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Thermoish diffusion/wave equation  metal plate and temperature difference 
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#1
Jul3112, 11:33 AM

P: 60

1. The problem statement, all variables and given/known data
The edges of a thin plate are held at the temperature described below. Determine the steadystate temperature distribution in the plate. Assume the large flat surfaces to be insulated. If the plate is lying along the xy plane, then one corner would be at the origin. The height of the plate would be 1m along the yaxis and the length would be 2m along the xaxis. The edge along the yaxis is being held at 0 C. The edge along the xaxis is being held at 0 C. The edge parallel to the xaxis is being held at 0 C. The edge parallel to the yaxis is being held at 50sin(pi*y) C. 2. Relevant equations So I'm assuming this question is actually just a diffusion equation or a wave equation, because that's what the rest of our homework was on. Alpha^{2}u_{xx}=u_{t} and u(x,t)=X(x)T(t)=(C_{1}coskx+C_{2}sinkx)e^{K2alpha2t}+C_{3}+C_{4}x 3. The attempt at a solution So I tried to solve this like the wave equations and it seems to just be blowing out of proportion and not making sense... Also... I think we need to consider a thrid position variable here, we need x,y AND t. I don';t know how to do this at all :( 


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