# Temperature Profile

1. Jan 17, 2008

### ZeroScope

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,
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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2. Jan 17, 2008

### ZeroScope

Its just accured to me that as the question states that "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.

Does this just mean the the profile is : T(x,0) = kx? (proportional to x)