In the present discussion of the 2nd Law of Thermodynamics let us go back to this post from 2011 exposing the 19th century battle between 1-way transfer (Pictet) vs 2-way transfer (Prevost) of heat energy by radiation playing a central role in climate science today.
In 1-way transfer a warm body heats a colder body in accordance with the 2nd Law.
In 2-way heat transfer both warm and cold bodies are viewed to heat each other, but the warm heats more and so there is a net transfer of heat energy from warm to cold. But a cold body heating a warm body violates the 2nd Law of thermodynamics, and so there is something fishy here.
Yet the basic mathematical model of radiative heat transfer in the form of Schwarzschild's equation involve 2-way transfer of heat energy, in apparent violation of the 2nd Law.
I have discussed this situation at length on this blog with tags such as 2nd law of thermodynamics and radiative heat transfer with more on Computational Blackbody Radiation.
If you worry about the 2nd Law, you can ask yourself how 2-way radiative heat transfer is physically possible, when it appears to violate the 2nd Law? What is false here: 2nd Law or 2-way heat transfer?
What is your verdict?
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2 AI sites state that the 2nd law of thermodynamics applies at every point of heat transfer. Thus heat transfer can only be in one direction (ie from hot to cold). One can go further for example heat balances around a furnace. It can be measured that there is little or no heat loss through the insulated surface and that the insulated walls on the inside have a temperature close to the source of heat (eg a flame) which then by the S-B equation results in little or relatively no heat transfer. The heat is mainly transferred to the load or out in the exhaust. One factor missing in all your equations is an efficiency factor as nothing in practical life is a an idealised black body. In a furnace the emissivity of the load changes with temperature but is usually well known. But flames can have a large range of emissivities. I have made adjustment of natural gas flames from about 0.45 (mainly due to the water vapour) upto about 0.8 by causing the CH4 to crack to form carbon. As an engineer I am always happier to see in an equation a constant which represents an efficiency factor eg dq=UdA(t1-t2) where U is the overall coefficient of heat transfer (by conduction).
SvaraRadera