Skin temperature increase due to radiation absorption

[fog37]

Hello,

I am trying to figure out how much the human skin temperature would increase when the skin is illuminated by radiation of a certain intensity (W/m^2). We can assume that the skin has an emissivity and absorptivity both equal to 1. For instance, imagine the skin illuminated by the sun (I= 1000W/m^2) or by another radiation source..
We know the initial temperature of the skin and the intensity of the incident radiation.

What equation would I use?

Thanks!

 

[256bits]

What equation would I use?

You have poked on the Intermediate Level.
Are you familiar with the Stefan-Boltzmann law?

The Stefan–Boltzmann law states that the power emitted per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature

P_rad = σ T⁴

 

[OmCheeto]

Hello,

I am trying to figure out how much the human skin temperature would increase when the skin is illuminated by radiation of a certain intensity (W/m^2). We can assume that the skin has an emissivity and absorptivity both equal to 1. For instance, imagine the skin illuminated by the sun (I= 1000W/m^2) or by another radiation source..
We know the initial temperature of the skin and the intensity of the incident radiation.

What equation would I use?

Thanks!

Interesting question.
I worked out a similar problem for a black rock about 6 months ago. Unfortunately, I can't remember how I did it, nor do I know whether or not my answer was correct.

I would recommend looking at the wiki entry on "Black-body radiation", subsection "Human body emission".
It may not give you the answer, but it has a couple of equations that will get you started:

P_net = P_emit - P_absorb
and
P_net = Aσε(T⁴ - T₀⁴)

A is body surface area
T is body surface temperature
ε is body emissivity
T₀ is the ambient temperature
σ is the Stefan–Boltzmann constant​

Of course, your problem is a bit more complicated, as rocks don't sweat.

 

[hilbert2]

The heat that the skin absorbs is continuously being transferred away with the blood flow through the capillary veins in the skin, so this can't be calculated as a simple radiative transfer problem.