A person with estimated surface area of 20 ft2 and effective

A person with estimated surface area of 20 ft² and effective surface temperature (including clothing) of 84 °F is standing in a room where the walls, ceiling, and floor are all at 68 °F. If the emissivity of the person is 0.8, what is the radiation heat transfer (BTU/hr) from the person to the room surfaces?

Hint 1: Use equation for radiation exchange where total radiation leaving one surface (floor) is intercepted by another surface (walls and ceiling - since all are at same temperature). What is the shape factor in this case?

Hint 2: Use Kirchhoff\'s identity to find absorptivity. Use radiation balance (absorptivity, reflectivity, transmissivity) on a surface to find reflectivity values.

Hint 3: Simplify the third term in the denominator of the radiation exchange equation by realizing for this application that A₁<< A₂ (A₁ is much smaller than A₂).

Solution

net hear radiation transfer q = (T_h⁴ - T_c⁴) A_c

=0.8 given

T_h = 84  ^oF

T_c= 64 ^oF

= tefan-Boltzmann Constant = 1.714 x10^-9 ( Btu/(h ft^2oR⁴) )

A_C= 20 ft²

q = 0.8 *1.714 10^-9*(84⁴ -64⁴ )20 = 0.9052 BTU/hr