Heat propagation in radiating surface

In summary, the conversation is about the flow of heat in a material that is struck by sunlight in a vacuum. The person is looking for a solution to this problem which involves calculating the heat when the material is absorbing and emitting radiation according to the Stephan-Boltzmann law. They are also considering using an analytical or numerical solution and have been searching for sources for a few days without success. Suggestions are made to use Fourier analysis and the Raleigh-Jeans approximation or Wien's law. The conversation also touches on factors such as the thickness of the material, the radiated power distribution, and the temperature of the "universe." Finally, the conversation concludes with a mention of finding examples on the internet using the Stefan-Boltzmann law
  • #1
Jairo Amaral
8
1
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.
 
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  • #2
A great question. What first comes to mind is that for a material of thickness d>>lambdasunlight 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~lambdasunlight, then I would try an approximation technique, like using Fourier analysis on either the Raleigh-Jeans approximation or a form of Wien's law.
 
  • #3
Sorry if I made the problem too complicated. It should be easier. I'll try to figure it out.
 
  • #4
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.
 
  • #5
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.
 
Last edited:

What is heat propagation in radiating surface?

Heat propagation in radiating surface is the transfer of thermal energy from one surface to another through the emission, absorption, and transmission of electromagnetic radiation.

How does heat propagate in radiating surfaces?

Heat propagates in radiating surfaces through the process of radiation, where thermal energy is emitted in the form of electromagnetic waves from a source surface and absorbed by a receiving surface.

What factors affect heat propagation in radiating surfaces?

The factors that affect heat propagation in radiating surfaces include the temperature difference between the emitting and receiving surfaces, the emissivity of the surfaces, the distance between the surfaces, and the properties of the medium between the surfaces.

What is the difference between radiative heat transfer and conductive heat transfer?

Radiative heat transfer occurs through the emission and absorption of electromagnetic radiation, while conductive heat transfer occurs through direct physical contact between two surfaces. Radiative heat transfer can occur even in a vacuum, while conductive heat transfer requires a medium.

Why is heat propagation in radiating surfaces important in engineering and science?

Understanding heat propagation in radiating surfaces is important in designing and optimizing many engineering systems, such as thermal insulation, solar energy systems, and electronic devices. It is also relevant in fields such as astrophysics and climate science.

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