Question

Radiation from the head is a major source of heat loss from the human body. Model a head as a 21-cm-diameter, 20-cm-tall cylinder with a flat top.
If the body's surface temperature is 36?C , what is the net rate of heat loss on a chilly 9?C day? All skin, regardless of color, is effectively black in the infrared where the radiation occurs, so use an emissivity of 0.95.

I have worked it through three times with other written solutions however i cannot arrive at the correct answer. A final answer as well as a solution would be appreciated! Thanks!

Answer 1

We have the following assumptions:
The temperature of the surroundings remains constant.
The entire surface area of head emits radiation.

From the problem, we have the given values:
emissivity = 0.95
T2 = 36 degrees C
T1 = 9 degrees C

Solving for the area:
A = πD² + πDh = π(21)² + π(21)(20) = 2709.91 cm² = 0.2710 m²

Using the heat transfer equation for radiation:
q = εAσ(T₂⁴ - T₁⁴)
q = 0.95 (0.2710)(5.67 x 10-8)[(36+273)⁴-(9+273)⁴]
q = 3.9 x 10^9 W