When Does Heat Transfer from a Colder Body to a Warmer One?
The answer is never. While radiant heat always transfers from a warmer to a cooler body, when cooler body is a good radiator, its emissivity is large and has little effect on radiant heat transfer for all temperature differences
Proof. Heat transfers between materials by three mechanisms: conduction, convection and radiation.
The rate laws are:
Conduction Q = Cp (Tw – Tc), Q is rate of heat transfer from w to c by conduction. Tw is temperature of warmer body, Tc is temperature of colder body, and Cp > 0 is heat capacity of material between w and c. By definition, Tw > Tc, so Q > 0.
Convection Q = Cv (Tw – Tc), Q is rate of heat transfer from w to c by convection. Tw is temperature of warmer body, Tc is temperature of colder body, and Cv > 0 is convection heat transfer coefficient of material between w and c. By definition, Tw > Tc, so Q > 0.
Radiation Q = σ Aw (Tw4 – Tc4) / [1/εw + Aw/Ac (1/εc – 1)]. Aw > 0 is radiating area of Tw, and Ac > 0 is radiating area of Tc. Denominator D = [1/εw + Aw/Ac (1/εc – 1)]. rate of radiant energy transfer between two dissimilar radiators – Google Search
If D < 0, then Q < 0 and heat flows from cooler Tc to warmer Tw. This cannot happen in nature because both εw and εc > 0, D > 0 and Q > 0.
However, as εc approaches 1, a good radiator, (1/εc – 1) approaches 0 and D approaches 1/εw. In that case Q approaches σ εw Aw (Tw4 – Tc4). This means the emissivity of c has little effect on Q.
In that situation raising atmospheric CO2 at 400 to 800 ppmv does not have much effect on Q and hence Earth’s surface radiating temperature, Tw.
If w is a poor radiator too, εw also approaches 0, and Q approaches 0 even when Tw > Tc. This means when both atmosphere and surface are poor radiators with low emissivity’s, Q is very small, no matter what the emissivity’s and Tw – Tc are.
This radiant heat transfer phenomenon was not properly included in global warming/climate change hoax analyses of 1995-2020.
Some parts of Earth atmosphere have low emissivity: N2 + O2 = 0, CO2 = 0.08. Surface is higher: water = 0.96, snow = 0.80-0.90, asphalt = 0.88. emissivity of co2 and h2o – Google Search emissivity of co2 and h2o – Google Search
Tom
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Like going to Neptune to get warmer.
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