Please post with matlab code asap! 1- Temperature distribution in a part of a he

Question

Please post with matlab code asap!

1- Temperature distribution in a part of a heat exchanger in the steady state condition should be determined. The part is shown in Figure-l has a thermal conductivity of k-25W/m.K and dimensions and boundary conditions are specified in Figure-1 and Figure-2 respectively Develop a computer code to find the temperature distribution in the part (use --1 mm). Under operating conditions for which ho-1000 W/m2K, T-o-1 700 K. h= 200 W/m2 K, and T 400 K. Also, at what location is the temperature a maximum? 5mm 2mm 3mm 2mm Figure-I. Dimensions

Explanation / Answer

clear all close all %Specify grid size Nx = 10; Ny = 10; %Specify boundary conditions Tbottom = 100 Ttop = 150 Tleft = 250 Tright = 300 % initialize coefficient matrix and constant vector with zeros A = zeros(Nx*Ny); C = zeros(Nx*Ny,1); % initial 'guess' for temperature distribution T(1:Nx*Ny,1) = 100; % Build coefficient matrix and constant vector % inner nodes for n = 2:(Ny-1) for m = 2:(Nx-1) i = (n-1)*Nx + m; A(i,i+Nx) = 1; A(i,i-Nx) = 1; A(i,i+1) = 1; A(i,i-1) = 1; A(i,i) = -4; end end % Edge nodes % bottom for m = 2:(Nx-1) %n = 1 i = m; A(i,i+Nx) = 1; A(i,i+1) = 1; A(i,i-1) = 1; A(i,i) = -4; C(i) = -Tbottom; end %top: for m = 2:(Nx-1) % n = Ny i = (Ny-1)*Nx + m; A(i,i-Nx) = 1; A(i,i+1) = 1; A(i,i-1) = 1; A(i,i) = -4; C(i) = -Ttop; end %left: for n=2:(Ny-1) %m = 1 i = (n-1)*Nx + 1; A(i,i+Nx) = 1; A(i,i+1) = 1; A(i,i-Nx) = 1; A(i,i) = -4; end %right: for n=2:(Ny-1) %m = Nx i = (n-1)*Nx + Nx; A(i,i+Nx) = 1; A(i,i-1) = 1; A(i,i-Nx) = 1; A(i,i) = -4; C(i) = -Tright; end % Corners %bottom left (i=1): i=1; A(i,Nx+i) = 1; A(i,2) = 1; A(i,1) = -4; C(i) = -(Tbottom + Tleft); %bottom right: i = Nx; A(i,i+Nx) = 1; A(i,i-1) = 1; A(i,i) = -4; C(i) = -(Tbottom + Tright); %top left: i = (Ny-1)*Nx + 1; A(i,i+1) = 1; A(i,i) = -4; A(i,i-Nx) = 1; C(i) = -(Ttop + Tleft); %top right: i = Nx*Ny; A(i,i-1) = 1; A(i,i) = -4; A(i,i-Nx) = 1; C(i) = -(Tright + Ttop); %Solve using Gauss-Seidel residual = 100; iterations = 0; while (residual > 0.0001) % The residual criterion is 0.0001 in this example % You can test different values iterations = iterations+1; %Transfer the previously computed temperatures to an array Told Told = T; %Update estimate of the temperature distribution for n=1:Ny for m=1:Nx i = (n-1)*Nx + m; Told(i) = T(i); end end % iterate through all of the equations for n=1:Ny for m=1:Nx i = (n-1)*Nx + m; %sum the terms based on updated temperatures sum1 = 0; for j=1:i-1 sum1 = sum1 + A(i,j)*T(j); end %sum the terms based on temperatures not yet updated sum2 = 0; for j=i+1:Nx*Ny sum2 = sum2 + A(i,j)*Told(j); end % update the temperature for the current node T(i) = (1/A(i,i)) * (C(i) - sum1 - sum2); end end residual = max(T(i) - Told(i)); end %compute residual deltaT = abs(T - Told); residual = max(deltaT); iterations; % report the number of iterations that were executed %Now transform T into 2-D network so it can be plotted. delta_x = 0.03/(Nx+1); delta_y = 0.03/(Ny+1); for n=1:Ny for m=1:Nx i = (n-1)*Nx + m; T2d(m,n) = T(i); x(m) = m*delta_x; y(n) = n*delta_y; end end T2d; surf(x,y,T2d) figure contour(x,y,T2d)

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