create a steady state heat transfer with conduction on the left side of the wall and convection on all the other sides in matlab

To simulate a steady-state heat transfer with conduction on the left side of the wall and convection on all the other sides in MATLAB, you can use the pdepe function.

First, define the geometry and initial conditions. Let's assume a rectangular wall with dimensions L and W:

main.m
L = 1; % length of the wall
W = 1; % width of the wall
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Define the thermal properties of the wall, such as thermal conductivity k and heat transfer coefficient h:

main.m
k = 1; % thermal conductivity
h = 10; % heat transfer coefficient
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Next, define the boundary conditions. In this case, the left side of the wall has a fixed temperature T_left, while the other sides have a convection boundary condition:

main.m
T_left = 100; % temperature on the left side of the wall
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Define the heat equation as a function:

main.m
function [c, f, s] = heat_equation(x, t, u, DuDx)
    c = 1 / (k * DuDx);
    f = DuDx;
    s = 0;
end
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Solve the heat equation using pdepe:

main.m
x = linspace(0, L, 100); % spatial discretization
t = linspace(0, 100, 1000); % time discretization

m = 0; % number of equations
n = 2; % number of spatial derivatives

sol = pdepe(m, @heat_equation, @(x) T_left, @convection_bc, x, t);

T = sol(:,:,1); % temperature distribution
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The above code assumes that the convection boundary condition function convection_bc is defined separately. You can define it according to your specific problem.