In the metal processing industry, heat treatment of metals is commonly done using electrically heated draw batch furnaces. Consider a furnace that is situated in a room with surrounding air temperature of 30°C and an average convection heat transfer coefficient of 12?W/m2•K. The furnace front is made of a steel plate with thickness of 20 mm and a thermal conductivity of 25?W/m•K. The outer furnace front surface has an emissivity of 0.23, and the inside surface is subjected to a heat flux of 8?kW/m2. Determine the outside surface temperature of the furnace front.

Question

Answer 1

A draw batch furnace front is subjected to uniform heat flux on the inside surface, while the outside surface is subjected to convection and radiation heat transfer. The outside surface temperature is to be determined.

Assumptions 1 Heat conduction is steady. 2 One dimensional heat conduction across the furnace front thickness. 3 Uniform heat flux on inside surface.

Properties Emissivity and convective heat transfer coefficient are given to be 0.23 and 12 W/m2?K, respectively.

Analysis The uniform heat flux subjected on the inside surface is equal to the sum of heat fluxes transferred by convection and radiation on the outside surface



Solving for the outer surface temperature yields



Solved by EES Software. Solutions can be verified by copying-and-pasting the following lines on a blank EES screen.



h=12 [W/m^2-K]

q_dot_0=8000 [W/m^2]

T_surr=303 [K]

epsilon=0.23

sigma=5.67e-8 [W/m^2-K^4]

q_dot_0=h*(T_o-T_surr)+epsilon*sigma#*(T_o^4-T_surr^4)



Discussion By insulating the furnace front, heat loss from the outer surface can be reduced..