Steady state temp. distribution

AI Thread Summary
The discussion revolves around a non-homogeneous 2D heat conduction problem, with confusion about whether the heat flow is truly 2D or can be simplified to 1D. Participants question the necessity of defining temperature as a function of both x and y, suggesting that it may only depend on x. There is a proposal to eliminate the non-homogeneous term by introducing a new variable, Q. Boundary conditions are also discussed, with a proposed solution being evaluated for its compliance with these conditions. The conversation highlights the complexities of solving heat conduction problems and the importance of correctly identifying dimensions and boundary conditions.
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Homework Statement


upload_2016-1-20_18-10-38.png


Homework Equations


ıt is nonhomog type ,2D heat conduction problem

The Attempt at a Solution


I don't understant To parts so I couldn't attemp a solution.
 
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What makes you think it is a 2D problem?
 
Shouldn't we found T(x,y)
and for upper and lower parts should I write as afuction of x To(x) and then define new temperature variable Q=T-To to eliminate nonhomog on the left side
 
From the figure, it looks to me like the heat flow is 1D from the left side to the right side. T = T(x).
 
What about the upper and lower boundaries?
Bc should be x=0 t=to
X=b/2 t=to
Y=0 dt/dy =0
Y=b t= to(x)
 
Does the following satisfy all the boundary conditions: ##T=T_0\left(1-\frac{x}{a}\right)##?
 
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