Find the steady-state distribution of temperature in a cube of side

  

Find the steady-state distribution of temperature in a cube of side 10 if the temperature is 100 degrees on the face z = 0 and 0 degrees on the other five faces.
Hint: Seperate Laplace’s equation in three dimensions in rectangular coordinates, and follow the method of “Laplace equation ; steady-state temperature in a rectangular plate” (section 2)
You will want to expand 100 in the double Fourier series:


 

The coeffiecients are determined by using the orthogonality of the functions over the square, that is,

unless n=p, m=q.

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