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J. Geankoplis, Transport Processes and \ Unit Operations, 3rd edition, Prentice Hall, 1993.", FontWeight->"Bold"]], "Subsubtitle", Background->RGBColor[1, 1, 0.643137]], Cell[TextData[{ "We use the Schmidt numerical method with M=2. \n\nThermal diffusivity is \ \[Alpha]=2 ", Cell[BoxData[ \(TraditionalForm\`10\^\(-5\)\ m\^2\)]], "/s. \n\nThe slab is 1m thick. We choose \[CapitalDelta]x=0.05m. Thus, \ 1m/0.05m=20 slices will be used. \n\nWe want to compute the temperature \ profile at ", Cell[BoxData[ \(TraditionalForm\`t\_final = 9600 \( \(s\)\(.\)\(\ \)\)\)]], "Since M=2=", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]x\^2\/\(\[Alpha]\ \ \[CapitalDelta]t\)\)]], ", we get \[CapitalDelta]t=62.5s. Hence, ", Cell[BoxData[ \(TraditionalForm\`t\_final\)]], "/\[CapitalDelta]t=9600/62.5=96 time increments will be used. \n\nSince \ M=2, temperature at the next time step is computed using the following \ relation: T[t,x]\[Equal]1/2 (T[t-1,x-1]+T[t-1,x+1])\n\nTemperature at x=0 is \ fixed equal to 0\[Degree]C.\n\nThe slab is insulated at x=1m.\n\nInitial \ temperature is 100\[Degree]C expect at x=0 where we take it equal to \ (100+0)/2=50\[Degree]C.\n" }], "Subsubtitle", Background->RGBColor[1, 1, 0.658824]], Cell["\<\ Eq[t_,x_]:=T[t,x]\[Equal]1/2 (T[t-1,x-1]+T[t-1,x+1])\ \>", "Input"], Cell["Eq[t_,0]:=T[t,0]\[Equal]0.", "Input"], Cell["Eq[t_,20]:=T[t,20]\[Equal]T[t-1,19]", "Input"], Cell["T[0,x_]:=If[x>0,100.,50.]", "Input"], Cell["t=1;", "Input"], Cell["\<\ While[t<97,x=0;While[x<21,sol=Solve[Eq[t,x],T[t,x]];T[t,x]=T[t,x]/.sol[[1]];x+\ =1];t+=1]\ \>", "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Results are the same as those presented in Table \ 5.4-1 page 356 C. 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