Dear Anatoly:
I think the general answer is : it depends on the object.
It depends on how you treat the analyzed object/body. If the object is punctual, then the answer certainly is No.
but if the object is a big compound body (composed of protons, neutrons, atoms and molecules which reacts with one another to produce heat), certainly it is possible.
For example, the Sun. This macroscopic body can be approximated to a Black Body for terms of practice in Solar Thermal (and Photovoltaic) Engineering problems. The Sun is in a physical state of Plasma, and it is composed by p+, n0 and electrons. And even though it can be considered as homogeneous at a macroscopic scale. However, if you go to tiny scales, you'll see it is composed by regions of different density, temperature, pressure, etc ...
Because of this, the density of nuclear reactions can vary from region to region, so the rate of energy generation vary too, as well as the temperature.
Then, because the Thermal Radiation generated by the Nuclear Reactions in the Sun is a Spherical Electromagnetic Wave, part of these emitted waves (emitted by the atomic transitions between states and thermonuclear reactions) can be absorbed by other regions in the own Sun. So in this case, Yes, then Sun can and will, absorbe its own emitted Thermal Radiation.
But if you think in a model of a puntual body, e.g. a Black Hole. Black Holes are punctual objects to Thermodynamics regards. Then all the Black Body Radiation (called Hawking Radiation in this particular case) is just emitted radially outwards in all directions, and is never absorbed again by the BH.
So, in Conclusion. I think it much depends on how many considerations you want to apply to your problem. Whether you want to view a given body as a homogeneous and being in total thermal equilibrium, or you want to include further considerations to your analysis, e.g. constraining the body/object to have stratifications in Temperature and Energy Density, etc.
Hope this helps for the discussion :)
Best Regards !
BTW, If you can use, or have to use the Stefan-Boltzmann Law for Thermal Radiation :
Qrad = eps*AsupF12*(T4sup-T4surroundings)
The fraction of the thermal energy radiated by a surface/body and absorbed by the same surface/body is considered in this expression, by the term F12, which is called the "View Factor", this can be a simple number, or an expression in terms of geometrical parameters. But at the end, this F factor results in a fraction, a number between 0 and 1, which represents somehow the fraction of a given radiated heat energy "viewed" by a given surface of the body.
Where F12 represent the heat transfer energy by radiation emited by surface "1" and "viewed" by surface "2".
If you go to a Heat Transfer Handbook like: "HEAT TRANSFER HANDBOOK. ADRIAN BEJAN and ALLAN D. KRAUS. WILEY. JOHN WILEY & SONS, INC." you will find tables with the View Factors for different geometries and cases.
Regards !
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