@0000]0@00300004098@3`0000000000h0^0]`1`00 100002d100040000;@4200@0003`0@401`000?`2002LGY`000040000;@4100@0 000]0@00300004098@3`0000000000/0^0]n1`00100002d100040000;@4200@0 003`0@401`000?`2002JG9X000040000;@4100@0000]0@00300004098@3`0000 000000/0^0^91`00100002d100040000;@4200@0003`0@401`000?`2002HFiP0 00040000;@4100@0000]0@00300004098@3`0000000000P0^0^D1`00100002d1 00040000;@4200@0003`0@401`000?`2002FFYH000040000;@4100@0000]0@00 300004098@3`000000000100^0^L1`00100002d100040000;@4200@0003`0@40 1`000?`2002DFI@000040000;@4100@0000]0@00300004098@3`0000000000/0 ^0^/1`00100002d100040000;@4200@0003`0@401`000?`2002BF98000040000 ;@4100@0000]0@00300004098@3`0000000000d0^0^g1`00100002d100040000 ;@4200@0003`0@401`000?`2002@Ei0000040000;@4100@0000]0@0030000409 8@3`0000000000/0^0_41`00100002d100040000;@4200@0003`0@401`000?`2 002>EHh000040000;@4100@0000]0@00300004098@3`0000000000l0^0_?1`00 100002d100040000;@4200@0003`0@401`000?`2002TY01`0003k0U[oBP000000T04000021`8045=i KF9_K00000000000000000000000000000000000100002d11`040000l04600T0 000b2XX3F@<10000:NTY00D0000D0V/3R`<500004`9[0bT41@0001@2J`?/1@D0 000C0V/3RPH50000508B1c031@0001<24PLA1Q`0003k0[Oo00000000T0400000 1`8045AYKFEc84iUMb1BKfeQKP0000000000000000000000100002d11P040000 l04700T0000b2U/7fPD10000<^TU00T0000b2P47Y`@10000<>TU00T0000b2/@4 b`810000<>TU01`0003k0X?o00000000T04000001`8045AYKFEc84iUMb1BKfeQ KP0000000000000000000000100002d11`040000l04600T0000b2Y<7d0<10000 <^To00T0000b2Y<7:`<10000TZ00T0000b2R86APL10000<>To00T0000b2R86M0H10000;>TO00T0 000b2R86n`<10000To00T0000b2V<5`@H10000<>To00T0000b2V<5f0D10000;>TO00T0000b2V<5 V`D10000<>To00T0000b2V<5b@<10000To00T0000b2Z@4J0H10000<>To00T0000b2Z@4UPD10000 ;>TO00T0000b2Z@4F@D10000<>To00T0000b2Z@4K@<10000To00T0000b2X/3c0P10000;>TO00T0000b2X/3T0P10000<>To01`0 003k0X?o00000000T04100001`8045AYKFEc84iUMb1BKfeQKP00000000000000 00000000100002d11P040000l04700T0000b2Y<7O`D10000E>U600T0000b2Y<7 :PD10000H^U000T0000b2Y<7J@@10000E>U500T0000b2Y<77P@10000HNTo00T0 000b2^46K0@10000JnTg00T0000b2S47<0810000E>U600T0000b2S47b0410000 JnTg00T0000b2R86W`H10000M>TS00T0000b2R86<@D10000N>Tg00X0000b2R86 YP@20000HG@o02<02@00038:8PJo0P40001DjDH02@00038:8PK00@40001DjDH0 2@00038:H`D<1P40001hjCL02@00038:H`Gd1040001djB<02P00038:H`Ec1080 001QM3l08`090000U600T0000b2Z@4`0410000E>U600T0000b2X/3 0`T10000M>TS00T0000b2X/3f@L10000N>Tg00`0000b2X/37@L30000IVmb02<0 ?`0a00T0000b2^d3A@H10000M>TS00T0000b2S`3<0H10000E>U600T0000b2X/3 A`D10000@nUC00T0000b2^d3g0<10000N>Tg00T0000b2S`3cP<10000E>U600T0 000b2X/3oP810000E>U600T0000b2X/3W@810000JnTg00T0000b2^d33@810000 N>Tg01`0003k0[Oo00000000T04100001`8045AYKFEc84iUMb1BKfeQKP000000 0000000000000000100002d11`040000l04600T0000b2T86o@810000JNTD00T0 000b2X<5bP810000JNTD00T0000b2ZX3YPD10000L>TU01`0003k0X?o00000000 T04000021`8045=iKF9_K00000000000000000000000000000000000100002d1 1P040000l04700T0000b2Y<7dP@10000:nU500T0000b2Y<7M0<10000:nU500T0 000b2S47c0810000?NU500T0000b2R86iPH10000?^U500T0000b2R866PH10000 YNUI00T0000b2R86Q@D10000[^Uk00T0000b2R86?@<10000?NU500T0000b2R86 <0810000[^Uk00T0000b2V<5H@H10000/nU500T0000b2V<5>`D10000?NU500T0 000b2V<52`<10000?NU400T0000b2V<5@@10000mnT`00T0000b2_`3>@@10000n>T`00T0000b2TD3 >@@10000m^T`00T0000b2YD3GP810000inT`00T0000b2_`3GP810000j>T`00T0 000b2TD3GP810000i^T`00T0000b2^d3W`<10000]^Tm00T0000b2S`3T@<10000 ]^Tm00T0000b2^d3d0410000]^Tm00T0000b2S`3j`410000]^Tm01`0003k0X?o 00000000T04100021`8045=iKF9_K00000000000000000000000000000000000 100002d11`040000l04600T0000b2X/3j`@10000L^U301`0003k0PD00P000000 _08000001`828U=iLgAUK@0000000000000000000000000000000000100002d1 1P040000l04700@0000]0@40100002d10P0L0000n`85008000000;`200000042 0R9CNG=dIFd0000000010000L0000000080H=aD0000000@0000]0@L010000?01 1@040000l04600@0000]0@80100002d10@0400009`7ooa`0003k0PD00P000000 _08000000@828U=iLgAUK@00KIV0O?`h5@3l>1D0?;4J01Pg5@1hi@Di900000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000\>"], "Graphics", ImageSize->{360, 270}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Reference :", FontWeight->"Bold"], "\nM. N. \[CapitalODoubleDot]zisik, Heat Conduction, Wiley, New York, \ 1980." }], "Subsubtitle", Background->RGBColor[0.773449, 0.996109, 0.996109]], Cell[BoxData[ \(Off[General::"\"]\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Exact numerical Solution using NDSolve and the \ shooting technique", FontSize->18]], "Subsubtitle", TextAlignment->Left, Background->RGBColor[1, 1, 0.682353]], Cell[BoxData[ \(Off[General::"\"]\)], "Input"], Cell[BoxData[ \(\(\[Rho] = 1/Cp;\)\)], "Input"], Cell[BoxData[ \(k[T_] := \ 2/\((1 + 0.1\ \ T + 0.5\ T^2)\)\)], "Input"], Cell[BoxData[ \(SOL[\[Xi]_] := NDSolve[{D[\((k[T] /. T \[Rule] T[\[Eta]])\)/\((\[Rho]\ Cp)\)\ D[ T[\[Eta]], {\[Eta], 1}], {\[Eta], 1}] + 0.5\ \[Eta]\ D[T[\[Eta]], {\[Eta], 1}] \[Equal] 0, T[0] \[Equal] \ 1, \(T'\)[0] \[Equal] \ \[Xi]}, {T[\[Eta]]}, {\[Eta], 0, 100}]\)], "Input"], Cell[BoxData[ \(bend[\[Xi]_?NumericQ] := \(T[\[Eta]] /. SOL[\[Xi]]\) /. \[Eta] \[Rule] \ 100\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(bc = FindRoot[bend[\[Xi]] \[Equal] \ 0, {\[Xi], \(-2\)}]\)], "Input"], Cell[BoxData[ \({\[Xi] \[Rule] \(-0.5645281798144357`\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(plt1 = Plot[First[\((\(T[\[Eta]] /. SOL[\[Xi] /. bc]\) /. \[Eta] \[Rule] a)\)], {a, 0, 10}, PlotStyle \[Rule] RGBColor[1, 0, 0], PlotRange \[Rule] All, DisplayFunction \[Rule] \ Identity]\)], "Input"], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Initial guess is obtained for \[Alpha]=", FontSize->18], Cell[BoxData[ \(TraditionalForm\`\(k(T)\)\/\(\[Rho]\ Cp\)\)], FontSize->18], StyleBox["= constant=5", FontSize->18] }], "Subsubtitle", TextAlignment->Left, Background->RGBColor[1, 1, 0.682353]], Cell[BoxData[ \(\(\[Alpha]0 = 5;\)\)], "Input"], Cell[BoxData[ \(\[Theta]0[\[Eta]_] := \ 1 - Erf[\[Eta]/\((2\ \@\[Alpha]0)\)]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(plt2 = Plot[\[Theta]0[\[Eta]], {\[Eta], 0, 10}, PlotStyle \[Rule] \ RGBColor[0, 0, 1], PlotRange \[Rule] \ All, DisplayFunction \[Rule] \ Identity]\)], "Input"], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[plt1, plt2, DisplayFunction \[Rule] \ $DisplayFunction]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.0147148 0.588604 [ [.21429 .00221 -3 -9 ] [.21429 .00221 3 0 ] [.40476 .00221 -3 -9 ] [.40476 .00221 3 0 ] [.59524 .00221 -3 -9 ] [.59524 .00221 3 0 ] [.78571 .00221 -3 -9 ] [.78571 .00221 3 0 ] [.97619 .00221 -6 -9 ] [.97619 .00221 6 0 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01471 m .21429 .02096 L s [(2)] .21429 .00221 0 1 Mshowa .40476 .01471 m .40476 .02096 L s [(4)] .40476 .00221 0 1 Mshowa .59524 .01471 m .59524 .02096 L s [(6)] .59524 .00221 0 1 Mshowa .78571 .01471 m .78571 .02096 L s [(8)] .78571 .00221 0 1 Mshowa .97619 .01471 m .97619 .02096 L s [(10)] .97619 .00221 0 1 Mshowa .125 Mabswid .07143 .01471 m .07143 .01846 L s .11905 .01471 m .11905 .01846 L s .16667 .01471 m .16667 .01846 L s .2619 .01471 m .2619 .01846 L s .30952 .01471 m .30952 .01846 L s .35714 .01471 m .35714 .01846 L s .45238 .01471 m .45238 .01846 L s .5 .01471 m .5 .01846 L s .54762 .01471 m .54762 .01846 L s .64286 .01471 m .64286 .01846 L s .69048 .01471 m .69048 .01846 L s .7381 .01471 m .7381 .01846 L s .83333 .01471 m .83333 .01846 L s .88095 .01471 m .88095 .01846 L s .92857 .01471 m .92857 .01846 L s .25 Mabswid 0 .01471 m 1 .01471 L s .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 1 0 0 r .5 Mabswid .02381 .60332 m .06244 .47915 L .10458 .36693 L .14415 .28118 L .18221 .21431 L .22272 .15773 L .26171 .11559 L .30316 .08204 L .32392 .06894 L .34309 .05875 L .3815 .04301 L .40022 .03724 L .42085 .03207 L .44189 .02787 L .46114 .02484 L .48124 .02233 L .49991 .02052 L .51889 .01907 L .53962 .01787 L .56014 .01698 L .57875 .01638 L .59799 .01591 L .61881 .01555 L .63875 .0153 L .64892 .0152 L .65982 .01511 L .67946 .01498 L .69779 .0149 L .70796 .01487 L .71903 .01484 L .72859 .01482 L .73915 .0148 L .75892 .01477 L .76976 .01476 L .77993 .01475 L .78976 .01474 L .80011 .01474 L .81862 .01473 L .82816 .01473 L .83836 .01472 L .85673 .01472 L .86697 .01472 L .87807 .01472 L .88856 .01472 L .89823 .01472 L .90727 .01472 L .91699 .01472 L .92765 .01472 L .93763 .01472 L .94709 .01472 L Mistroke .95741 .01472 L .96716 .01472 L .97619 .01472 L Mfstroke 0 0 1 r .02381 .60332 m .06244 .54324 L .10458 .47886 L .14415 .42054 L .18221 .36725 L .22272 .31429 L .26171 .26756 L .30316 .22287 L .34309 .18487 L .3815 .15302 L .42237 .12403 L .46172 .10062 L .49955 .08193 L .53984 .06571 L .57861 .05324 L .61984 .04286 L .65954 .03519 L .69774 .02957 L .73838 .02511 L .77751 .02197 L .79749 .02072 L .81909 .01959 L .85916 .01798 L .8791 .01737 L .90016 .01684 L .93814 .01613 L .9565 .01587 L .97619 .01564 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`005@3oool00`000000oooo0?ooo`1W0?ooo`H0o`00@03oool50000oeH0oooo000E0?oo o`030000003oool0oooo0680oooo1@3o00110?ooo`D0003oF`3oool001D0oooo00<000000?ooo`3o ool0H03oool20?l00400oooo1P000?mP0?ooo`005@3oool2000005h0oooo0`3o000m0?ooo`D0003o IP3oool001D0oooo00<000000?ooo`3oool0F`3oool20?l003X0oooo1P000?m[0?ooo`005@3oool0 0`000000oooo0?ooo`1H0?ooo`<0o`00>03oool40000og40oooo000E0?ooo`030000003oool0oooo 05H0oooo0P3o000h0?ooo`<0003oM@3oool001D0oooo00<000000?ooo`3oool0E03oool20?l003P0 