1D Heat equation in Matlab with heat Flux at one side

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Steffen B. 2022-6-20

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https://ww2.mathworks.cn/matlabcentral/answers/1743940-1d-heat-equation-in-matlab-with-heat-flux-at-one-side

编辑： Torsten 2022-6-21

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I’m solving the 1D heat equation with Matlab pdepe function.

The geometry is a steel rod of 1m length, which has a constant temperature on the right side and a constant flux on the other side.

I’m struggeling a little bit with specifying the value of p and q.

Here is the code I use:

function [c,f,s] = heatequation(x,t,u,dudx)
rho=7850; % density
cp=420;   % heat capacity
lambda=40;% conductivity
c = rho*cp;
f = lambda*dudx;
s = 0;
end
function u0 = ic(x)
Tini=300; % initial temperature at t= 0 s
u0 = Tini;
end
function [pl,ql,pr,qr] = bc(xl,ul,xr,ur,t)
pl = 0;      
ql = 10;     % Flux at the left end = 10 W/m2
pr = ur-300; % Temperature at the rigth end = 300 K
qr = 0 
end
m = 0;
sol = pdepe(m,@heatequation,@ic,@bc,x,t);

I'm not sure if I wrote the BC's correct? The notation with p and q is still confusing

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Torsten 2022-6-20

编辑：Torsten 2022-6-21

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@Steffen B.

If your boundary condition at the left end is

-lambda*dT/dx = 10

, then

pl = 10, ql = 1

Steffen B. 2022-6-20

编辑：Steffen B. 2022-6-20

在 MATLAB Online 中打开

@Torsten thanks for your fast answer. You are rigth, I mixed someting up in the BC function. Now it's working just fine

function [pl,ql,pr,qr] = bc(xl,ul,xr,ur,t)
pl = 10;     % Flux at the left end = 10 W/m2   
ql = 1;      
pr = ur-300; % Temperature at the rigth end = 300 K
qr = 0 
end