A warmed can (4-1/2 inches tall x 2-1/2 inches diameter) is placed into the free

Question

A warmed can (4-1/2 inches tall x 2-1/2 inches diameter) is placed into the freezer compartment of a refrigerator. The can is assumed to radiate heat from all its surfaces to the enclosure (even though it may be set down on its end). The can is at 65 degrees F while the freezer walls are at 30 degrees F. Determine the net heat exchanged by radiation under these conditions, if the surfaces of the can and of the freezer behave like black bodies. Take the freezer - wall area to be very large.

a) q1-2 = 29.8 BTU/hr
b) q1-2 = 100 BTU/hr
c) q1-2 = 9.86 BTU/hr
d) q1-2 = 986 BTU/hr

Explanation / Answer

Since the freezer walls area is very large compared to the can's, the view factor will be unity.
Now, for black bodies radiation heat transfer Q = σA(T14 - T24) where

σ = Stefan Boltzman constant = 0.119*10-10 BTU/hr in2R4.

A= Area of heat transfer. T1 and T2 are temperatures of the two bodies.

Here, A = Total surface area of can = π/4*((2.5)^2)*4.5 + 2*(π/4*(2.5)^2) = 31.89 sq inches.

Hence, by putting values Q = 0.119*10-10 * 31.89 *  ((65+460)4 - (30+460)4) = 6.95 BTU/hr

 

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