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Multi-Dimensional Heat Conduction

Multi-Dimensional Heat Conduction

Multi-Dimensional Heat Conduction

(OP)
I have a problem of Multi-Dimensional Heat Conduction as follows:

What is the analytical solution of 3D Steady-State Heat Conduction with no heat generation in Cartesian Co-ordinates subjecting to boundary conditions as:

T(x=0) = 100 K
T(x=2) = 500 k
T(y=0) = 300 K
T(y=1) = 600 K
T(z=0) = 500 K
T(z=1) = 2000 K

Basically, I just the mathematical expression for the above problem because I need to compare the analytical exact solution with numerical methods (coded in MATLAB).

If you can explain on how to solve it, that would be great too. Keep posting relevant links. Thank you.

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