# A Discussion of the Equations of Transfer

Written by Joseph E Postma

I was having an email discussion with an old professor of mine (from undergad) about the fraud of the radiative greenhouse effect who has himself implied doubt about the greenhouse effect.  Actually the proff is Dr. Essex who wrote the book “Taken by Storm“.  He suggested that I look at the “equations of transfer” in regard to the problem, which of course I have already done extensively and am quite familiar with.  I will post the reply here since it may help some people:

“Are you still using Haberman’s “Applied Partial Differential Equations with Fourier Series and Boundary Value Problems”?  We used that when I took your class in 2000.

For the flow of heat in matter we end with the diffusion equation as a function of space and time.  If there is a heat source, then Q (heat) gets tacked on to the equation and Q can also be a function of space and time.  The scenario with the radiative greenhouse effect is that you have matter, the ground surface, where there is basically no internal heat generation, but you do have Q at the surface boundary, i.e. at the very first element of the surface, due to sunlight.

Q of course is heat.  Making this simpler than the Sun “going around” the surface location, we can just use constant values to inspect the qualitative and some quantitative features of the solution to this type of problem.  To do that we must use and understand what Q is since whatever is governing Q is basically setting the boundary conditions of the problem, and the behaviour of these solutions are typically largely determined by the boundary conditions.

Q, being heat, is not simply the energy from sunlight, but is given from radiant transfer by a difference of flux values, which are of course proportional to temperature.  For example in a plane-parallel model with emissivities and absorptivities all unity, then Q = Flux_hot – Flux_cool = sigma(T_hot^4 – T_cool^4), and the positive Q means that the heat is flowing to the cooler object, which would cause the cooler object to increase in temperature until Q = 0.  It is simpler to use local flux when dealing with sunlight so that you don’t need to think about how the surface flux of the Sun is diluted by distance, but of course that is there.

So radiant Q is a flow given by a difference of local fluxes between two source objects.  The argument of the radiative greenhouse effect from climate alarm is that Q from the atmosphere to the surface is increased by increasing greenhouse gases, therefore causing the surface to increase in temperature.  Quite plainly, this argument reverses heat flow directionality since the relation between the cooler atmosphere and warmer surface (this is their general state relative to each other) is that heat, using the definition of heat, flows from the warmer surface to the cooler atmosphere.  They call their heat-reversal mechanism “back-radiation”, the argument being that any additional presence of radiant energy in the atmosphere will cause temperature increase on the surface; this conflates energy for heat, because energy is not always heat and can only manifest or act as heat when flowing from warm to cool, causing the cool to increase in temperature.

Q between the Earth’s surface and Earth’s atmosphere is positive, meaning that heat is flowing from the warmer surface to the cooler atmosphere.  Their other argument attempting to explain the mechanism of “back-radiation” is that making Q less positive will increase the temperature of the warmer surface.  This is a complete fabrication and pseudoscience of thermodynamics, and here is where their argument reduces to Zeno’s Paradox.  Q is supposed to become less positive, in fact it is supposed to go to zero, but if in doing so this increased the temperature of the warmer object, then this would also increase the temperature of the cooler object, and then you effectively have Zeno’s Paradox or a variation on it (you never reach the end because the finish line of Q = 0 is itself running away from you).  What they are doing is treating Q as a conserved, constant quantity, which of course heat isn’t, and typically denote heat as given by the energy from sunlight, which is of course not Q (heat) in the first place given that Q is a difference of source fluxes, not a source flux in and of itself.”