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.
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
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
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