Simultaneous Conduction and Radiation Energy Transfer
Written by Pierre R Latour PhD, PE, Chemical Process Control Engineer
Radiant energy can transfer from a colder to a warmer radiator.
Abstract: The rigorous model of simultaneous thermal and radiant energy transfer proves energy transfer by radiation can flow from a colder radiator to a warmer one, heating the warmer one further. It explains and quantifies how dissimilar walls in a room can have different steady-state temperatures.
Only the general laws of thermal and radiant energy transfer and the First Law of Thermodynamics, conservation of energy, are employed. [Editor’s note: since publication PSI has negatively reviewed this post*]
Introduction: Many claim radiant energy can only transfer from a hot radiator to a colder one. Otherwise the Second Law of Thermodynamics would be violated.
While this is true for thermal energy transfer by conduction or convection, it is not true for radiant energy transfer. How does a cold radiator transfer energy to warmer surroundings? It depends on absorptivity, emissivity and intensity differences at each radiating surface and on the presence of simultaneous conduction. We will show why temperatures of dissimilar room walls at steadystate are not be equal.
Confusion: Many err claiming radiant energy cannot transfer from the colder radiator to the warmer one, heating it further, because they incorrectly assume the driving force (at a distance) is temperature difference, which is true for conduction/convection through a matter field, while the driving forces for radiant energy transfer between radiators are intensity differences at radiator surfaces through a radiation field.
As proved by Martin Hertzberg15 . Radiant energy does not transfer due to a temperature difference at a distance. Temperature is a point property of matter proportional to the kinetic energy of its atoms and molecules. The transfer directions switch at T = Ts, when Qc = Qr.
Radiation direction is always opposite to conduction direction according to the First Law. So when surroundings are Ts, a room wall at T can be greater or less than Ts, depending on its radiating properties compared to radiating properties of surroundings. Rate in by conduction = rate out by radiation = a nonzero constant at different temperatures, unless Kirchhoff’s Law applies.
When it does the temperatures are equal and no energy transfers between the radiator and surroundings either way. Atmosphere Since atmospheric temperature decreases with altitude, why doesn’t energy transfer up by conduction, equalizing T above?
Because thermal energy indicated by T, is kinetic energy of molecular motion and it must decrease as potential energy increases with altitude in Earth’s gravitational field to maintain fixed total energy of each m3 of gas.
Another energy mechanism is involved. Some popular explanations of Green House Gas Theory say radiant energy transfers from cold atmospheric CO2 down to warmer surface, which absorbs it, warming it further, i. e. global warming. Actually surface partly radiates directly to space because atmosphere has some transmissivity and the rest is absorbed by the atmosphere, including trace 400 ppm CO2, and then reemitted to space.
A recent paper2 derived rigorous equations for the coupled atmosphere and surface temperatures. Only system properties are needed, no empiricism. When one warming and three cooling mechanisms are included in the whole system, the net effect of CO2 on temperature is small and likely < 0.
The remaining question to quantify the effect of CO2 changes on temperatures is: how much does CO2 affect the atmosphere’s radiating properties: absorptivity and emissivity? Assuming2 a 1% increase in the atmosphere’s radiating properties, perhaps due to increased CO2, surface temperature change is – 0.76C and atmosphere change is -0.39C.
The net effect is slight cooling. Applying (3) we see Qr > 0 for transfer from surface up to and absorbed by atmosphere, even when Ts > Ta. That is because there is no conduction involved, as proved above. The presence of radiating CO2 increases atmosphere emissivity, a resistance to radiant energy transfer. CO2 is not an energy blocker or trapper; it is an absorber and transmitter.
No radiant energy transfers from cold atmosphere with CO2 down to warm surface, warming the surface. A shiny white car has greater reflectivity than rough black car. So it has lower absorptivity and emissivity. Since white absorbs less radiant energy than black, it emits less, causing it to be cooler.
Conclusion. According to the First Law of Thermodynamics, radiant energy transfers from a cold to a warmer radiator in the presence of energy transfer by conduction the other way. The temperature difference between radiators at steady-state depends on their radiating properties: absorptivity and emissivity. This paper is not a mere theory because it is based on well-known laws of physics and mathematics, confirmed by observation.
So the Hertzberg general rate law disproves the notion radiant energy transfer only flows from the hot radiator to the cold one. That is only true if one radiator is sufficiently hotter than the other or both radiators obey Kirchhoff’s Law, emissivity = absorptivity. That is not easy to guarantee. The Earth’s atmosphere has several energy transfer mechanisms within it and hence does not obey Kirchhoff’s Law.
Read the full paper with all equations at:
*This post was peer-reviewed by PSI and the equations used refuted. Read more at: