Chapter 13, Problem 13.107P

A row of regularly spaced, cylindrical healing elements (1) is used to cure a surface coating that is applied to a large panel (2) positioned below the elements. A second large panel (3), whose top surface is well insulated, is positioned above the elements. The elements are black and maintained at $T_1=600\text{K}$ , while the panel has an emissivity of ${\epsilon }_2=0.5$ and is maintained at $T_2=400\text{K}$ . The cavity is tilled with a nonparticipating gas and convection heat transfer occurs a surfaces 1 and 2, with ${\bar{h}}_1=10{\text{W/m}}^2\cdot \text{K}$ and ${\bar{h}}_2=2{\text{W/m}}^2\cdot \text{K}$ . (Convection at the Insulated panel may be neglected.)

(a) Evaluate the mean gas temperature, T_m.
(b) What is the rate per Unit axial length at which electrical energy must be supplied to each element to maintain its prescribed temperature?
(c) What is the rate of heat transfer to a portion of the coated panel that is 1 m wide by 1 m long?