oooo0P000?mh0?ooo`005@3oool00`000000oooo0?ooo`1B0?ooo`80o`00=`3oool30000ogX0oooo 000E0?ooo`030000003oool0oooo0500oooo0P3o000f0?ooo`<0003oO@3oool001D0oooo00<00000 0?ooo`3oool0C`3oool00`3o0000oooo0?ooo`0c0?ooo`<0003oP03oool001D0oooo0P00001>0?oo o`80o`00=03oool20000oh<0oooo000E0?ooo`030000003oool0oooo04/0oooo0P3o000c0?ooo`<0 003oQ@3oool001D0oooo00<000000?ooo`3oool0B@3oool20?l003<0oooo0P000?n80?ooo`005@3o ool00`000000oooo0?ooo`180?ooo`030?l0003oool0oooo0340oooo0P000?n:0?ooo`005@3oool0 0`000000oooo0?ooo`160?ooo`80o`00P3oool0 0`3o0000oooo0?ooo`0Z0?ooo`80003oW`3oool000050?ooo`000000oooo0?ooo`0000002@3oool0 0`000000oooo0?ooo`040?ooo`<00000>@3oool00`3o0000oooo0?ooo`0Z0?ooo`030000o`3oool0 oooo09l0oooo00001@3oool000000?ooo`3oool0000000X0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`0h0?ooo`030?l0003oool0oooo02X0oooo00<0003o0?ooo`3oool0X03oool0 00050?ooo`000000oooo0?ooo`000000203oool010000000oooo0?ooo`0000040?ooo`030000003o ool0oooo03P0oooo00<0o`000?ooo`3oool0:03oool20000oj<0oooo00020?ooo`8000002P3oool2 000000D0oooo00<000000?ooo`3oool0=`3oool00`3o0000oooo0?ooo`0X0?ooo`030000o`3oool0 oooo0:<0oooo000E0?ooo`030000003oool0oooo03H0oooo00<0o`000?ooo`3oool0:03oool00`00 0?l0oooo0?ooo`2T0?ooo`005@3oool00`000000oooo0?ooo`0e0?ooo`030?l0003oool0oooo02L0 oooo0P000?nW0?ooo`005@3oool00`000000oooo0?ooo`0d0?ooo`030?l0003oool0oooo02L0oooo 00<0003o0?ooo`3oool0Y`3oool001D0oooo00<000000?ooo`3oool0<`3oool00`3o0000oooo0?oo o`0W0?ooo`030000o`3oool0oooo0:P0oooo000E0?ooo`800000<`3oool00`3o0000oooo0?ooo`0V 0?ooo`80003oZ`3oool001D0oooo00<000000?ooo`3oool040oooo000E0?ooo`030000003oool0oooo0100oooo00<0o`000?ooo`3o ool0403oool00`000?l0oooo0?ooo`3R0?ooo`005@3oool200000140oooo00<0o`000?ooo`3oool0 3`3oool00`000?l0oooo0?ooo`3S0?ooo`005@3oool00`000000oooo0?ooo`0?0?ooo`030?l0003o ool0oooo0100oooo00<0003o0?ooo`3oool0h`3oool001D0oooo00<000000?ooo`3oool03`3oool0 0`3o0000oooo0?ooo`0?0?ooo`030000o`3oool0oooo0>@0oooo000E0?ooo`030000003oool0oooo 00l0oooo00<0o`000?ooo`3oool03P3oool00`000?l0oooo0?ooo`3U0?ooo`005@3oool00`000000 oooo0?ooo`0>0?ooo`030?l0003oool0oooo00h0oooo00<0003o0?ooo`3oool0iP3oool001D0oooo 00<000000?ooo`3oool03P3oool00`3o0000oooo0?ooo`0>0?ooo`030000o`3oool0oooo0>H0oooo 000E0?ooo`030000003oool0oooo00d0oooo00<0o`000?ooo`3oool03P3oool00`000?l0oooo0?oo o`3W0?ooo`005@3oool00`000000oooo0?ooo`0=0?ooo`030?l0003oool0oooo00d0oooo00<0003o 0?ooo`3oool0j03oool001D0oooo0P00000>0?ooo`030?l0003oool0oooo00d0oooo00<0003o0?oo o`3oool0j03oool001D0oooo00<000000?ooo`3oool0303oool00`3o0000oooo0?ooo`0=0?ooo`03 0000o`3oool0oooo0>T0oooo000E0?ooo`030000003oool0oooo00`0oooo00<0o`000?ooo`3oool0 303oool00`000?l0oooo0?ooo`3Z0?ooo`005@3oool00`000000oooo0?ooo`0;0?ooo`030?l0003o ool0oooo00d0oooo00<0003o0?ooo`3oool0jP3oool001D0oooo00<000000?ooo`3oool02`3oool0 0`3o0000oooo0?ooo`0<0?ooo`030000o`3oool0oooo0>/0oooo000E0?ooo`030000003oool0oooo 00/0oooo00<0o`000?ooo`3oool02`3oool00`000?l0oooo0?ooo`3/0?ooo`005@3oool00`000000 oooo0?ooo`0:0?ooo`030?l0003oool0oooo00/0oooo00<0003o0?ooo`3oool0k@3oool001D0oooo 00<000000?ooo`3oool02P3oool00`3o0000oooo0?ooo`0;0?ooo`030000o`3oool0oooo0>d0oooo 000E0?ooo`8000002P3oool00`3o0000oooo0?ooo`0;0?ooo`030000o`3oool0oooo0>h0oooo000E 0?ooo`030000003oool0oooo00T0oooo00<0o`000?ooo`3oool02P3oool00`000?l0oooo0?ooo`3_ 0?ooo`005@3oool00`000000oooo0?ooo`090?ooo`030?l0003oool0oooo00X0oooo00<0003o0?oo o`3oool0k`3oool001D0oooo00<000000?ooo`3oool0203oool00`3o0000oooo0?ooo`0:0?ooo`03 0000o`3oool0oooo0?00oooo000E0?ooo`030000003oool0oooo00P0oooo00<0o`000?ooo`3oool0 2@3oool00`000?l0oooo0?ooo`3a0?ooo`005@3oool00`000000oooo0?ooo`070?ooo`030?l0003o ool0oooo00X0oooo00<0003o0?ooo`3oool0l@3oool00080oooo0P0000040?ooo`800000103oool2 000000D0oooo00<000000?ooo`3oool01`3oool00`3o0000oooo0?ooo`090?ooo`030000o`3oool0 oooo0?80oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103o ool00`000000oooo0?ooo`070?ooo`030?l0003oool0oooo00P0oooo00<0003o0?ooo`3oool0l`3o ool000050?ooo`000000oooo0?ooo`000000203oool010000000oooo0?ooo`0000040?ooo`<00000 1P3oool00`3o0000oooo0?ooo`090?ooo`030000o`3oool0oooo0?<0oooo00001@3oool000000?oo o`3oool0000000T0oooo0P0000050?ooo`030000003oool0oooo00H0oooo00<0o`000?ooo`3oool0 203oool00`000?l0oooo0?ooo`3d0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000 003oool0oooo000000@0oooo00<000000?ooo`3oool01P3oool00`3o0000oooo0?ooo`070?ooo`03 0000o`3oool0oooo0?D0oooo00020?ooo`8000002P3oool2000000D0oooo00<000000?ooo`3oool0 1P3oool00`3o0000oooo0?ooo`070?ooo`030000o`3oool0oooo0?D0oooo000E0?ooo`030000003o ool0oooo00D0oooo00<0o`000?ooo`3oool01`3oool00`000?l0oooo0?ooo`3f0?ooo`005@3oool0 0`000000oooo0?ooo`050?ooo`030?l0003oool0oooo00H0oooo00<0003o0?ooo`3oool0m`3oool0 01D0oooo00<000000?ooo`3oool01@3oool00`3o0000oooo0?ooo`060?ooo`030000o`3oool0oooo 0?L0oooo000E0?ooo`030000003oool0oooo00@0oooo00<0o`000?ooo`3oool01P3oool00`000?l0 oooo0?ooo`3h0?ooo`005@3oool2000000D0oooo00<0o`000?ooo`3oool01@3oool00`000?l0oooo 0?ooo`3i0?ooo`005@3oool00`000000oooo0?ooo`040?ooo`030?l0003oool0oooo00D0oooo00<0 003o0?ooo`3oool0n@3oool001D0oooo00<000000?ooo`3oool00`3oool00`3o0000oooo0?ooo`05 0?ooo`030000o`3oool0oooo0?X0oooo000E0?ooo`030000003oool0oooo00<0oooo00<0o`000?oo o`3oool0103oool00`000?l0oooo0?ooo`3k0?ooo`005@3oool00`000000oooo0?ooo`030?ooo`03 0?l0003oool0oooo00@0oooo00<0003o0?ooo`3oool0n`3oool001D0oooo00<000000?ooo`3oool0 0`3oool00`3o0000oooo0?ooo`030?ooo`030000o`3oool0oooo0?`0oooo000E0?ooo`030000003o ool0oooo0080oooo00<0o`000?ooo`3oool00`3oool00`000?l0oooo0?ooo`3m0?ooo`005@3oool0 0`000000oooo0?ooo`020?ooo`030?l0003oool0oooo00<0oooo00<0003o0?ooo`3oool0o@3oool0 01D0oooo0P0000030?ooo`030?l0003oool0oooo0080oooo00<0003o0?ooo`3oool0oP3oool001D0 oooo00D000000?ooo`3oool0oooo0?l000040?ooo`030000o`3oool0oooo0?l0oooo000E0?ooo`05 0000003oool0oooo0?ooo`3o0000103oool00`000?l0oooo0?ooo`3o0?ooo`005@3oool01@000000 oooo0?ooo`3oool0o`0000<0oooo00<0003o0?ooo`3oool0o`3oool10?ooo`005@3oool01@000000 oooo0?ooo`3oool0o`000080oooo00<0003o0?ooo`3oool0o`3oool20?ooo`005@3oool010000000 oooo0?ooo`3o00030?ooo`030000o`3oool0oooo0?l0oooo0P3oool001D0oooo00@000000?ooo`3o ool0o`000P3oool00`000?l0oooo0?ooo`3o0?ooo`<0oooo000E0?ooo`040000003oool0oooo0?l0 0080oooo00<0003o0?ooo`3oool0o`3oool30?ooo`005@3oool2000000040?l0003oool0oooo0000 ool0oooo1P3oool001D0oooo00D000000?ooo`3o0000oooo0000o`3o0?ooo`L0oooo000E0?ooo`05 0000003oool0o`000?ooo`000?l0o`3oool70?ooo`005@3oool010000000o`000?ooo`000?oo0?oo o`P0oooo000E0?ooo`030000003o0000003o0?l0oooo2@3oool001D0oooo00<000000?l000000?l0 o`3oool90?ooo`003@3oool5000000<0oooo00<000000000o`3oool0o`3oool90?ooo`003`3oool0 0`000000oooo0?ooo`030?ooo`030?l000000?l0oooo0?l0oooo2@3oool000l0oooo00<000000?oo o`3oool00`3oool00`000?l000000000003o0?ooo`T0oooo000?0?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool0o`3oool90?ooo`003`3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo0?l0oooo2@3oool000h0oooo0P0000050?ooo`030000003oool0oooo0?l0oooo2@3o ool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.82995, -0.0774874, \ 0.0386185, 0.00624861}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["First approximation is constructed using the method given in ", FontSize->18], StyleBox["M. N. \[CapitalODoubleDot]zisik, Heat Conduction, Wiley, New \ York, 1980.", FontSize->18] }], "Subsubtitle", TextAlignment->Left, Background->RGBColor[1, 1, 0.682353]], Cell[BoxData[ \(T0[\[Eta]_] := 0.9\ \[Theta]0[\[Eta]] + 0.1\)], "Input"], Cell[BoxData[ \(f0[\[Eta]_] := 1/10\ \[Eta]\)], "Input"], Cell[BoxData[ \(g0[\[Eta]p_?NumericQ] := NIntegrate[First[f0[\[Eta]pp]], {\[Eta]pp, 0, \[Eta]p}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Int0 = \(\(1/ NIntegrate[ Exp[\(-g0[\[Eta]p]\)], {\[Eta]p, 0, 10}]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(0.15819767068693263`\)], "Output"] }, Open ]], Cell[BoxData[ \(\[Theta]1[\[Eta]_] := 1 - NIntegrate[ Exp[\(-g0[\[Eta]p]\)], {\[Eta]p, 0, \[Eta]}]\ Int0\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(plt3 = ListPlot[Table[{\[Eta], \[Theta]1[\[Eta]]}, {\[Eta], 0, 10, 0.1}], PlotStyle \[Rule] \ RGBColor[0, 1, 0], PlotRange \[Rule] \ All, PlotJoined \[Rule] True, DisplayFunction \[Rule] \ Identity]\)], "Input"], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[plt2, plt3, plt1, DisplayFunction \[Rule] \ $DisplayFunction]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.0147151 0.588604 [ [.21429 .00222 -3 -9 ] [.21429 .00222 3 0 ] [.40476 .00222 -3 -9 ] [.40476 .00222 3 0 ] [.59524 .00222 -3 -9 ] [.59524 .00222 3 0 ] [.78571 .00222 -3 -9 ] [.78571 .00222 3 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(10)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 1 r .5 Mabswid .02381 .60332 m .06244 .54324 L .10458 .47886 L .14415 .42054 L .18221 .36725 L .22272 .31429 L .26171 .26756 L .30316 .22287 L .34309 .18487 L .3815 .15302 L .42237 .12403 L .46172 .10062 L .49955 .08193 L .53984 .06571 L .57861 .05324 L .61984 .04286 L .65954 .03519 L .69774 .02957 L .73838 .02511 L .77751 .02197 L .79749 .02072 L .81909 .01959 L .85916 .01798 L .8791 .01737 L .90016 .01684 L .93814 .01613 L .9565 .01587 L .97619 .01564 L s 0 1 0 r .02381 .60332 m .03333 .59405 L .04286 .58488 L .05238 .5758 L .0619 .56681 L .07143 .55791 L .08095 .54909 L .09048 .54037 L .1 .53173 L .10952 .52318 L .11905 .51471 L .12857 .50632 L .1381 .49802 L .14762 .48981 L .15714 .48167 L .16667 .47362 L .17619 .46564 L .18571 .45775 L .19524 .44993 L .20476 .44219 L .21429 .43453 L .22381 .42694 L .23333 .41943 L .24286 .412 L .25238 .40464 L .2619 .39735 L .27143 .39013 L .28095 .38299 L .29048 .37592 L .3 .36891 L .30952 .36198 L .31905 .35512 L .32857 .34832 L .3381 .34159 L .34762 .33493 L .35714 .32834 L .36667 .32181 L .37619 .31534 L .38571 .30894 L .39524 .30261 L .40476 .29633 L .41429 .29012 L .42381 .28398 L .43333 .27789 L .44286 .27186 L .45238 .26589 L .4619 .25999 L .47143 .25414 L .48095 .24835 L .49048 .24261 L Mistroke .5 .23694 L .50952 .23132 L .51905 .22575 L .52857 .22025 L .5381 .21479 L .54762 .20939 L .55714 .20405 L .56667 .19875 L .57619 .19351 L .58571 .18833 L .59524 .18319 L .60476 .17811 L .61429 .17307 L .62381 .16809 L .63333 .16315 L .64286 .15827 L .65238 .15343 L .6619 .14864 L .67143 .1439 L .68095 .13921 L .69048 .13456 L .7 .12996 L .70952 .1254 L .71905 .12089 L .72857 .11643 L .7381 .11201 L .74762 .10763 L .75714 .1033 L .76667 .09901 L .77619 .09476 L .78571 .09056 L .79524 .08639 L .80476 .08227 L .81429 .07819 L .82381 .07415 L .83333 .07015 L .84286 .06619 L .85238 .06227 L .8619 .05839 L .87143 .05455 L .88095 .05074 L .89048 .04697 L .9 .04325 L .90952 .03955 L .91905 .0359 L .92857 .03228 L .9381 .02869 L .94762 .02515 L .95714 .02164 L .96667 .01816 L Mistroke .97619 .01472 L Mfstroke 1 0 0 r .02381 .60332 m .06244 .47915 L .10458 .36693 L .14415 .28118 L .18221 .21431 L .22272 .15773 L .26171 .11559 L .30316 .08204 L .32392 .06894 L .34309 .05875 L .3815 .04301 L .40022 .03724 L .42085 .03207 L .44189 .02787 L .46114 .02484 L .48124 .02233 L .49991 .02052 L .51889 .01907 L .53962 .01787 L .56014 .01698 L .57875 .01638 L .59799 .01592 L .61881 .01555 L .63875 .0153 L .64892 .0152 L .65982 .01511 L .67946 .01498 L .69779 .0149 L .70796 .01487 L .71903 .01484 L .72859 .01482 L .73915 .0148 L .75892 .01477 L .76976 .01476 L .77993 .01475 L .78976 .01474 L .80011 .01474 L .81862 .01473 L .82816 .01473 L .83836 .01472 L .85673 .01472 L .86697 .01472 L .87807 .01472 L .88856 .01472 L .89823 .01472 L .90727 .01472 L .91699 .01472 L .92765 .01472 L .93763 .01472 L .94709 .01472 L Mistroke .95741 .01472 L .96716 .01472 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`005@3oool00`000000oooo0?oo o`1]0?ooo`D0o`00@03oool80000oc/0oooo0`00o`0@0?ooo`005@3oool00`000000oooo0?ooo`1W 0?ooo`H0o`00@03oool50000od00oooo0`00o`0C0?ooo`005@3oool00`000000oooo0?ooo`1R0?oo o`D0o`00@@3oool50000od<0oooo0P00o`0F0?ooo`005@3oool00`000000oooo0?ooo`1P0?ooo`80 o`00@03oool60000odD0oooo0`00o`0H0?ooo`005@3oool2000005h0oooo0`3o000m0?ooo`D0003o B@3oool2003o01/0oooo000E0?ooo`030000003oool0oooo05/0oooo0P3o000j0?ooo`H0003oB`3o ool3003o01d0oooo000E0?ooo`030000003oool0oooo05P0oooo0`3o000h0?ooo`@0003oCP3oool3 003o0200oooo000E0?ooo`030000003oool0oooo05H0oooo0P3o000h0?ooo`<0003oD03oool2003o 02<0oooo000E0?ooo`030000003oool0oooo05@0oooo0P3o000h0?ooo`80003oD03oool3003o02D0 oooo000E0?ooo`030000003oool0oooo0580oooo0P3o000g0?ooo`<0003oD03oool2003o02P0oooo 000E0?ooo`030000003oool0oooo0500oooo0P3o000f0?ooo`<0003oD03oool3003o02X0oooo000E 0?ooo`030000003oool0oooo04l0oooo00<0o`000?ooo`3oool0<`3oool30000oe40oooo0P00o`0] 0?ooo`005@3oool2000004h0oooo0P3o000d0?ooo`80003oD@3oool3003o02l0oooo000E0?ooo`03 0000003oool0oooo04/0oooo0P3o000c0?ooo`<0003oD03oool3003o0380oooo000E0?ooo`030000 003oool0oooo04T0oooo0P3o000c0?ooo`80003oD@3oool2003o03D0oooo000E0?ooo`030000003o ool0oooo04P0oooo00<0o`000?ooo`3oool0<@3oool20000oe40oooo0P00o`0g0?ooo`005@3oool0 0`000000oooo0?ooo`160?ooo`80o`0003o ool00`3o0000oooo0?ooo`0X0?ooo`80003oBP3oool3003o05H0oooo00020?ooo`8000002P3oool2 000000D0oooo00<000000?ooo`3oool0=`3oool00`3o0000oooo0?ooo`0X0?ooo`030000o`3oool0 oooo04L0oooo0`00o`1I0?ooo`005@3oool00`000000oooo0?ooo`0f0?ooo`030?l0003oool0oooo 02P0oooo00<0003o0?ooo`3oool0AP3oool2003o05`0oooo000E0?ooo`030000003oool0oooo03D0 oooo00<0o`000?ooo`3oool09`3oool20000odP0oooo00<00?l00?ooo`3oool0G03oool001D0oooo 00<000000?ooo`3oool0=03oool00`3o0000oooo0?ooo`0W0?ooo`030000o`3oool0oooo04H0oooo 0P00o`1O0?ooo`005@3oool00`000000oooo0?ooo`0c0?ooo`030?l0003oool0oooo02L0oooo00<0 003o0?ooo`3oool0A@3oool2003o0640oooo000E0?ooo`800000<`3oool00`3o0000oooo0?ooo`0V 0?ooo`80003oAP3oool2003o06<0oooo000E0?ooo`030000003oool0oooo0380oooo00<0o`000?oo o`3oool09@3oool00`000?l0oooo0?ooo`140?ooo`800?l0I@3oool001D0oooo00<000000?ooo`3o ool0<@3oool00`3o0000oooo0?ooo`0U0?ooo`030000o`3oool0oooo04@0oooo00<00?l00?ooo`3o ool0I@3oool001D0oooo00<000000?ooo`3oool0<03oool00`3o0000oooo0?ooo`0U0?ooo`030000 o`3oool0oooo0480oooo0`00o`1X0?ooo`005@3oool00`000000oooo0?ooo`0_0?ooo`030?l0003o ool0oooo02@0oooo0P000?m30?ooo`800?l0J`3oool001D0oooo00<000000?ooo`3oool0;`3oool0 0`3o0000oooo0?ooo`0S0?ooo`030000o`3oool0oooo0440oooo0P00o`1]0?ooo`005@3oool00`00 0000oooo0?ooo`0^0?ooo`030?l0003oool0oooo02<0oooo00<0003o0?ooo`3oool0@@3oool00`00 o`00oooo0?ooo`1]0?ooo`005@3oool00`000000oooo0?ooo`0]0?ooo`030?l0003oool0oooo02<0 oooo00<0003o0?ooo`3oool0@03oool2003o0700oooo000E0?ooo`800000;@3oool00`3o0000oooo 0?ooo`0S0?ooo`030000o`3oool0oooo03l0oooo0P00o`1b0?ooo`005@3oool00`000000oooo0?oo o`0/0?ooo`030?l0003oool0oooo0280oooo00<0003o0?ooo`3oool0?`3oool00`00o`00oooo0?oo o`1b0?ooo`005@3oool00`000000oooo0?ooo`0[0?ooo`030?l0003oool0oooo0280oooo00<0003o 0?ooo`3oool0?@3oool3003o07D0oooo000E0?ooo`030000003oool0oooo02X0oooo00<0o`000?oo o`3oool08P3oool00`000?l0oooo0?ooo`0l0?ooo`800?l0N03oool001D0oooo00<000000?ooo`3o ool0:@3oool00`3o0000oooo0?ooo`0R0?ooo`030000o`3oool0oooo03/0oooo0P00o`1j0?ooo`00 5@3oool00`000000oooo0?ooo`0Y0?ooo`030?l0003oool0oooo0240oooo00<0003o0?ooo`3oool0 >`3oool00`00o`00oooo0?ooo`1j0?ooo`005@3oool00`000000oooo0?ooo`0X0?ooo`030?l0003o ool0oooo0240oooo00<0003o0?ooo`3oool0>P3oool2003o07d0oooo000E0?ooo`030000003oool0 oooo02L0oooo00<0o`000?ooo`3oool08@3oool00`000?l0oooo0?ooo`0i0?ooo`800?l0O`3oool0 01D0oooo0P00000X0?ooo`030?l0003oool0oooo0200oooo00<0003o0?ooo`3oool0>@3oool00`00 o`00oooo0?ooo`1o0?ooo`005@3oool00`000000oooo0?ooo`0V0?ooo`030?l0003oool0oooo0200 oooo00<0003o0?ooo`3oool0>03oool2003o0880oooo000E0?ooo`030000003oool0oooo02H0oooo 00<0o`000?ooo`3oool07`3oool00`000?l0oooo0?ooo`0g0?ooo`800?l0Q03oool001D0oooo00<0 00000?ooo`3oool09@3oool00`3o0000oooo0?ooo`0O0?ooo`030000o`3oool0oooo03H0oooo0P00 o`260?ooo`005@3oool00`000000oooo0?ooo`0U0?ooo`030?l0003oool0oooo01h0oooo00<0003o 0?ooo`3oool0=@3oool2003o08P0oooo000E0?ooo`030000003oool0oooo02@0oooo00<0o`000?oo o`3oool07P3oool00`000?l0oooo0?ooo`0e0?ooo`03003o003oool0oooo08P0oooo00020?ooo`80 0000103oool2000000D0oooo0`0000030?ooo`030000003oool0oooo02@0oooo00<0o`000?ooo`3o ool07@3oool00`000?l0oooo0?ooo`0d0?ooo`800?l0R`3oool000050?ooo`000000oooo0?ooo`00 00002`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo02<0oooo00<0o`000?ooo`3o ool07@3oool00`000?l0oooo0?ooo`0c0?ooo`800?l0S@3oool000050?ooo`000000oooo0?ooo`00 0000203oool5000000<0oooo0`00000R0?ooo`030?l0003oool0oooo01h0oooo00<0003o0?ooo`3o ool00?ooo`030?l0003oool0oooo00h0 oooo00<0003o0?ooo`3oool05`3oool00`00o`00oooo0?ooo`3<0?ooo`005@3oool00`000000oooo 0?ooo`0>0?ooo`030?l0003oool0oooo00h0oooo00<0003o0?ooo`3oool05@3oool2003o00?oo o`030?l0003oool0oooo00d0oooo00<0003o0?ooo`3oool04`3oool00`00o`00oooo0?ooo`3B0?oo o`005@3oool00`000000oooo0?ooo`0<0?ooo`030?l0003oool0oooo00d0oooo00<0003o0?ooo`3o ool04`3oool00`00o`00oooo0?ooo`3C0?ooo`005@3oool00`000000oooo0?ooo`0<0?ooo`030?l0 003oool0oooo00`0oooo00<0003o0?ooo`3oool04`3oool00`00o`00oooo0?ooo`3D0?ooo`005@3o ool00`000000oooo0?ooo`0;0?ooo`030?l0003oool0oooo00d0oooo00<0003o0?ooo`3oool04@3o ool2003o0=L0oooo000E0?ooo`030000003oool0oooo00/0oooo00<0o`000?ooo`3oool0303oool0 0`000?l0oooo0?ooo`0A0?ooo`03003o003oool0oooo0=L0oooo000E0?ooo`030000003oool0oooo 00/0oooo00<0o`000?ooo`3oool02`3oool00`000?l0oooo0?ooo`0A0?ooo`03003o003oool0oooo 0=P0oooo000E0?ooo`030000003oool0oooo00X0oooo00<0o`000?ooo`3oool02`3oool00`000?l0 oooo0?ooo`0A0?ooo`03003o003oool0oooo0=T0oooo000E0?ooo`030000003oool0oooo00X0oooo 00<0o`000?ooo`3oool02`3oool00`000?l0oooo0?ooo`0?0?ooo`800?l0g03oool001D0oooo0P00 000:0?ooo`030?l0003oool0oooo00/0oooo00<0003o0?ooo`3oool03`3oool00`00o`00oooo0?oo o`3L0?ooo`005@3oool00`000000oooo0?ooo`090?ooo`030?l0003oool0oooo00X0oooo00<0003o 0?ooo`3oool03`3oool00`00o`00oooo0?ooo`3M0?ooo`005@3oool00`000000oooo0?ooo`090?oo o`030?l0003oool0oooo00X0oooo00<0003o0?ooo`3oool03P3oool00`00o`00oooo0?ooo`3N0?oo o`005@3oool00`000000oooo0?ooo`080?ooo`030?l0003oool0oooo00X0oooo00<0003o0?ooo`3o ool03P3oool00`00o`00oooo0?ooo`3O0?ooo`005@3oool00`000000oooo0?ooo`080?ooo`030?l0 003oool0oooo00T0oooo00<0003o0?ooo`3oool03P3oool00`00o`00oooo0?ooo`3P0?ooo`005@3o ool00`000000oooo0?ooo`070?ooo`030?l0003oool0oooo00X0oooo00<0003o0?ooo`3oool03@3o ool00`00o`00oooo0?ooo`3Q0?ooo`000P3oool2000000@0oooo0P0000040?ooo`8000001@3oool0 0`000000oooo0?ooo`070?ooo`030?l0003oool0oooo00T0oooo00<0003o0?ooo`3oool0303oool2 003o0>@0oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103o ool00`000000oooo0?ooo`070?ooo`030?l0003oool0oooo00P0oooo00<0003o0?ooo`3oool0303o ool00`00o`00oooo0?ooo`3T0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003o ool0oooo000000@0oooo0`0000060?ooo`030?l0003oool0oooo00T0oooo00<0003o0?ooo`3oool0 2`3oool00`00o`00oooo0?ooo`3U0?ooo`0000D0oooo0000003oool0oooo000000090?ooo`800000 1@3oool00`000000oooo0?ooo`060?ooo`030?l0003oool0oooo00P0oooo00<0003o0?ooo`3oool0 2`3oool00`00o`00oooo0?ooo`3V0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000 