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

Net Radiation Loss Rate

If an hot object is radiating energy to its cooler surroundings,then the net radiation heat loss rate can be expressed as

q = ? ? (T_h⁴ - T_c⁴) A_c   

where

q = heat transfer per unit time (W)

? = 5.6703 10^-8 (W/m²K⁴) - The Stefan-Boltzmann Constant

T_h= hot body absolute temperature (K)

T_c= cold surroundings absolute temperature (K)

A_c = area of the object (m²)

Dear student, please keep in mind that you should use absolute values of temperature for both temperatures involved, that is in kelvin scale which is a temperature scale relative to absolute zero; otherwise this formula will not work. With that in mind let us substitute of all the known data into this equation.

, from here we get that

from where

from where

,

but where the first term stands for the area of the flat top and the second term corresponds to the area of the lateral surface of the cylinder. So we get:

from where

. Notice I have used only si units for the radius of the cylinder, that is meters. Keep in mind that the radius is half the diameter, so .

Finally then

from where

And this is the net rate of heat loss from your head on a chilly 9C day.

I hope this can be of great help for you Dear student

Best regards

Jose

End