Heat treatment of metals is commonly done using electrically heated draw batch furnaces. Consider a furnace that is situated in a room with a surrounding air temperature of 30°C and an average convection heat transfer coefficient of 15?W/m2•K. The outer furnace front surface has an emissivity of 0.7, and the inside surface is subjected to a heat flux of 5?kW/m2. To ensure safety and avoid thermal burns to people working around the furnace, the outer front surface of the furnace should be kept below 50°C. Based on the information given about the furnace, does the furnace front surface require insulation to prevent thermal burns?

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 whether it is below 50°C or not.

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 0.7 and 15 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=15 [W/m^2-K]

q_dot_0=5000 [W/m^2]

T_surr=303 [K]

epsilon=0.7

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 Yes, insulation is required on the furnace front surface to avoid thermal burn upon contact with skin.