A black sphere (2.5-cm in diameter) is placed in a large infrared heating oven whose walls are maintained at 370°C. The temperature of the air in the oven is 90°C and the heat-transfer coefficient for convection between the surface of the sphere and the air is 30 W/(m2 K). Estimate the net rate of heat flow to the sphere when its surface temperature is 35°C.

Question

GIVEN

• A black sphere in a large infrared heating oven

• Sphere diameter (D) = 2.5 cm = 0.025 m

• Oven wall temperature (T2) = 370°C = 643 K

• Oven air temperature (T?) = 90°C = 363 K

• Convective heat transfer coefficient (hc) = 30 W/(m2 K)

• Sphere surface temperature (T1) = 35°C = 308 K

FIND

• The net rate of heat flow to the sphere (qtotal)

ASSUMPTIONS

• The oven walls are diffuse

SKETCH



PROPERTIES AND CONSTANTS

the Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/m2K4

Answer 1

Since the sphere is black:



Since A1 cannot see itself, F11 = 0



Solving for J2







since ?2 = (1 – ?2), this simplifies to



Since A2 is very large compared to



The total rate of heat transfer is the sum of the convective and radiative heat transfer