(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of 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). 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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[ 201519, 6550]*) (*NotebookOutlinePosition[ 202574, 6586]*) (* CellTagsIndexPosition[ 202530, 6582]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[ "(*\tCR418\t\tHW 7.1\tFogler Problem 4-32\t\t *)\n(*\tUnsteady Flow \ Problem - Startup of 3 Series CSTRs \t*)\n(* Rxn: A + B --> C, elementary. \ Equimolar feed rate *)\n(* Find the time required for the exit of the third \ \t*)\n(* reactor to reach 99% of its steady-state value\t\t*)"], "Input", AspectRatioFixed->True], Cell[TextData[ "\n(* Important! 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Also\t*)\n(* assign values to the constants. \ \"ca3ss\" is the\t\t*)\n(* steady-state value solved in a separate notbook.\t\ \t*)\nca1 = na1[t]/v; ca2 = na2[t]/v; ca3 = na3[t]/v;\nfao = 20; v = 200; \ vdot = 20; tfinal = 65; k = 0.025;\nca3ss = 0.609;"], "Input", AspectRatioFixed->True], Cell[TextData[ "(* NDSolve numerically evaluates the coupled ODEs given\t*)\n(* the initial \ conditions.\t\t\t\t\t\t\t\t*)\nsol = NDSolve[{\tna1'[t] == dna1dt,\n\t\t\t\t\ na2'[t] == dna2dt,\n\t\t\t\tna3'[t] == dna3dt,\n\t\t\t\tna1[0] == 0,\n\t\t\t\t\ na2[0] == 0,\n\t\t\t\tna3[0] == 0},\n\t\t\t\t{na1, na2, na3},\n\t\t\t\t{t, 0, \ tfinal}];"], "Input", AspectRatioFixed->True], Cell[TextData[ "(* The direct output of NDSolve is a List. 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the point at which the exit conc. of Reactor 3 is\t*)\n(* 99% of its \ steady-state value.\t\t\t\t\t\t\t*)\nFindRoot[na3r[t]/v == 0.99 ca3ss, {t, \ 0}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {t -> 59.68256178699735}\ \>", "\<\ {t -> 59.6826}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData["(*\tPart d.\tSplit the feed of B\t\t*)"], "Input", AspectRatioFixed->True], Cell[TextData[ "Clear[dna1dt, dna2dt, dna3dt,ca1, ca2, ca3,\n\t\tna1, na2, na3, na1r, na2r, \ na3r,\n\t\tdnb1dt, dnb2dt, dnb3dt, nb1, nb2, nb3]"], "Input", AspectRatioFixed->True], Cell[TextData[ "dna1dt = fao - vdot1 ca1 - k ca1 cb1 v;\ndna2dt = vdot1 ca1 - vdot2 ca2 - k \ ca2 cb2 v;\ndna3dt = vdot2 ca2 - vdot3 ca3 - k ca3 cb3 v;\ndnb1dt = fbo1 - \ vdot1 cb1 - k ca1 cb1 v;\ndnb2dt = vdot1 cb1 + fbo2 - vdot2 cb2 - k ca2 cb2 \ v;\ndnb3dt = vdot2 cb2 - vdot3 cb3 - k ca2 cb3 v;"], "Input", AspectRatioFixed->True], Cell[TextData[ "vdot1 = 15; vdot2 = vdot3 = 20; fbo1 = fbo2 = 10;\nca1 = na1[t]/v; ca2 = \ na2[t]/v; ca3 = na3[t]/v;\ncb1 = nb1[t]/v; cb2 = nb2[t]/v; cb3 = nb3[t]/v;"], "Input", AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[ "sol2 = NDSolve[{\tna1'[t] == dna1dt,\n\t\t\t\t\tna2'[t] == dna2dt,\n\t\t\t\t\ \tna3'[t] == dna3dt,\n\t\t\t\t\tnb1'[t] == dnb1dt,\n\t\t\t\t\tnb2'[t] == \ dnb2dt,\n\t\t\t\t\tnb3'[t] == dnb3dt,\n\t\t\t\t\tna1[0] == 0, na2[0] == 0, \ na3[0] == 0,\n\t\t\t\t\tnb1[0] == 0, nb2[0] == 0, nb3[0] == 0},\n\t\t\t\t\t\ {na1, na2, na3, nb1, nb2, nb3},\n\t\t\t\t\t{t, 0, tfinal}]"], "Input", AspectRatioFixed->True], Cell[OutputFormData[ "\<\ {{na1 -> InterpolatingFunction[{0., 65.}, {{0., 0., {0., 0}, {0}}, \ {0.00004999998520710716, 0., {0.0009999959541553, 19.99992500024094}, {0}}, {0.0000999999704142143, 0.00004999998520710716, {0.001999988158331568, \ 19.99985000063813}, {0}}, {0.02562199699725007, 0.0000999999704142143, {0.5119478331043758, \ 19.9615875318437, -0.7495978616836365}, {0, 0}}, {0.05114399402408595, 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