003oool0oooo000000@0oooo00<000000?ooo`3oool01P3oool00`3o0000oooo0?ooo`070?ooo`03 0000o`3oool0oooo00X0oooo0P00o`3Y0?ooo`000P3oool2000000X0oooo0P0000050?ooo`030000 003oool0oooo00H0oooo00<0o`000?ooo`3oool01`3oool00`000?l0oooo0?ooo`090?ooo`03003o 003oool0oooo0>T0oooo000E0?ooo`030000003oool0oooo00D0oooo00<0o`000?ooo`3oool01`3o ool00`000?l0oooo0?ooo`090?ooo`03003o003oool0oooo0>X0oooo000E0?ooo`030000003oool0 oooo00D0oooo00<0o`000?ooo`3oool01P3oool00`000?l0oooo0?ooo`090?ooo`03003o003oool0 oooo0>/0oooo000E0?ooo`030000003oool0oooo00D0oooo00<0o`000?ooo`3oool01P3oool00`00 0?l0oooo0?ooo`080?ooo`03003o003oool0oooo0>`0oooo000E0?ooo`030000003oool0oooo00@0 oooo00<0o`000?ooo`3oool01P3oool00`000?l0oooo0?ooo`080?ooo`03003o003oool0oooo0>d0 oooo000E0?ooo`8000001@3oool00`3o0000oooo0?ooo`050?ooo`030000o`3oool0oooo00P0oooo 00<00?l00?ooo`3oool0kP3oool001D0oooo00<000000?ooo`3oool0103oool00`3o0000oooo0?oo o`050?ooo`030000o`3oool0oooo00H0oooo0P00o`3a0?ooo`005@3oool00`000000oooo0?ooo`03 0?ooo`030?l0003oool0oooo00D0oooo00<0003o0?ooo`3oool01P3oool00`00o`00oooo0?ooo`3a 0?ooo`005@3oool00`000000oooo0?ooo`030?ooo`030?l0003oool0oooo00@0oooo00<0003o0?oo o`3oool01P3oool00`00o`00oooo0?ooo`3b0?ooo`005@3oool00`000000oooo0?ooo`030?ooo`03 0?l0003oool0oooo00@0oooo00<0003o0?ooo`3oool01P3oool00`00o`00oooo0?ooo`3b0?ooo`00 5@3oool00`000000oooo0?ooo`030?ooo`030?l0003oool0oooo00<0oooo00<0003o0?ooo`3oool0 1P3oool00`00o`00oooo0?ooo`3c0?ooo`005@3oool00`000000oooo0?ooo`020?ooo`030?l0003o ool0oooo00<0oooo00<0003o0?ooo`3oool01@3oool2003o0?H0oooo000E0?ooo`030000003oool0 oooo0080oooo00<0o`000?ooo`3oool00`3oool00`000?l0oooo0?ooo`040?ooo`03003o003oool0 oooo0?H0oooo000E0?ooo`8000000`3oool00`3o0000oooo0?ooo`020?ooo`030000o`3oool0oooo 00@0oooo00<00?l00?ooo`3oool0m`3oool001D0oooo00D000000?ooo`3oool0oooo0?l000040?oo o`030000o`3oool0oooo00@0oooo00<00?l00?ooo`3oool0n03oool001D0oooo00D000000?ooo`3o ool0oooo0?l000040?ooo`030000o`3oool0oooo00<0oooo00<00?l00?ooo`3oool0n@3oool001D0 oooo00D000000?ooo`3oool0oooo0?l000030?ooo`030000o`3oool0oooo00<0oooo00<00?l00?oo o`3oool0nP3oool001D0oooo00D000000?ooo`3oool0oooo0?l000020?ooo`030000o`3oool0oooo 00<0oooo00<00?l00?ooo`3oool0n`3oool001D0oooo00@000000?ooo`3oool0o`000`3oool01000 0?l0oooo0?ooo`3oool2003o0?h0oooo000E0?ooo`040000003oool0oooo0?l00080oooo00D0003o 0?ooo`3oool0oooo003o003o0?ooo`40oooo000E0?ooo`040000003oool0oooo0?l00080oooo00@0 003o0?ooo`3oool00?l0o`3oool20?ooo`005@3oool2000000040?l0003oool0oooo0000o`<0oooo 00<00?l00?ooo`3oool0o`3oool001D0oooo00D000000?ooo`3o0000oooo0000o`030?ooo`03003o 003oool0oooo0?l0oooo0@3oool001D0oooo00H000000?ooo`3o0000oooo0000o`3oool2003o0?l0 oooo103oool001D0oooo00H000000?l0003oool0003o0?ooo`00o`3o0?ooo`H0oooo000E0?ooo`05 0000003o0000003o0?ooo`00o`00o`3oool70?ooo`005@3oool010000000o`000000o`00o`3o0?oo o`P0oooo000=0?ooo`D000000`3oool00`000000o`00003o003o0?ooo`T0oooo000?0?ooo`030000 003oool0oooo00<0oooo00<0o`00003o003oool0o`3oool90?ooo`003`3oool00`000000oooo0?oo o`030?ooo`030?l00000000000000?l0oooo2@3oool000l0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`3o0?ooo`T0oooo000?0?ooo`030000003oool0oooo00<0oooo00<000000?oo o`3oool0o`3oool90?ooo`003P3oool2000000D0oooo00<000000?ooo`3oool0o`3oool90?ooo`00 5@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.829852, -0.07747, \ 0.0386179, 0.00624851}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Second approximation is built using the method given in ", FontSize->18], StyleBox["M. N. \[CapitalODoubleDot]zisik, Heat Conduction, Wiley, New \ York, 1980.", FontSize->18] }], "Subsubtitle", TextAlignment->Left, Background->RGBColor[1, 1, 0.682353]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Theta]1i = Interpolation[ Table[{\[Eta], \[Theta]1[\[Eta]]}, {\[Eta], 0, 10, 0.1}]]\)], "Input"], Cell[BoxData[ TagBox[\(InterpolatingFunction[{{0.`, 10.`}}, "<>"]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(T1[\[Eta]_] := 0.9\ \[Theta]1i[\[Eta]] + 0.1\)], "Input"], Cell[BoxData[ \(alpha[\[Eta]_] := \ \((k[T] /. T \[Rule] \ T0[\[Eta]])\)/\((\[Rho]\ Cp)\)\)], "Input"], Cell[BoxData[ \(d[\[Eta]_] := \((D[k[T]/\((\[Rho]\ Cp)\), {T, 1}] /. T \[Rule] \ T0[\[Eta]])\)\ 0.9\ D[\[Theta]1i[x], {x, 1}] /. x \[Rule] \ \[Eta]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(D[\[Theta]1i[x], {x, 1}] /. x \[Rule] \ \[Eta]\)], "Input"], Cell[BoxData[ RowBox[{ TagBox[\(InterpolatingFunction[{{0.`, 10.`}}, "<>"]\), False, Editable->False], "[", "\[Eta]", "]"}]], "Output"] }, Open ]], Cell[BoxData[ \(f1[a_] := 1/2\ \ a/alpha[a] + 1/alpha[a] d[a]\)], "Input"], Cell[BoxData[ \(g1[\[Eta]p_?NumericQ] := NIntegrate[First[f1[\[Eta]pp]], {\[Eta]pp, 0, \[Eta]p}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Int1 = \(\(1/ NIntegrate[ Exp[\(-g1[\[Eta]p]\)], {\[Eta]p, 0, 20}]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(0.44817432069831553`\)], "Output"] }, Open ]], Cell[BoxData[ \(\[Theta]2[\[Eta]_] := 1 - NIntegrate[ Exp[\(-g1[\[Eta]p]\)], {\[Eta]p, 0, \[Eta]}]\ Int1\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(plt4 = ListPlot[Table[{\[Eta], \[Theta]2[\[Eta]]}, {\[Eta], 0, 10, 0.1}], PlotStyle \[Rule] \ RGBColor[0, 1, 1], PlotRange \[Rule] \ All, PlotJoined \[Rule] True, DisplayFunction \[Rule] \ Identity]\)], "Input"], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[plt2, plt3, plt1, plt4, DisplayFunction \[Rule] \ $DisplayFunction]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.0147151 0.588604 [ [.21429 .00222 -3 -9 ] [.21429 .00222 3 0 ] [.40476 .00222 -3 -9 ] [.40476 .00222 3 0 ] [.59524 .00222 -3 -9 ] [.59524 .00222 3 0 ] [.78571 .00222 -3 -9 ] [.78571 .00222 3 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(10)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 1 r .5 Mabswid .02381 .60332 m .06244 .54324 L .10458 .47886 L .14415 .42054 L .18221 .36725 L .22272 .31429 L .26171 .26756 L .30316 .22287 L .34309 .18487 L .3815 .15302 L .42237 .12403 L .46172 .10062 L .49955 .08193 L .53984 .06571 L .57861 .05324 L .61984 .04286 L .65954 .03519 L .69774 .02957 L .73838 .02511 L .77751 .02197 L .79749 .02072 L .81909 .01959 L .85916 .01798 L .8791 .01737 L .90016 .01684 L .93814 .01613 L .9565 .01587 L .97619 .01564 L s 0 1 0 r .02381 .60332 m .03333 .59405 L .04286 .58488 L .05238 .5758 L .0619 .56681 L .07143 .55791 L .08095 .54909 L .09048 .54037 L .1 .53173 L .10952 .52318 L .11905 .51471 L .12857 .50632 L .1381 .49802 L .14762 .48981 L .15714 .48167 L .16667 .47362 L .17619 .46564 L .18571 .45775 L .19524 .44993 L .20476 .44219 L .21429 .43453 L .22381 .42694 L .23333 .41943 L .24286 .412 L .25238 .40464 L .2619 .39735 L .27143 .39013 L .28095 .38299 L .29048 .37592 L .3 .36891 L .30952 .36198 L .31905 .35512 L .32857 .34832 L .3381 .34159 L .34762 .33493 L .35714 .32834 L .36667 .32181 L .37619 .31534 L .38571 .30894 L .39524 .30261 L .40476 .29633 L .41429 .29012 L .42381 .28398 L .43333 .27789 L .44286 .27186 L .45238 .26589 L .4619 .25999 L .47143 .25414 L .48095 .24835 L .49048 .24261 L Mistroke .5 .23694 L .50952 .23132 L .51905 .22575 L .52857 .22025 L .5381 .21479 L .54762 .20939 L .55714 .20405 L .56667 .19875 L .57619 .19351 L .58571 .18833 L .59524 .18319 L .60476 .17811 L .61429 .17307 L .62381 .16809 L .63333 .16315 L .64286 .15827 L .65238 .15343 L .6619 .14864 L .67143 .1439 L .68095 .13921 L .69048 .13456 L .7 .12996 L .70952 .1254 L .71905 .12089 L .72857 .11643 L .7381 .11201 L .74762 .10763 L .75714 .1033 L .76667 .09901 L .77619 .09476 L .78571 .09056 L .79524 .08639 L .80476 .08227 L .81429 .07819 L .82381 .07415 L .83333 .07015 L .84286 .06619 L .85238 .06227 L .8619 .05839 L .87143 .05455 L .88095 .05074 L .89048 .04697 L .9 .04325 L .90952 .03955 L .91905 .0359 L .92857 .03228 L .9381 .02869 L .94762 .02515 L .95714 .02164 L .96667 .01816 L Mistroke .97619 .01472 L Mfstroke 1 0 0 r .02381 .60332 m .06244 .47915 L .10458 .36693 L .14415 .28118 L .18221 .21431 L .22272 .15773 L .26171 .11559 L .30316 .08204 L .32392 .06894 L .34309 .05875 L .3815 .04301 L .40022 .03724 L .42085 .03207 L .44189 .02787 L .46114 .02484 L .48124 .02233 L .49991 .02052 L .51889 .01907 L .53962 .01787 L .56014 .01698 L .57875 .01638 L .59799 .01592 L .61881 .01555 L .63875 .0153 L .64892 .0152 L .65982 .01511 L .67946 .01498 L .69779 .0149 L .70796 .01487 L .71903 .01484 L .72859 .01482 L .73915 .0148 L .75892 .01477 L .76976 .01476 L .77993 .01475 L .78976 .01474 L .80011 .01474 L .81862 .01473 L .82816 .01473 L .83836 .01472 L .85673 .01472 L .86697 .01472 L .87807 .01472 L .88856 .01472 L .89823 .01472 L .90727 .01472 L .91699 .01472 L .92765 .01472 L .93763 .01472 L .94709 .01472 L Mistroke .95741 .01472 L .96716 .01472 L .97619 .01472 L Mfstroke 0 1 1 r .02381 .60332 m .03333 .57696 L .04286 .5507 L .05238 .52464 L .0619 .49888 L .07143 .47351 L .08095 .4486 L .09048 .42422 L .1 .40046 L .10952 .37736 L .11905 .35497 L .12857 .33335 L .1381 .31251 L .14762 .2925 L .15714 .27333 L .16667 .25502 L .17619 .23758 L .18571 .22101 L .19524 .2053 L .20476 .19045 L .21429 .17644 L .22381 .16327 L .23333 .1509 L .24286 .13933 L .25238 .12852 L .2619 .11844 L .27143 .10908 L .28095 .10039 L .29048 .09235 L .3 .08493 L .30952 .07809 L .31905 .0718 L .32857 .06604 L .3381 .06076 L .34762 .05595 L .35714 .05156 L .36667 .04757 L .37619 .04396 L .38571 .04069 L .39524 .03774 L .40476 .03508 L .41429 .03269 L .42381 .03054 L .43333 .02863 L .44286 .02692 L .45238 .0254 L .4619 .02404 L .47143 .02284 L .48095 .02178 L .49048 .02085 L Mistroke .5 .02002 L .50952 .0193 L .51905 .01867 L .52857 .01812 L .5381 .01763 L .54762 .01721 L .55714 .01685 L .56667 .01653 L .57619 .01626 L .58571 .01603 L .59524 .01583 L .60476 .01565 L .61429 .01551 L .62381 .01538 L .63333 .01527 L .64286 .01518 L .65238 .01511 L .6619 .01504 L .67143 .01499 L .68095 .01494 L .69048 .0149 L .7 .01487 L .70952 .01484 L .71905 .01482 L .72857 .0148 L .7381 .01478 L .74762 .01477 L .75714 .01476 L .76667 .01475 L .77619 .01475 L .78571 .01474 L .79524 .01473 L .80476 .01473 L .81429 .01473 L .82381 .01473 L .83333 .01472 L .84286 .01472 L .85238 .01472 L .8619 .01472 L .87143 .01472 L .88095 .01472 L .89048 .01472 L .9 .01472 L .90952 .01472 L .91905 .01472 L .92857 .01472 L .9381 .01472 L .94762 .01472 L .95714 .01472 L .96667 .01472 L Mistroke .