analytical solution for steady state 2d heat transfer

45 views (last 30 days)
analytical solution for a 2d steady state sqaure bar
my plot for 'analytical solution1' isnt symmetric so i have tried using anathor equation 'analytical solution2' and now it is showing new errors.pls help
here i am attaching my full code.
here input conditions a=5,b=5,nx=ny=5
clear all
close all
clc
%Solving the Steady State 2D Heat Conduction Equation
%Length of Domain in x and y directions (unit square)
Lx=input("enter value of a");
Ly=input("enter value of b");
%No. of grid points
nx=1+input("enter no.of grids along x direction");
ny=1+input("enter no.of grids along y direction");
%Creating the mesh
x=linspace(0,Lx,nx);
y=linspace(0,Ly,ny);
dx=x(2)-x(1);
dy=abs(y(2)-y(1));
%Initial Conditions
T=298*ones(nx,ny);
K1 = dy^2/(2*((dx)^2 + (dy^2)));
K2 = dx^2/(2*((dx^2) + (dy^2)));
%Boundary Conditions
T(1,:) = 0; %First row or Bottom row of nodes in the matrix
T(end,:) = 0; %Last row or Top row of nodes in the matrix
T(:,1) = 100; %First column or Left side column of nodes in the matrix
T(:,end) = 0; %Last column or Right side column of nodes in the matrix
T_old=T; %Initializing the values for T_old for the first loop
tol=1e-4; %tolerance limit to attain convergence
error=9e9; %initial error to execute while loop
%Code for Solvers
%Jacobi Method
count=1;
while(error>tol)
for i=2:(nx-1)
for j=2:(ny-1)
h =K1*(T_old(i-1,j)+T_old(i+1,j));
v = K2*(T_old(i,j-1)+T_old(i,j+1));
T(i,j) = h+v;
end
end
error=max(abs(T(i,j)-T_old(i,j)));
T_old=T;
count=count+1;
end
% Plotting the Results
figure(1)
[a,b] = contourf(x,y,T);
clabel(a,b); colorbar;
colormap(jet);
xlabel('X Axis');
ylabel('Y Axis');
text = sprintf('2D steady state Heat Conduction n No. of iterations: %d',count);
title(text);
%analytical sol1
a=Lx;
b=Ly;
TA=298*ones(nx,ny);
%Boundary Conditions
TA(1,:) = 0; %First row or Bottom row of nodes in the matrix
TA(end,:) = 0; %Last row or Top row of nodes in the matrix
TA(:,1) = 100; %First column or Left side column of nodes in the matrix
TA(:,end) = 0; %Last column or Right side column of nodes in the matrix
sum=0;
for f=2:(nx-1)
for g=2:(ny-1)
for n=0:10
th=((b-g)*(2*n+1)*pi)/a;
tg=((2*n+1)*pi*f)/a;
tj=((2*n+1)*pi*b)/a;
tr=1/(2*n+1);
sum=sum+(sin(tg)*sinh(th)*tr)/sinh(tj)
end
TA(f,g)= (((4*100)*sum)/pi);
sum=0;
end
end
figure(2)
[a,b] = contourf(x,y,TA);
clabel(a,b); colorbar;
colormap(jet);
xlabel('X Axis');
ylabel('Y Axis');
text = sprintf('2D Transient Heat Conduction using analytical Method n No. of iterations: %d',count);
title(text);
TAA=298*ones(nx,ny);
%analytical sol2
%Boundary Conditions
TAA(1,:) = 0; %First row or Bottom row of nodes in the matrix
TAA(end,:) = 0; %Last row or Top row of nodes in the matrix
TAA(:,1) = 100; %First column or Left side column of nodes in the matrix
TAA(:,end) = 0; %Last column or Right side column of nodes in the matrix
sumA=0;
for fA=2:(nx-1)
for gA=2:(ny-1)
for nA=1:10
thA=(gA*nA*pi)./a;
tgA=(nA*pi*fA)./a;
tjA=(nA* (pi)*b)/a;
trA=1/nA;
sumA=sumA+(sin(tgA)*sinh(thA)*trA*(1-(1^nA)))/sinh(tjA);
end
TAA(fA,gA)= (((2*100)*sumA)/pi);
sumA=0;
end
end
figure(3)
[a,b] = contourf(x,y,TAA);
clabel(a,b); colorbar;
colormap(jet);
xlabel('X Axis');
ylabel('Y Axis');
text = sprintf('2D Transient Heat Conduction using analytical Method n No. of iterations: %d',count);
title(text);
  2 Comments
KSSV
KSSV on 9 Jun 2020
Repalce this line
tjA=(nA* (pi)*b)/a;
with
tjA=(nA* (pi)*b)./a;
By the way the variable a got overwritten.
NIRANJAN PATNANA
NIRANJAN PATNANA on 9 Jun 2020
Operator '*' is not supported for operands of type 'matlab.graphics.chart.primitive.Contour'.
its showing the above error.

Sign in to comment.

Answers (1)

Abhishek Kumar
Abhishek Kumar on 13 Dec 2020
Hi Niranjan, having run your code i see that you are getting the above error, when you try to display variable "b", you find that it is of contour type
>> b
b =
Contour with properties:
LineColor: [0 0 0]
LineStyle: '-'
LineWidth: 0.5000
Fill: on
LevelList: [0 10 20 30 40 50 60 70 80 90 100]
XData: [0 14.3333 28.6667 43]
YData: [0 7.6667 15.3333 23]
ZData: [4×4 double]
Show all properties
and thus you can't use the operator '*' directly with it but you can access the its content by using "b.option", format, you can follow the for more info on contour type:

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!