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Heat Flow

A uniform thin metal plate extends over the first quadrant of the , plane. Assume that the temperature of the plate depends only on and ; specifically that: .

is a coefficient whose units are . has been introduced solely to make the units on both sides of the equation consistent.

Now let .

Problem 20:

On the grid, sketch the isotherms (or contour curves) for . (What types of curves are these?)

Problem 21:

On the basis of the orthogonality of the directions of the isotherms and the heat flux, show the direction of the heat flux vector at each of the following points: , , .

Problem 22:

Assuming , use equations (1.1) and (2.1) to find the heat flux vectors at points , , and . Do the results agree (in orientation and direction) with the vectors you drew in part b)?

Answer

Problem 23:

What is the magnitude of the heat flux vector at C?

Answer

 
 
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