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`005@3oool00`000000oooo0?ooo`1Y 0?ooo`D00?oo103o00100?ooo`P0003o>`3oool3003o0100oooo000E0?ooo`030000003oool0oooo 06@0oooo1@00ool40?l00400oooo1@000?m00?ooo`<00?l04`3oool001D0oooo00<000000?ooo`3o ool0H@3oool3003oo`<0o`00@@3oool50000od<0oooo0P00o`0F0?ooo`005@3oool00`000000oooo 0?ooo`1O0?ooo`800?oo00<0o`000?ooo`3oool0?P3oool60000odD0oooo0`00o`0H0?ooo`005@3o ool2000005d0oooo0`00ool00`3o0000oooo0?ooo`0k0?ooo`D0003oB@3oool2003o01/0oooo000E 0?ooo`030000003oool0oooo05X0oooo0P00ool00`3o0000oooo0?ooo`0h0?ooo`H0003oB`3oool3 003o01d0oooo000E0?ooo`030000003oool0oooo05L0oooo0`00ool00`3o0000oooo0?ooo`0f0?oo o`@0003oCP3oool3003o0200oooo000E0?ooo`030000003oool0oooo05@0oooo0`00ool00`3o0000 oooo0?ooo`0f0?ooo`<0003oD03oool2003o02<0oooo000E0?ooo`030000003oool0oooo0580oooo 0P00ool20?l003P0oooo0P000?m@0?ooo`<00?l09@3oool001D0oooo00<000000?ooo`3oool0D@3o ool00`00ool0o`000?l0000g0?ooo`<0003oD03oool2003o02P0oooo000E0?ooo`030000003oool0 oooo04l0oooo0P00ool00`3o0000oooo0?ooo`0d0?ooo`<0003oD03oool3003o02X0oooo000E0?oo o`030000003oool0oooo04d0oooo0P00ool00`3o0000oooo0?ooo`0c0?ooo`<0003oD@3oool2003o 02d0oooo000E0?ooo`800000C@3oool00`00ool0o`000?l0000d0?ooo`80003oD@3oool3003o02l0 oooo000E0?ooo`030000003oool0oooo04/0oooo00<00?oo0?l0003oool0@3oool001D0oooo00<000000?ooo`3oool0A@3oool00`00ool0oooo0?ooo`0`0?ooo`80 003oDP3oool00`00o`00oooo0?ooo`0i0?ooo`005@3oool00`000000oooo0?ooo`140?ooo`03003o o`3oool0oooo02l0oooo0P000?mA0?ooo`<00?l0?03oool001D0oooo00<000000?ooo`3oool0@`3o ool00`00ool0oooo0?ooo`0^0?ooo`80003oD03oool3003o03l0oooo000E0?ooo`800000@`3oool0 0`00ool0oooo0?ooo`0]0?ooo`80003oD03oool2003o0480oooo000E0?ooo`030000003oool0oooo 0400oooo00<0o`00003oo`3oool0;P3oool00`000?l0oooo0?ooo`1=0?ooo`<00?l0A03oool001D0 oooo00<000000?ooo`3oool0?`3oool00`3o00000?oo0?ooo`0]0?ooo`80003oCP3oool2003o04L0 oooo000E0?ooo`030000003oool0oooo03h0oooo00<0o`00003oo`3oool0;03oool20000odl0oooo 00<00?l00?ooo`3oool0A`3oool001D0oooo00<000000?ooo`3oool0?@3oool00`3o00000?oo0?oo o`0/0?ooo`030000o`3oool0oooo04d0oooo0P00o`1:0?ooo`005@3oool00`000000oooo0?ooo`0l 0?ooo`030?l00000ool0oooo02/0oooo0P000?m=0?ooo`<00?l0C03oool00080oooo0P0000040?oo o`8000000`3oool4000000@0oooo00<000000?ooo`3oool0>`3oool00`3o00000?oo0?ooo`0[0?oo o`030000o`3oool0oooo04/0oooo0P00o`1?0?ooo`0000D0oooo0000003oool0oooo000000080?oo o`030000003oool0oooo00D0oooo00<000000?ooo`3oool0>P3oool00`3o00000?oo0?ooo`0Z0?oo o`80003oC03oool2003o0540oooo00001@3oool000000?ooo`3oool0000000T0oooo00<000000?oo o`3oool0103oool3000003T0oooo00<0o`00003oo`3oool0:P3oool00`000?l0oooo0?ooo`1:0?oo o`800?l0D`3oool000050?ooo`000000oooo0?ooo`0000002P3oool00`000000oooo0?ooo`030?oo o`030000003oool0oooo03P0oooo00<0o`000?ooo`00ool0:P3oool00`000?l0oooo0?ooo`1:0?oo o`03003o003oool0oooo05<0oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?oo o`3oool00000103oool00`000000oooo0?ooo`0h0?ooo`030?l00000ool0oooo02P0oooo0P000?m: 0?ooo`<00?l0EP3oool00080oooo0P00000:0?ooo`8000001@3oool00`000000oooo0?ooo`0g0?oo o`030?l00000ool0oooo02P0oooo00<0003o0?ooo`3oool0A`3oool3003o05T0oooo000E0?ooo`03 0000003oool0oooo03H0oooo00<0o`00003oo`3oool0:03oool00`000?l0oooo0?ooo`160?ooo`80 0?l0G03oool001D0oooo00<000000?ooo`3oool0=@3oool00`3o00000?oo0?ooo`0W0?ooo`80003o B03oool00`00o`00oooo0?ooo`1L0?ooo`005@3oool00`000000oooo0?ooo`0d0?ooo`030?l00000 ool0oooo02L0oooo00<0003o0?ooo`3oool0AP3oool2003o05l0oooo000E0?ooo`030000003oool0 oooo03<0oooo00<0o`00003oo`3oool09`3oool00`000?l0oooo0?ooo`150?ooo`800?l0H@3oool0 01D0oooo0P00000c0?ooo`030?l00000ool0oooo02H0oooo0P000?m60?ooo`800?l0H`3oool001D0 oooo00<000000?ooo`3oool0`3oool2003o07X0oooo000E0?ooo`030000003oool0oooo02T0oooo 00<0o`000?ooo`00ool08@3oool00`000?l0oooo0?ooo`0k0?ooo`03003o003oool0oooo07X0oooo 000E0?ooo`030000003oool0oooo02P0oooo00<0o`000?ooo`00ool08@3oool00`000?l0oooo0?oo o`0j0?ooo`800?l0O@3oool001D0oooo00<000000?ooo`3oool09`3oool0103o0000oooo0?ooo`00 oolP0?ooo`030000o`3oool0oooo03T0oooo0P00o`1o0?ooo`005@3oool2000002P0oooo00<0o`00 0?ooo`00ool0803oool00`000?l0oooo0?ooo`0i0?ooo`03003o003oool0oooo07l0oooo000E0?oo o`030000003oool0oooo02H0oooo00<0o`000?ooo`00ool0803oool00`000?l0oooo0?ooo`0h0?oo o`800?l0PP3oool001D0oooo00<000000?ooo`3oool09P3oool00`3o0000oooo003oo`0O0?ooo`03 0000o`3oool0oooo03L0oooo0P00o`240?ooo`005@3oool00`000000oooo0?ooo`0U0?ooo`030?l0 003oool00?oo01l0oooo00<0003o0?ooo`3oool0=P3oool2003o08H0oooo000E0?ooo`030000003o ool0oooo02D0oooo00<0o`000?ooo`00ool07P3oool00`000?l0oooo0?ooo`0e0?ooo`800?l0R03o ool001D0oooo00<000000?ooo`3oool0903oool00`3o0000oooo003oo`0N0?ooo`030000o`3oool0 oooo03D0oooo00<00?l00?ooo`3oool0R03oool00080oooo0P0000040?ooo`8000001@3oool30000 00<0oooo00<000000?ooo`3oool0903oool00`3o00000?oo0?ooo`0M0?ooo`030000o`3oool0oooo 03@0oooo0P00o`2;0?ooo`0000D0oooo0000003oool0oooo0000000;0?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool08`3oool00`3o0000oooo003oo`0M0?ooo`030000o`3oool0oooo 03<0oooo0P00o`2=0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`D000000`3oool30000 0280oooo00<0o`000?ooo`00ool07P3oool00`000?l0oooo0?ooo`0b0?ooo`03003o003oool0oooo 08d0oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103oool0 0`000000oooo0?ooo`0R0?ooo`030?l0003oool00?oo01d0oooo00<0003o0?ooo`3oool00?ooo`0000D0oooo0000003oool0oooo000000090?ooo`030000003oool0 000000@0oooo00<000000?ooo`3oool08@3oool00`3o0000oooo003oo`0M0?ooo`030000o`3oool0 oooo0340oooo0P00o`2A0?ooo`000P3oool2000000/0oooo0P0000040?ooo`030000003oool0oooo 0240oooo00<0o`000?ooo`00ool0703oool00`000?l0oooo0?ooo`0a0?ooo`03003o003oool0oooo 0940oooo000E0?ooo`030000003oool0oooo0200oooo00<0o`000?ooo`00ool0703oool00`000?l0 oooo0?ooo`0`0?ooo`800?l0U03oool001D0oooo00<000000?ooo`3oool0803oool00`3o0000oooo 003oo`0K0?ooo`030000o`3oool0oooo02l0oooo0P00o`2F0?ooo`005@3oool00`000000oooo0?oo o`0O0?ooo`030?l0003oool00?oo01/0oooo00<0003o0?ooo`3oool0;`3oool00`00o`00oooo0?oo o`2F0?ooo`005@3oool00`000000oooo0?ooo`0O0?ooo`030?l0003oool00?oo01X0oooo00<0003o 0?ooo`3oool0;P3oool2003o09T0oooo000E0?ooo`8000007`3oool00`3o0000oooo003oo`0J0?oo o`030000o`3oool0oooo02h0oooo00<00?l00?ooo`3oool0V@3oool001D0oooo00<000000?ooo`3o ool07P3oool00`3o0000oooo003oo`0I0?ooo`030000o`3oool0oooo02d0oooo0P00o`2L0?ooo`00 5@3oool00`000000oooo0?ooo`0M0?ooo`030?l0003oool00?oo01T0oooo00<0003o0?ooo`3oool0 ;03oool2003o09h0oooo000E0?ooo`030000003oool0oooo01d0oooo00<0o`000?ooo`00ool0603o ool00`000?l0oooo0?ooo`0/0?ooo`03003o003oool0oooo09h0oooo000E0?ooo`030000003oool0 oooo01`0oooo00<0o`000?ooo`00ool06@3oool00`000?l0oooo0?ooo`0[0?ooo`03003o003oool0 oooo09l0oooo000E0?ooo`030000003oool0oooo01`0oooo00<0o`000?ooo`00ool0603oool00`00 0?l0oooo0?ooo`0Z0?ooo`800?l0XP3oool001D0oooo00<000000?ooo`3oool06`3oool00`3o0000 oooo003oo`0H0?ooo`030000o`3oool0oooo02T0oooo0P00o`2T0?ooo`005@3oool00`000000oooo 0?ooo`0K0?ooo`030?l0003oool00?oo01L0oooo00<0003o0?ooo`3oool0:03oool2003o0:H0oooo 000E0?ooo`8000006`3oool00`3o0000oooo003oo`0G0?ooo`030000o`3oool0oooo02P0oooo00<0 0?l00?ooo`3oool0YP3oool001D0oooo00<000000?ooo`3oool06P3oool00`3o0000oooo003oo`0F 0?ooo`030000o`3oool0oooo02P0oooo00<00?l00?ooo`3oool0Y`3oool001D0oooo00<000000?oo o`3oool06@3oool00`3o0000oooo003oo`0F0?ooo`030000o`3oool0oooo02L0oooo0P00o`2Z0?oo o`005@3oool00`000000oooo0?ooo`0I0?ooo`030?l0003oool00?oo01H0oooo00<0003o0?ooo`3o ool09@3oool2003o0:`0oooo000E0?ooo`030000003oool0oooo01P0oooo00<0o`000?ooo`00ool0 5P3oool00`000?l0oooo0?ooo`0U0?ooo`03003o003oool0oooo0:`0oooo000E0?ooo`030000003o ool0oooo01P0oooo00<0o`000?ooo`00ool05@3oool00`000?l0oooo0?ooo`0U0?ooo`03003o003o ool0oooo0:d0oooo000E0?ooo`030000003oool0oooo01P0oooo00<0o`00003oo`3oool0503oool0 0`000?l0oooo0?ooo`0T0?ooo`800?l0/03oool001D0oooo00<000000?ooo`3oool05`3oool00`3o 0000oooo003oo`0E0?ooo`030000o`3oool0oooo02<0oooo00<00?l00?ooo`3oool0/03oool001D0 oooo0P00000H0?ooo`030?l0003oool00?oo01@0oooo00<0003o0?ooo`3oool08P3oool2003o0;<0 oooo000E0?ooo`030000003oool0oooo01H0oooo00<0o`000?ooo`00ool0503oool00`000?l0oooo 0?ooo`0R0?ooo`03003o003oool0oooo0;<0oooo000E0?ooo`030000003oool0oooo01H0oooo00<0 o`000?ooo`00ool04`3oool00`000?l0oooo0?ooo`0R0?ooo`03003o003oool0oooo0;@0oooo000E 0?ooo`030000003oool0oooo01D0oooo00<0o`000?ooo`00ool0503oool00`000?l0oooo0?ooo`0Q 0?ooo`03003o003oool0oooo0;D0oooo000E0?ooo`030000003oool0oooo01D0oooo00<0o`000?oo o`00ool04`3oool00`000?l0oooo0?ooo`0P0?ooo`800?l0^03oool001D0oooo00<000000?ooo`3o ool0503oool0103o0000oooo0?ooo`00oolB0?ooo`030000o`3oool0oooo0200oooo00<00?l00?oo o`3oool0^03oool00080oooo0P0000040?ooo`8000000`3oool3000000D0oooo00<000000?ooo`3o