heat transfer

S. Yavuzkurt ME 410 - HW #2

1. Using the following differential control volume in cylindrical coordinates and starting with conservation of energy equation derive the heat diffusion equation in cylindrical coordinates:

2 1 1

p

T T T T kr k k q c

r r r z z tr 

 

                  

          

•

2. An electrical wire is dissipating 50W per meter length of electric power. It is insulated as shown in the figure. The diameter of the wire is 1 mm. The thermal conductivity of the insulation is k=0.29 W/(mK). The inside surface of the insulation where it contacts the wire is at Ti=100oC.

qi’’ Insulation

a. Starting from 3-D unsteady heat diffusion equation and making proper assumptions, show that the steady state temperature distribution in the insulation is T=Ti-(qi”Ri)/kln(r/Ri), where qi’’ is the conduction heat transfer rate per unit area from wire to insulation.

b. Calculate the thickness of the insulation required to maintain the outside surface temperature of the insulation at To=65oC.