Determine the temperature profile in a long thin plate 30 units wide and kept at zero temperature at three sides. The remaining short edge is heated in such a way that a temperature profile falling off, linearly on either side of the centre of the edge, is produced. To establish the two-dimensional temperature profile,(adsbygoogle = window.adsbygoogle || []).push({});

T(x,y),

i) sketch the situation,

ii) decide which type of differential equation describes the problem,

iii) rephrase the boundary conditions given in the description as formulae,

This is half a question for an exam that i am taking tomorrow. I can solve everything else about the question but there is one thing that i cant get my head around.

When deciding boundary conditions all are equal to zero apart from the heated edge.

Now i know in order to find the BC for the heated edge that the gradient of the temperature profile must be calculated. (this is a triangle on a T, x graph).

Obviously i would get two gradients, one for the positive slope and one for the negative slope. Do i add these together? If so then i get 2t for the T(x,0) edge.

For more insight into what i mean by the graph i have attached a paint document showing it.

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# Homework Help: Temperature Profile

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