ool0503oool00`3o0000oooo003oo`0B0?ooo`030000o`3oool0oooo01l0oooo0P00o`2k0?ooo`00 00D0oooo0000003oool0oooo000000080?ooo`040000003oool0oooo000000@0oooo00<000000?oo o`3oool04`3oool0103o0000oooo0?ooo`00oolB0?ooo`030000o`3oool0oooo01d0oooo0P00o`2m 0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003oool0oooo000000@0oooo0`00 000C0?ooo`030?l0003oool00?oo0180oooo00<0003o0?ooo`3oool07@3oool00`00o`00oooo0?oo o`2m0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`<000001@3oool00`000000oooo0?oo o`0C0?ooo`030?l0003oool00?oo0140oooo00<0003o0?ooo`3oool0703oool2003o0<00oooo0000 1@3oool000000?ooo`3oool0000000T0oooo00<000000?ooo`3oool0103oool00`000000oooo0?oo o`0B0?ooo`030?l0003oool00?oo0180oooo00<0003o0?ooo`3oool06`3oool00`00o`00oooo0?oo o`300?ooo`000P3oool2000000X0oooo0`0000040?ooo`030000003oool0oooo0180oooo00<0o`00 0?ooo`00ool04@3oool00`000?l0oooo0?ooo`0K0?ooo`03003o003oool0oooo0<40oooo000E0?oo o`030000003oool0oooo0140oooo00@0o`000?ooo`3oool00?oo403oool00`000?l0oooo0?ooo`0K 0?ooo`03003o003oool0oooo0<80oooo000E0?ooo`030000003oool0oooo0140oooo00<0o`000?oo o`00ool0403oool00`000?l0oooo0?ooo`0J0?ooo`800?l0a@3oool001D0oooo00<000000?ooo`3o ool04@3oool00`3o0000oooo003oo`0@0?ooo`030000o`3oool0oooo01T0oooo00<00?l00?ooo`3o ool0a@3oool001D0oooo00<000000?ooo`3oool0403oool0103o0000oooo0?ooo`00ool?0?ooo`03 0000o`3oool0oooo01T0oooo00<00?l00?ooo`3oool0aP3oool001D0oooo0P00000A0?ooo`030?l0 003oool00?oo00l0oooo00<0003o0?ooo`3oool06@3oool00`00o`00oooo0?ooo`370?ooo`005@3o ool00`000000oooo0?ooo`0?0?ooo`040?l0003oool0oooo003oo`l0oooo00<0003o0?ooo`3oool0 5`3oool2003o00?ooo`030000o`3oool0oooo01D0oooo 00<00?l00?ooo`3oool0c`3oool001D0oooo00<000000?ooo`3oool03@3oool00`3o0000oooo003o o`0=0?ooo`030000o`3oool0oooo01@0oooo0P00o`3B0?ooo`005@3oool2000000h0oooo00<0o`00 0?ooo`00ool03@3oool00`000?l0oooo0?ooo`0C0?ooo`03003o003oool0oooo0=80oooo000E0?oo o`030000003oool0oooo00`0oooo00<0o`000?ooo`00ool03@3oool00`000?l0oooo0?ooo`0C0?oo o`03003o003oool0oooo0=<0oooo000E0?ooo`030000003oool0oooo00`0oooo00<0o`000?ooo`00 ool0303oool00`000?l0oooo0?ooo`0C0?ooo`03003o003oool0oooo0=@0oooo000E0?ooo`030000 003oool0oooo00/0oooo00@0o`000?ooo`3oool00?oo303oool00`000?l0oooo0?ooo`0A0?ooo`80 0?l0e`3oool001D0oooo00<000000?ooo`3oool02`3oool0103o0000oooo0?ooo`00ool;0?ooo`03 0000o`3oool0oooo0140oooo00<00?l00?ooo`3oool0e`3oool001D0oooo00<000000?ooo`3oool0 2`3oool00`3o0000oooo003oo`0;0?ooo`030000o`3oool0oooo0140oooo00<00?l00?ooo`3oool0 f03oool001D0oooo00<000000?ooo`3oool02P3oool0103o0000oooo0?ooo`00ool:0?ooo`030000 o`3oool0oooo0140oooo00<00?l00?ooo`3oool0f@3oool001D0oooo00<000000?ooo`3oool02P3o ool0103o0000oooo0?ooo`00ool:0?ooo`030000o`3oool0oooo00l0oooo0P00o`3L0?ooo`005@3o ool2000000X0oooo00@0o`000?ooo`3oool00?oo2P3oool00`000?l0oooo0?ooo`0?0?ooo`03003o 003oool0oooo0=`0oooo000E0?ooo`030000003oool0oooo00T0oooo00@0o`000?ooo`3oool00?oo 2@3oool00`000?l0oooo0?ooo`0?0?ooo`03003o003oool0oooo0=d0oooo000E0?ooo`030000003o ool0oooo00T0oooo00<0o`000?ooo`00ool02P3oool00`000?l0oooo0?ooo`0>0?ooo`03003o003o ool0oooo0=h0oooo000E0?ooo`030000003oool0oooo00P0oooo00@0o`000?ooo`3oool00?oo2@3o ool00`000?l0oooo0?ooo`0>0?ooo`03003o003oool0oooo0=l0oooo000E0?ooo`030000003oool0 oooo00P0oooo00<0o`000?ooo`00ool02@3oool00`000?l0oooo0?ooo`0>0?ooo`03003o003oool0 oooo0>00oooo000E0?ooo`030000003oool0oooo00L0oooo00@0o`000?ooo`3oool00?oo2@3oool0 0`000?l0oooo0?ooo`0=0?ooo`03003o003oool0oooo0>40oooo00020?ooo`800000103oool20000 00@0oooo0P0000050?ooo`030000003oool0oooo00L0oooo00@0o`000?ooo`3oool00?oo203oool0 0`000?l0oooo0?ooo`0<0?ooo`800?l0i03oool000050?ooo`000000oooo0?ooo`000000203oool0 10000000oooo0?ooo`0000040?ooo`030000003oool0oooo00L0oooo00<0o`000?ooo`00ool0203o ool00`000?l0oooo0?ooo`0<0?ooo`03003o003oool0oooo0>@0oooo00001@3oool000000?ooo`3o ool0000000P0oooo00@000000?ooo`3oool00000103oool3000000H0oooo00@0o`000?ooo`3oool0 0?oo203oool00`000?l0oooo0?ooo`0;0?ooo`03003o003oool0oooo0>D0oooo00001@3oool00000 0?ooo`3oool0000000T0oooo0P0000050?ooo`030000003oool0oooo00H0oooo00<0o`000?ooo`00 ool0203oool00`000?l0oooo0?ooo`0;0?ooo`03003o003oool0oooo0>H0oooo00001@3oool00000 0?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`060?oo o`030?l0003oool00?oo00L0oooo00<0003o0?ooo`3oool02P3oool2003o0>T0oooo00020?ooo`80 00002P3oool2000000D0oooo00<000000?ooo`3oool01P3oool00`3o00000?oo0?ooo`070?ooo`03 0000o`3oool0oooo00T0oooo00<00?l00?ooo`3oool0j@3oool001D0oooo00<000000?ooo`3oool0 1@3oool00`3o0000oooo003oo`070?ooo`030000o`3oool0oooo00T0oooo00<00?l00?ooo`3oool0 jP3oool001D0oooo00<000000?ooo`3oool01@3oool00`3o0000oooo003oo`060?ooo`030000o`3o ool0oooo00T0oooo00<00?l00?ooo`3oool0j`3oool001D0oooo00<000000?ooo`3oool01@3oool0 0`3o00000?oo0?ooo`060?ooo`030000o`3oool0oooo00P0oooo00<00?l00?ooo`3oool0k03oool0 01D0oooo00<000000?ooo`3oool0103oool00`3o0000oooo003oo`060?ooo`030000o`3oool0oooo 00P0oooo00<00?l00?ooo`3oool0k@3oool001D0oooo0P0000050?ooo`030?l0003oool00?oo00D0 oooo00<0003o0?ooo`3oool0203oool00`00o`00oooo0?ooo`3^0?ooo`005@3oool00`000000oooo 0?ooo`040?ooo`030?l0003oool00?oo00D0oooo00<0003o0?ooo`3oool01P3oool2003o0?40oooo 000E0?ooo`030000003oool0oooo00<0oooo00<0o`000?ooo`00ool01@3oool00`000?l0oooo0?oo o`060?ooo`03003o003oool0oooo0?40oooo000E0?ooo`030000003oool0oooo00<0oooo00<0o`00 0?ooo`00ool0103oool00`000?l0oooo0?ooo`060?ooo`03003o003oool0oooo0?80oooo000E0?oo o`030000003oool0oooo00<0oooo00<0o`000?ooo`00ool0103oool00`000?l0oooo0?ooo`060?oo o`03003o003oool0oooo0?80oooo000E0?ooo`030000003oool0oooo00<0oooo00<0o`00003oo`3o ool00`3oool00`000?l0oooo0?ooo`060?ooo`03003o003oool0oooo0?<0oooo000E0?ooo`030000 003oool0oooo0080oooo00<0o`000?ooo`00ool00`3oool00`000?l0oooo0?ooo`050?ooo`800?l0 mP3oool001D0oooo00<000000?ooo`3oool00P3oool00`3o00000?oo0?ooo`030?ooo`030000o`3o ool0oooo00@0oooo00<00?l00?ooo`3oool0mP3oool001D0oooo0P0000030?ooo`030?l00000ool0 oooo0080oooo00<0003o0?ooo`3oool0103oool00`00o`00oooo0?ooo`3g0?ooo`005@3oool01P00 0000oooo0?ooo`3oool0o`00003oo`<0oooo00<0003o0?ooo`3oool0103oool00`00o`00oooo0?oo o`3h0?ooo`005@3oool01P000000oooo0?ooo`3oool0o`00003oo`<0oooo00<0003o0?ooo`3oool0 0`3oool00`00o`00oooo0?ooo`3i0?ooo`005@3oool01P000000oooo0?ooo`3oool0o`00003oo`80 oooo00<0003o0?ooo`3oool00`3oool00`00o`00oooo0?ooo`3j0?ooo`005@3oool01@000000oooo 0?ooo`3oool00?oo0080oooo00<0003o0?ooo`3oool00`3oool00`00o`00oooo0?ooo`3k0?ooo`00 5@3oool01@000000oooo0?ooo`3o00000?oo0080oooo00@0003o0?ooo`3oool0oooo0P00o`3n0?oo o`005@3oool01`000000oooo0?ooo`3o00000?oo0?ooo`000?l00`3oool00`00o`00oooo0?ooo`3n 0?ooo`005@3oool01`000000oooo0?ooo`3o00000?oo0?ooo`000?l00P3oool00`00o`00oooo0?oo o`3o0?ooo`005@3oool2000000040?l00000ool0oooo0000o`<0oooo00<00?l00?ooo`3oool0o`3o ool001D0oooo00D000000?ooo`3o00000?oo0000o`030?ooo`03003o003oool0oooo0?l0oooo0@3o ool001D0oooo00H000000?ooo`3o00000?oo0000o`3oool2003o0?l0oooo103oool001D0oooo00H0 00000?l00000ool0003o0?ooo`00o`3o0?ooo`H0oooo000E0?ooo`050000003o00000?oo0?ooo`00 o`00o`3oool70?ooo`005@3oool0100000000?oo0000o`00o`3o0?ooo`P0oooo000=0?ooo`D00000 0`3oool00`0000000?oo003o003o0?ooo`T0oooo000?0?ooo`030000003oool0oooo00<0oooo00<0 0?oo003o003oool0o`3oool90?ooo`003`3oool00`000000oooo0?ooo`030?ooo`03003oo`000000 00000?l0oooo2@3oool000l0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3o0?oo o`T0oooo000?0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0o`3oool90?ooo`00 3P3oool2000000D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool00`000000oooo0?oo o`3o0?ooo`T0oooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.829852, -0.07747, \ 0.0386179, 0.00624851}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Third approximation is built using the method given in ", FontSize->18], StyleBox["M. N. \[CapitalODoubleDot]zisik, Heat Conduction, Wiley, New \ York, 1980.", FontSize->18] }], "Subsubtitle", TextAlignment->Left, Background->RGBColor[1, 1, 0.682353]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Theta]2i = Interpolation[ Table[{\[Eta], \[Theta]2[\[Eta]]}, {\[Eta], 0, 10, 0.1}]]\)], "Input"], Cell[BoxData[ TagBox[\(InterpolatingFunction[{{0.`, 10.