Heat propagation in radiating surface

[Jairo Amaral]

I would like to know how heat would flow in a material being struck by sunlight in vacuum. The usual examples of Fourier heat equation always uses boundaries with fixed temperature or under convection. How do I calculate this when the surface is absorbing and emitting radiation according to Stephan-Boltzmann law?

I'm considering a 1-dimensional material in vacuum, with one ending being lit, and the other being insulated. Is the analytical solution too hard to be pratically solved? If yes, do you know some source for computing this numerically? If no, do you know some source that shows this solution?

This problem seems simple, but I've tried internet, teachers and books for some days, and I've still found nothing.

Thanks.

 

[Loren Booda]

A great question. What first comes to mind is that for a material of thickness d>>lambda_sunlight and relatively finite time, the heat of sunlight (for ultraviolet or infrared divergence) may not need strict representation in an eigenvalue problem, and gives a constant specific heat in this visual range. If d~lambda_sunlight, then I would try an approximation technique, like using Fourier analysis on either the Raleigh-Jeans approximation or a form of Wien's law.

 

[Loren Booda]

Sorry if I made the problem too complicated. It should be easier. I'll try to figure it out.

 

[alvaros]

Jairo Amaral:
I would like to know how heat would flow in a material being struck by sunlight in vacuum.

It seems simple.

I think the problem is knowing how the radiated power is distributed in function of the angle of emission. I don't know the answer.
And you have to know the temperature of the "universe" ( where there is no sun ).
And you have to know the shape of the material.
Once you know all this, just make a big integral.


If the material is very near to the sun ( the material sees the sun at all angles ) the temperature will be the same.

 

[Loren Booda]

Jairo,

q=-k grad (T)=-k grad (W/s)^1/4

where q is the heat flux per unit time, k is the thermal conductivity, T is temperature, W is the radiant emittance of a blackbody, and the Stefan-Boltzmann constant s=5.67 x 10^-12 watts cm^-2 deg^-4.

It's a start. You may want to consider this for a unit area and flat surface (your one dimensional simplification).

The internet has examples of "sunlight striking Earth" using the "Stefan-Boltzmann law" and the "Heat Equation" or similar combinations of terms.

Again, please forgive my poor attempt.