Solve Heat Conduction for 3D Rectangular Solid

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To solve the heat conduction problem for a 3D rectangular solid, start with the general solution of the Laplace equation, given that Laplace T = 0. Apply the specified boundary conditions: T=0 at x=0 and z=0, zero heat flux at x=a and y=0, y=b, and T=f(x,y) at z=c. This involves using separation of variables or other analytical methods to find T(x,y,z) in the interior. The steady-state nature of the problem implies that the temperature distribution does not change over time. Proper application of the boundary conditions will yield the temperature distribution within the solid.
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Given the 3-D rectangular solid with sides of length a, b and c in the x, y and z direction respectively.
Find T(x,y,z) in the interior of the solid when laplace T = 0
Boundary condition are following conditions:
1) x=0, T=0
2) x=a, dT/dx=0
3) y=0, dT/dy=0
4) y=b, dT/dy=0
5) z=0, T=0
6) z=c, T=f(x,y)
please suggest me, How to solve it?
 
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Well, start with the general solution of the Laplace equation, and apply the boundary conditions. This is a steady-state heat conduction problem in 3 dimensions.
 

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