`}}, "<>"]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(T2[\[Eta]_] := 0.9\ \[Theta]2i[\[Eta]] + 0.1\)], "Input"], Cell[BoxData[ \(alpha[\[Eta]_] := \ \((k[T] /. T \[Rule] \ T1[\[Eta]])\)/\((\[Rho]\ Cp)\)\)], "Input"], Cell[BoxData[ \(d[\[Eta]_] := \((D[k[T]/\((\[Rho]\ Cp)\), {T, 1}] /. T \[Rule] \ T1[\[Eta]])\)\ 0.9\ D[\[Theta]2i[x], {x, 1}] /. x \[Rule] \ \[Eta]\)], "Input"], Cell[BoxData[ \(f2[a_] := 1/2\ \ a/alpha[a] + 1/alpha[a] d[a]\)], "Input"], Cell[BoxData[ \(g2[\[Eta]p_?NumericQ] := NIntegrate[First[f2[\[Eta]pp]], {\[Eta]pp, 0, \[Eta]p}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Int2 = \(\(1/ NIntegrate[ Exp[\(-g2[\[Eta]p]\)], {\[Eta]p, 0, 10}]\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(0.46800498524518297`\)], "Output"] }, Open ]], Cell[BoxData[ \(\[Theta]3[\[Eta]_] := 1 - NIntegrate[ Exp[\(-g2[\[Eta]p]\)], {\[Eta]p, 0, \[Eta]}]\ Int2\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(plt5 = ListPlot[Table[{\[Eta], \[Theta]3[\[Eta]]}, {\[Eta], 0, 10, 0.1}], PlotStyle \[Rule] \ RGBColor[1, 1, 0], PlotRange \[Rule] \ All, PlotJoined \[Rule] True, DisplayFunction \[Rule] \ Identity]\)], "Input"], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Second approximation and third approximation show the \ same behavior and are in agreement with the exact solution obtained using \ NDSolve and the shooting technique.This indicates that the methods has \ converged in two iterations.", FontSize->18]], "Subsubtitle", TextAlignment->Left, Background->RGBColor[1, 1, 0.682353]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[plt1, plt4, plt5, DisplayFunction \[Rule] \ $DisplayFunction]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.0147151 0.588604 [ [.21429 .00222 -3 -9 ] [.21429 .00222 3 0 ] [.40476 .00222 -3 -9 ] [.40476 .00222 3 0 ] [.59524 .00222 -3 -9 ] [.59524 .00222 3 0 ] [.78571 .00222 -3 -9 ] [.78571 .00222 3 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.01131 .13244 -18 -4.5 ] [.01131 .13244 0 4.5 ] [.01131 .25016 -18 -4.5 ] [.01131 .25016 0 4.5 ] [.01131 .36788 -18 -4.5 ] [.01131 .36788 0 4.5 ] [.01131 .4856 -18 -4.5 ] [.01131 .4856 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .01472 m .21429 .02097 L s [(2)] .21429 .00222 0 1 Mshowa .40476 .01472 m .40476 .02097 L s [(4)] .40476 .00222 0 1 Mshowa .59524 .01472 m .59524 .02097 L s [(6)] .59524 .00222 0 1 Mshowa .78571 .01472 m .78571 .02097 L s [(8)] .78571 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(10)] .97619 .00222 0 1 Mshowa .125 Mabswid .07143 .01472 m .07143 .01847 L s .11905 .01472 m .11905 .01847 L s .16667 .01472 m .16667 .01847 L s .2619 .01472 m .2619 .01847 L s .30952 .01472 m .30952 .01847 L s .35714 .01472 m .35714 .01847 L s .45238 .01472 m .45238 .01847 L s .5 .01472 m .5 .01847 L s .54762 .01472 m .54762 .01847 L s .64286 .01472 m .64286 .01847 L s .69048 .01472 m .69048 .01847 L s .7381 .01472 m .7381 .01847 L s .83333 .01472 m .83333 .01847 L s .88095 .01472 m .88095 .01847 L s .92857 .01472 m .92857 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .13244 m .03006 .13244 L s [(0.2)] .01131 .13244 1 0 Mshowa .02381 .25016 m .03006 .25016 L s [(0.4)] .01131 .25016 1 0 Mshowa .02381 .36788 m .03006 .36788 L s [(0.6)] .01131 .36788 1 0 Mshowa .02381 .4856 m .03006 .4856 L s [(0.8)] .01131 .4856 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04415 m .02756 .04415 L s .02381 .07358 m .02756 .07358 L s .02381 .10301 m .02756 .10301 L s .02381 .16187 m .02756 .16187 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .27959 m .02756 .27959 L s .02381 .30902 m .02756 .30902 L s .02381 .33845 m .02756 .33845 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .45617 m .02756 .45617 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 1 0 0 r .5 Mabswid .02381 .60332 m .06244 .47915 L .10458 .36693 L .14415 .28118 L .18221 .21431 L .22272 .15773 L .26171 .11559 L .30316 .08204 L .32392 .06894 L .34309 .05875 L .3815 .04301 L .40022 .03724 L .42085 .03207 L .44189 .02787 L .46114 .02484 L .48124 .02233 L .49991 .02052 L .51889 .01907 L .53962 .01787 L .56014 .01698 L .57875 .01638 L .59799 .01592 L .61881 .01555 L .63875 .0153 L .64892 .0152 L .65982 .01511 L .67946 .01498 L .69779 .0149 L .70796 .01487 L .71903 .01484 L .72859 .01482 L .73915 .0148 L .75892 .01477 L .76976 .01476 L .77993 .01475 L .78976 .01474 L .80011 .01474 L .81862 .01473 L .82816 .01473 L .83836 .01472 L .85673 .01472 L .86697 .01472 L .87807 .01472 L .88856 .01472 L .89823 .01472 L .90727 .01472 L .91699 .01472 L .92765 .01472 L .93763 .01472 L .94709 .01472 L Mistroke .95741 .01472 L .96716 .01472 L .97619 .01472 L Mfstroke 0 1 1 r .02381 .60332 m .03333 .57696 L .04286 .5507 L .05238 .52464 L .0619 .49888 L .07143 .47351 L .08095 .4486 L .09048 .42422 L .1 .40046 L .10952 .37736 L .11905 .35497 L .12857 .33335 L .1381 .31251 L .14762 .2925 L .15714 .27333 L .16667 .25502 L .17619 .23758 L .18571 .22101 L .19524 .2053 L .20476 .19045 L .21429 .17644 L .22381 .16327 L .23333 .1509 L .24286 .13933 L .25238 .12852 L .2619 .11844 L .27143 .10908 L .28095 .10039 L .29048 .09235 L .3 .08493 L .30952 .07809 L .31905 .0718 L .32857 .06604 L .3381 .06076 L .34762 .05595 L .35714 .05156 L .36667 .04757 L .37619 .04396 L .38571 .04069 L .39524 .03774 L .40476 .03508 L .41429 .03269 L .42381 .03054 L .43333 .02863 L .44286 .02692 L .45238 .0254 L .4619 .02404 L .47143 .02284 L .48095 .02178 L .49048 .02085 L Mistroke .5 .02002 L .50952 .0193 L .51905 .01867 L .52857 .01812 L .5381 .01763 L .54762 .01721 L .55714 .01685 L .56667 .01653 L .57619 .01626 L .58571 .01603 L .59524 .01583 L .60476 .01565 L .61429 .01551 L .62381 .01538 L .63333 .01527 L .64286 .01518 L .65238 .01511 L .6619 .01504 L .67143 .01499 L .68095 .01494 L .69048 .0149 L .7 .01487 L .70952 .01484 L .71905 .01482 L .72857 .0148 L .7381 .01478 L .74762 .01477 L .75714 .01476 L .76667 .01475 L .77619 .01475 L .78571 .01474 L .79524 .01473 L .80476 .01473 L .81429 .01473 L .82381 .01473 L .83333 .01472 L .84286 .01472 L .85238 .01472 L .8619 .01472 L .87143 .01472 L .88095 .01472 L .89048 .01472 L .9 .01472 L .90952 .01472 L .91905 .01472 L .92857 .01472 L .9381 .01472 L .94762 .01472 L .95714 .01472 L .96667 .01472 L Mistroke .97619 .01472 L Mfstroke 1 1 0 r .02381 .60332 m .03333 .57579 L .04286 .54837 L .05238 .52116 L .0619 .49427 L .07143 .46779 L .08095 .44181 L .09048 .41642 L .1 .39167 L .10952 .36766 L .11905 .34442 L .12857 .32202 L .1381 .30049 L .14762 .27987 L .15714 .26019 L .16667 .24145 L .17619 .22367 L .18571 .20685 L .19524 .19099 L .20476 .17608 L .21429 .1621 L .22381 .14903 L .23333 .13685 L .24286 .12553 L .25238 .11503 L .2619 .10533 L .27143 .09639 L .28095 .08817 L .29048 .08064 L .3 .07374 L .30952 .06746 L .31905 .06174 L .32857 .05655 L .3381 .05186 L .34762 .04762 L .35714 .0438 L .36667 .04037 L .37619 .0373 L .38571 .03455 L .39524 .0321 L .40476 .02992 L .41429 .02799 L .42381 .02627 L .43333 .02476 L .44286 .02343 L .45238 .02226 L .4619 .02123 L .47143 .02033 L .48095 .01954 L .49048 .01886 L Mistroke .5 .01826 L .50952 .01775 L .51905 .0173 L .52857 .01692 L .5381 .01659 L .54762 .0163 L .55714 .01606 L .56667 .01585 L .57619 .01567 L .58571 .01552 L .59524 .01539 L .60476 .01528 L .61429 .01519 L .62381 .01511 L .63333 .01504 L .64286 .01499 L .65238 .01494 L .6619 .0149 L .67143 .01487 L .68095 .01484 L .69048 .01482 L .7 .0148 L .70952 .01478 L .71905 .01477 L .72857 .01476 L .7381 .01475 L .74762 .01475 L .75714 .01474 L .76667 .01473 L .77619 .01473 L .78571 .01473 L .79524 .01473 L .80476 .01472 L .81429 .01472 L .82381 .01472 L .83333 .01472 L .84286 .01472 L .85238 .01472 L .8619 .01472 L .87143 .01472 L .88095 .01472 L .89048 .01472 L .9 .01472 L .90952 .01472 L .91905 .01472 L .92857 .01472 L .9381 .01472 L .94762 .01472 L .95714 .01472 L .96667 .01472 L Mistroke .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgP3oool01@3oo`00oooo0?ooo`3o00000?oo0@3oool0103oo`00oooo0?l00000ooo;0?ooo`0000D0 oooo0000003oool0oooo000000080?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0 >03oool0103oo`00oooo0?l00000ooo<0?ooo`0000D0oooo0000003oool0oooo000000090?ooo`03 0000003oool0oooo00@0oooo0`00000g0?ooo`040?oo003oool0o`00003oold0oooo00001@3oool0 00000?ooo`3oool0000000X0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`0f0?oo o`050?oo003oool0o`000?ooo`00ool0c@3oool000050?ooo`000000oooo0?ooo`000000203oool0 10000000oooo0?ooo`0000040?ooo`030000003oool0oooo03D0oooo00D0ool00?ooo`3oool0o`00 003oo`3>0?ooo`000P3oool2000000X0oooo0P0000050?ooo`030000003oool0oooo03@0oooo00D0 ool00?ooo`3oool0o`00003oo`3?0?ooo`005@3oool00`000000oooo0?ooo`0c0?ooo`050?oo003o ool0oooo0?l00000ool0d03oool001D0oooo00<000000?ooo`3oool040 oooo00020?ooo`800000103oool2000000D0oooo0`0000030?ooo`030000003oool0oooo02@0oooo 00<0ool0003oo`3oool0h@3oool000050?ooo`000000oooo0?ooo`0000002`3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo02<0oooo00<0ool00?ooo`00ool0hP3oool000050?ooo`00 0000oooo0?ooo`000000203oool5000000<0oooo0`00000R0?ooo`030?l0003oo`000?oo0><0oooo 00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103oool00`000000 oooo0?ooo`0R0?ooo`030?oo003oool00?oo0><0oooo00001@3oool000000?ooo`3oool0000000T0 oooo00<000000?ooo`000000103oool00`000000oooo0?ooo`0Q0?ooo`030?l0003oo`000?oo0>@0 oooo00020?ooo`8000002`3oool2000000@0oooo00<000000?ooo`3oool08@3oool00`3oo`00oooo 003oo`3T0?ooo`005@3oool00`000000oooo0?ooo`0P0?ooo`030?l0003oo`000?oo0>D0oooo000E 0?ooo`030000003oool0oooo0200oooo00<0ool00?ooo`00ool0i@3oool001D0oooo00<000000?oo o`3oool07`3oool00`3o0000ool0003oo`3V0?ooo`005@3oool00`000000oooo0?ooo`0O0?ooo`03 0?oo003oool00?oo0>H0oooo000E0?ooo`8000007`3oool00`3o0000ool0003oo`3W0?ooo`005@3o ool00`000000oooo0?ooo`0N0?ooo`030?oo003oool00?oo0>L0oooo000E0?ooo`030000003oool0 oooo01d0oooo00<0o`000?oo0000ool0j03oool001D0oooo00<000000?ooo`3oool07@3oool00`3o o`00oooo003oo`3X0?ooo`005@3oool00`000000oooo0?ooo`0L0?ooo`030?l0003oo`000?oo0>T0 oooo000E0?ooo`030000003oool0oooo01`0oooo00<0ool00?ooo`00ool0j@3oool001D0oooo00<0 00000?ooo`3oool06`3oool00`3o0000ool0003oo`3Z0?ooo`005@3oool00`000000oooo0?ooo`0K 0?ooo`030?oo003oool00?oo0>X0oooo000E0?ooo`8000006`3oool00`3o0000ool0003oo`3[0?oo o`005@3oool00`000000oooo0?ooo`0J0?ooo`030?oo003oool00?oo0>/0oooo000E0?ooo`030000 003oool0oooo01T0oooo00<0o`000?oo0000ool0k03oool001D0oooo00<000000?ooo`3oool06@3o ool00`3oo`00oooo003oo`3/0?ooo`005@3oool00`000000oooo0?ooo`0H0?ooo`030?l0003oo`00 0?oo0>d0oooo000E0?ooo`030000003oool0oooo01P0oooo00<0o`000?oo0000ool0k@3oool001D0 oooo00<000000?ooo`3oool0603oool00`3oo`000?oo0?ooo`3]0?ooo`005@3oool00`000000oooo 0?ooo`0G0?ooo`030?l0003oo`000?oo0>h0oooo000E0?ooo`800000603oool00`3o0000ool0003o o`3^0?ooo`005@3oool00`000000oooo0?ooo`0F0?ooo`030?l0003oo`000?oo0>l0oooo000E0?oo o`030000003oool0oooo01H0oooo00<0o`000?oo0000ool0k`3oool001D0oooo00<000000?ooo`3o ool05@3oool00`3o0000ool0003oo`3`0?ooo`005@3oool00`000000oooo0?ooo`0E0?ooo`030?l0 003oo`000?oo0?00oooo000E0?ooo`030000003oool0oooo01@0oooo00@0o`000?oo003oool00?oo l03oool00080oooo0P0000040?ooo`8000000`3oool3000000D0oooo00<000000?ooo`3oool0503o ool00`3o0000ool0003oo`3a0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool04`3oool0103o0000ool00?ooo`00oooa0?ooo`00 00D0oooo0000003oool0oooo000000080?ooo`040000003oool0oooo000000@0oooo0`00000C0?oo o`030?l0003oo`000?oo0?80oooo00001@3oool000000?ooo`3oool0000000P0oooo0`0000050?oo o`030000003oool0oooo01<0oooo00<0o`000?oo0000ool0lP3oool000050?ooo`000000oooo0?oo o`0000002@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo0180oooo00<0o`000?oo 0000ool0l`3oool00080oooo0P00000:0?ooo`<00000103oool00`000000oooo0?ooo`0B0?ooo`03 0?l0003oo`000?oo0?