Heat conduction
Homework #2
M. Mosharaf
1- The cross section of a long prism is a right angle isosceles triangle of side L, shown below as Case A.
Assuming the hypotenuse is insulated, determine the temperature T at the midpoint of the hypotenuse.
Repeat the problem for Case B.
Case B
Case A
2- Heat is generated in a rectangular plate of size 3𝐿 × 𝐻 at a uniform volumetric rate of 𝑞 ′′′ . The surface
at (0,y) is maintained at 𝑇0 . Along surface (3L,y) the plate exchanges heat by convection. The heat transfer
coefficient is h and the ambient temperature is 𝑇∞ . Surface (x,H) is divided into three equal segments which
are maintained at uniform temperatures 𝑇1 , 𝑇2 , and 𝑇3 respectively. Surface (x,0) is insulated. Determine
the two-dimensional steady state temperature distribution.
3- A semi-infinite plate of thickness 2L moves through a furnace with velocity 𝑈 and leaves at
temperature 𝑇0 . The plate is cooled outside the furnace by convection. The heat transfer coefficient is h and
the ambient temperature is T∞ . Determine the two-dimensional temperature distribution in the plate.
1