contestada

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!

Respuesta :

MissPhiladelphia
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

The net rate of the heat loss when the radiation from the head is a major source of heat loss from the human body will be 25.1W.

How to calculate the heat loss?

It should be noted that the net radiation heat loss rate can be expressed as:

q = (Th⁴ - Tc⁴) Ac

where

q = heat transfer per unit time

Therefore, the values will be slotted and this will be:

q = 0.95 × 5.67 × (10^8W/m²k⁴) × 309.15k⁴ - 282.15k⁴

q = 150.66W/m²

Note that Ac = 0.166

Therefore, the value will be:

q = (Th⁴ - Tc⁴) Ac

= 150.66 × 0.166

= 25.1W

Learn more about radiation on:

https://brainly.com/question/24469662

#SPJ5