: A flat body of thickness h and thermal conductivity λ has the shape of a right angled triangle whose short sides are of length l. The plane temperature profile of this body is given as ϑ(x, y) = ϑ0...

: A flat body of thickness h and thermal conductivity λ has the shape of a right angled triangle whose short sides are of length l. The plane temperature profile of this body is given as ϑ(x, y) = ϑ0 + ϑ1 (y/l)2 − (x/l)2; 0 ≤ x ≤ l, 0 ≤ y ≤ x.

 a) Where do the highest and lowest temperatures ϑmax and ϑmin appear? How are they related to the given temperatures ϑ0 and ϑ1? 0 <><>

 b) The values for grad ϑ and the vector q˙ for the heat flux have to be calculated. At which point is |q˙| largest?

c) Calculate the heat flow through the three boundary surfaces indicated by y = 0, x = l and y = x, and show that as much heat flows into the triangle as flows out.