<0oooo000E0?ooo`030000003oool0oooo0140oooo00@0o`000?ooo`3oo`00 0?ool`3oool001D0oooo00<000000?ooo`3oool04@3oool00`3o0000ool0003oo`3d0?ooo`005@3o ool00`000000oooo0?ooo`0A0?ooo`030?l0003oo`000?oo0?@0oooo000E0?ooo`030000003oool0 oooo0100oooo00@0o`000?ooo`3oo`000?oom03oool001D0oooo0P00000A0?ooo`030?l0003oo`00 0?oo0?D0oooo000E0?ooo`030000003oool0oooo00l0oooo00@0o`000?ooo`3oo`000?oom@3oool0 01D0oooo00<000000?ooo`3oool03`3oool00`3o0000ool0003oo`3f0?ooo`005@3oool00`000000 oooo0?ooo`0?0?ooo`030?l0003oo`000?oo0?H0oooo000E0?ooo`030000003oool0oooo00h0oooo 00<0o`000?oo0000ool0m`3oool001D0oooo00<000000?ooo`3oool03P3oool00`3o0000ool0003o o`3g0?ooo`005@3oool00`000000oooo0?ooo`0=0?ooo`030?l0003oool0ool00?P0oooo000E0?oo o`030000003oool0oooo00d0oooo00<0o`000?oo0000ool0n03oool001D0oooo0P00000>0?ooo`03 0?l0003oo`000?oo0?P0oooo000E0?ooo`030000003oool0oooo00`0oooo00<0o`000?ooo`3oo`00 n@3oool001D0oooo00<000000?ooo`3oool0303oool00`3o0000oooo0?oo003i0?ooo`005@3oool0 0`000000oooo0?ooo`0;0?ooo`040?l0003oool0ool0003oooT0oooo000E0?ooo`030000003oool0 oooo00/0oooo00@0o`000?ooo`3oo`000?oon@3oool001D0oooo00<000000?ooo`3oool02`3oool0 0`3o0000oooo0?oo003j0?ooo`005@3oool00`000000oooo0?ooo`0:0?ooo`040?l0003oool0ool0 003oooX0oooo000E0?ooo`030000003oool0oooo00X0oooo00@0o`000?ooo`3oo`000?oonP3oool0 01D0oooo0P00000:0?ooo`040?l0003oool0ool0003ooo/0oooo000E0?ooo`030000003oool0oooo 00T0oooo00@0o`000?ooo`3oo`000?oon`3oool001D0oooo00<000000?ooo`3oool02@3oool00`3o 0000ool0003oo`3l0?ooo`005@3oool00`000000oooo0?ooo`080?ooo`040?l0003oool0ool0003o oo`0oooo000E0?ooo`030000003oool0oooo00P0oooo00<0o`000?ooo`3oo`00o@3oool001D0oooo 00<000000?ooo`3oool01`3oool0103o0000oooo0?oo0000ooom0?ooo`000P3oool2000000@0oooo 0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`070?ooo`040?l0003oool0ool0003oood0 oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103oool00`00 0000oooo0?ooo`070?ooo`030?l0003oo`000?oo0?h0oooo00001@3oool000000?ooo`3oool00000 00P0oooo00@000000?ooo`3oool00000103oool3000000H0oooo00@0o`000?ooo`3oo`000?oooP3o ool000050?ooo`000000oooo0?ooo`0000002@3oool2000000D0oooo00<000000?ooo`3oool01P3o ool00`3o0000ool0003oo`3o0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool01P3oool00`3o0000ool0003oo`3o0?ooo`000P3o ool2000000X0oooo0P0000050?ooo`030000003oool0oooo00H0oooo00<0o`000?oo003oool0o`3o ool001D0oooo00<000000?ooo`3oool01@3oool00`3o0000ool0003oo`3o0?ooo`40oooo000E0?oo o`030000003oool0oooo00D0oooo00<0o`000?oo0000ool0o`3oool10?ooo`005@3oool00`000000 oooo0?ooo`050?ooo`030?l0003oo`00oooo0?l0oooo0@3oool001D0oooo00<000000?ooo`3oool0 103oool00`3o0000oooo0?oo003o0?ooo`80oooo000E0?ooo`8000001@3oool00`3o0000ool0003o o`3o0?ooo`80oooo000E0?ooo`030000003oool0oooo00@0oooo00<0o`000?oo0000ool0o`3oool2 0?ooo`005@3oool00`000000oooo0?ooo`030?ooo`030?l0003oool0ool00?l0oooo0`3oool001D0 oooo00<000000?ooo`3oool00`3oool00`3o0000oooo0?oo003o0?ooo`<0oooo000E0?ooo`030000 003oool0oooo00<0oooo00<0o`000?oo0000ool0o`3oool30?ooo`005@3oool00`000000oooo0?oo o`030?ooo`030?l0003oo`00oooo0?l0oooo0`3oool001D0oooo00<000000?ooo`3oool00P3oool0 0`3o0000ool0003oo`3o0?ooo`@0oooo000E0?ooo`030000003oool0oooo0080oooo00<0o`000?oo 003oool0o`3oool40?ooo`005@3oool2000000<0oooo00<0ool0003oo`3oool0o`3oool40?ooo`00 5@3oool01P000000oooo0?ooo`3oool0o`000?oo0?l0oooo1P3oool001D0oooo00H000000?ooo`3o ool0oooo0?l0003oo`3o0?ooo`H0oooo000E0?ooo`060000003oool0oooo0?ooo`3oo`000?ooo`3o ool60?ooo`005@3oool01@000000oooo0?ooo`3oool0ool00?l0oooo1`3oool001D0oooo00D00000 0?ooo`3oool0o`000?oo003o0?ooo`L0oooo000E0?ooo`050000003oool0oooo0?l0003oo`00o`3o ool70?ooo`005@3oool01@000000oooo0?ooo`3oo`000?oo0?l0oooo1`3oool001D0oooo0P000000 0`3o0000ool00?ooo`3o0?ooo`L0oooo000E0?ooo`040000003oool0o`000?oo0?l0oooo203oool0 01D0oooo00@000000?ooo`3o0000ool0o`3oool80?ooo`005@3oool00`000000o`000?oo003o0?oo o`T0oooo000E0?ooo`030000003o0000ool00?l0oooo2@3oool001D0oooo00<000000?oo003oool0 o`3oool90?ooo`003@3oool5000000<0oooo00<000000?oo003oool0o`3oool90?ooo`003`3oool0 0`000000oooo0?ooo`030?ooo`030?oo003oool0oooo0?l0oooo2@3oool000l0oooo00<000000?oo o`3oool00`3oool00`3oo`0000000000003o0?ooo`T0oooo000?0?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool0o`3oool90?ooo`003`3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo0?l0oooo2@3oool000h0oooo0P0000050?ooo`030000003oool0oooo0?l0oooo2@3o ool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.829852, -0.07747, \ 0.0386179, 0.00624851}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Closed]] }, Open ]] }, FrontEndVersion->"5.2 for Microsoft Windows", ScreenRectangle->{{0, 800}, {0, 517}}, WindowSize->{495, 359}, WindowMargins->{{50, Automatic}, {Automatic, 36}} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1776, 53, 744, 21, 295, "Title"], Cell[2523, 76, 41035, 633, 278, "Graphics"], Cell[CellGroupData[{ Cell[43583, 713, 220, 6, 67, "Subsubtitle"], Cell[43806, 721, 59, 1, 30, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[43902, 727, 189, 4, 72, "Subsubtitle"], Cell[44094, 733, 59, 1, 30, "Input"], Cell[44156, 736, 51, 1, 30, "Input"], Cell[44210, 739, 75, 1, 30, "Input"], Cell[44288, 742, 360, 7, 110, "Input"], Cell[44651, 751, 120, 2, 30, "Input"], Cell[CellGroupData[{ Cell[44796, 757, 89, 1, 30, "Input"], Cell[44888, 760, 74, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[44999, 766, 253, 4, 70, "Input"], Cell[45255, 772, 130, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[45434, 781, 304, 10, 59, "Subsubtitle"], Cell[45741, 793, 51, 1, 30, "Input"], Cell[45795, 796, 93, 1, 35, "Input"], Cell[CellGroupData[{ Cell[45913, 801, 205, 4, 70, "Input"], Cell[46121, 807, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[46288, 815, 93, 1, 30, "Input"], Cell[46384, 818, 20765, 495, 186, 4191, 286, "GraphicsData", "PostScript", \ "Graphics"], Cell[67152, 1315, 130, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[67331, 1324, 299, 8, 97, "Subsubtitle"], Cell[67633, 1334, 76, 1, 30, "Input"], Cell[67712, 1337, 60, 1, 30, "Input"], Cell[67775, 1340, 120, 2, 50, "Input"], Cell[CellGroupData[{ Cell[67920, 1346, 127, 3, 30, "Input"], Cell[68050, 1351, 54, 1, 29, "Output"] }, Open ]], Cell[68119, 1355, 140, 3, 30, "Input"], Cell[CellGroupData[{ Cell[68284, 1362, 265, 5, 70, "Input"], Cell[68552, 1369, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[68719, 1377, 106, 2, 50, "Input"], Cell[68828, 1381, 25371, 637, 186, 5805, 391, "GraphicsData", "PostScript", \ "Graphics"], Cell[94202, 2020, 130, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[94381, 2029, 294, 8, 97, "Subsubtitle"], Cell[CellGroupData[{ Cell[94700, 2041, 133, 3, 30, "Input"], Cell[94836, 2046, 120, 3, 29, "Output"] }, Open ]], Cell[94971, 2052, 77, 1, 30, "Input"], Cell[95051, 2055, 119, 2, 30, "Input"], Cell[95173, 2059, 188, 3, 70, "Input"], Cell[CellGroupData[{ Cell[95386, 2066, 79, 1, 30, "Input"], Cell[95468, 2069, 161, 4, 29, "Output"] }, Open ]], Cell[95644, 2076, 78, 1, 30, "Input"], Cell[95725, 2079, 120, 2, 50, "Input"], Cell[CellGroupData[{ Cell[95870, 2085, 127, 3, 30, "Input"], Cell[96000, 2090, 54, 1, 29, "Output"] }, Open ]], Cell[96069, 2094, 140, 3, 30, "Input"], Cell[CellGroupData[{ Cell[96234, 2101, 265, 5, 70, "Input"], Cell[96502, 2108, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[96669, 2116, 112, 2, 50, "Input"], Cell[96784, 2120, 27282, 746, 186, 7416, 496, "GraphicsData", "PostScript", \ "Graphics"], Cell[124069, 2868, 130, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[124248, 2877, 293, 8, 97, "Subsubtitle"], Cell[CellGroupData[{ Cell[124566, 2889, 133, 3, 30, "Input"], Cell[124702, 2894, 120, 3, 29, "Output"] }, Open ]], Cell[124837, 2900, 77, 1, 30, "Input"], Cell[124917, 2903, 119, 2, 30, "Input"], Cell[125039, 2907, 188, 3, 70, "Input"], Cell[125230, 2912, 78, 1, 30, "Input"], Cell[125311, 2915, 120, 2, 50, "Input"], Cell[CellGroupData[{ Cell[125456, 2921, 127, 3, 30, "Input"], Cell[125586, 2926, 54, 1, 29, "Output"] }, Open ]], Cell[125655, 2930, 140, 3, 30, "Input"], Cell[CellGroupData[{ Cell[125820, 2937, 265, 5, 70, "Input"], Cell[126088, 2944, 130, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[126267, 2953, 355, 6, 143, "Subsubtitle"], Cell[CellGroupData[{ Cell[126647, 2963, 106, 2, 50, "Input"], Cell[126756, 2967, 20779, 641, 186, 6960, 466, "GraphicsData", "PostScript", \ "Graphics"], Cell[147538, 3610, 130, 3, 29, "Output"] }, Open ]] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)