EME165 -- Heat Transfer
A sample program in C/C++ interpreter Ch
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/*********************************************************************
* File: example.ch *
* This program generates a graph containg two temperature curves. *
* To run this program, use computers in CAE lab or *
* download C/C++ interpreter Ch Professional Edition from *
* http://www.softintegration.com/download *
* ******************************************************************/
#include <stdio.h>
#include <numeric.h>
#include <chplot.h>
#define N 51
#define PMAX 100
int main() {
double Fo = 0.2, Tinit1 = 400, Tinit2 = 300, L = 0.1;
array double x[1:N], A[1:N][1:N], Told[1:N], Tnew[1:N],
Texplicit[1:N], Timplicit[1:N];
int i;
class CPlot plot;
linspace(x, 0, L);
for(i=2; i<=(N-1); i++) {
A[i][i-1] = 1;
A[i][i] = -2;
A[i][i+1] = 1;
}
// Explicit solution
Told = Tinit1;
Told[N] = Tinit2;
for(i=1; i<=PMAX; i++) {
Tnew = Told + Fo*A*Told;
Told = Tnew;
}
Texplicit = Tnew;
// Implicit solution
Told = Tinit1;
Told[N] = Tinit2;
for(i=1; i<=PMAX; i++) {
Tnew = inverse(identitymatrix(N)-Fo*A)*Told;
Told = Tnew;
}
Timplicit = Tnew;
// Plot the results
plot.data2D(x, Texplicit);
plot.data2D(x, Timplicit);
plot.title("Implicit and explicit temperature");
plot.label(PLOT_AXIS_X, "x");
plot.label(PLOT_AXIS_Y, "T");
plot.legend("Explicit", 0);
plot.legend("Implicit", 1);
plot.plotting();
return 0;
}
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Output
A sample program in MATLAB
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clear
N = 51;
Fo = 0.2;
Tinit1 = 400;
Tinit2 = 300;
Pmax = 100;
L = 0.1;
dx = L/(N-1);
x = [0:dx:L];
A = zeros(N);
Told = zeros(N,1);
Tnew = zeros(N,1);
for m = 2:N-1
A(m,m-1) = 1;
A(m,m) = -2;
A(m,m+1) = 1;
end
% Explicit Solution
for m = 1:N-1
Told(m) = Tinit1;
end
Told(N) = Tinit2;
for P=1:Pmax
Tnew = Told + Fo*A*Told;
Told = Tnew;
end
Texplicit = Tnew;
% Implicit Solution
for m = 1:N-1
Told(m) = Tinit1;
end
Told(N) = Tinit2;
for P=1:Pmax
Tnew = (eye(N) - Fo*A)\Told;
Told = Tnew;
end
Timplicit = Tnew;
% Plot the Results
plot(x, Texplicit, x, Timplicit), xlabel('x'), ylabel('T');
legend('Explicit','Implicit');
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