Logical Physics Maths
Heat Flow
The climate science greenhouse effect is a simulacrum. It is not science, nor is everything that is based on it science. All of climate alarm is a simulacrum, a fraud, and most of what could have been real climate science has been infected and ruined by it. 
It uses the words of science to give itself the appearance of science, but it does not actually contain the essence of science, i.e. the method or wisdom or rationality of science. See the last post for more detail on this. What it is, is an attack on human existence.
Let’s cover some basics about calculating the temperature that heating from sunlight is able to generate on a surface absorbing solar energy.
The temperature T induced by sunlight on a cooler surface when in thermal equilibrium is given by
F = ε*σ*T4
where F is the absorbed (and then re-emitted when in equilibrium) flux. The absorbed flux is the solar insolation, ‘I’, multiplied by the absorptivity, and absorptivity is 1 minus the albedo ‘α’. So then
I*(1-α) = ε*σ*T4
and you can rearrange for T to get the temperature of the surface absorbing the insolation:
T = (I*(1-α)/ε/σ)1/4
This equation predicts surface temperatures exposed to sunlight very accurately, as shown in real greenhouses, black asphalt, beach sand, car interiors, spacecraft, etc.
Now, the equation
Q = A*σ*(Th4 – Tc4)
is for heat flow. (‘A’ is the area here so that the units of heat are properly in Joules.) Q is just the portion of the energy which is flowing as heat. This is a different thing than what we just looked at. Q is not the value of absorbed solar insolation, I*(1-a). Q is not the solar insolation energy. If it was, then you would have
I*(1-α) = A*σ*(Th4 – Tc4)
but that equation is nonsensical, because the terms don’t make sense given the preexisting context of solar insolation absorbed into a surface. In the first place, the units on the left and right hand sides don’t even match! And then, what is Th? Is Th for the temperature of the surface being heated by the insolation? Let’s say it is. If it is, then what is Tc? Whatother surface is Tc the temperature of? There isn’t another surface, because there was only one surface being heated by insolation. Is Tc the temperature of the surface before being heated to Th? If it was, that’s not what the original equation meant in the first place, because Tc and Th were the temperatures of two different sources, a warm one and a cool one, and Q was just the heat flow between them, not the external energy input to either of them. If the left-side of the equation is the absorbed solar flux, then what is Th, and what is Tc? Why does the solar flux depend on the temperature difference between two arbitrary surfaces on the right hand side, when the solar flux is being absorbed only by the surface absorbing it, and is its own independent quantity? None of this makes any physical or logical sense any more.
The reason why this is important is because the believers in the alternative version of the greenhouse effect of climate science say that the last equation explains their greenhouse effect. This has been discussed previously in “How to Lie with Math“, and “The Tautology of GHE Math” relates to it too.
The original equation for heat flow is a sensible equation, it is just that what the “IPCC greenhouse effect” believers try to do with it which makes no logical sense, as just easily demonstrated. Let’s return to it and do the correct things with it:
Q = A*σ*(Th4 – Tc4)
So in the case of solar insolation on a surface, and in the reference frame of the laws of physics, thermodynamics and heat flow, heat only flows from hotter to cooler, and this is obviously what this equation describes. If the surface where the insolation is supposed to be going is independently warmer than what the absorbed insolation would have been able to induce, then the solar insolation will not warm the surface. The direction of heat flow will be from the surface outwards, rather than “from outwards” to the surface.
The radiative heat flow equation, in general, is simply about having two potential sources of heat, and determining how much energy can flow as heat between the two sources. So, in the case of solar insolation on a surface, we have thus identified the two sources: 1) the solar insolation, and 2) the surface absorbing the insolation. The heat flow equation is simply then
Q = A*(I*(1-α) – ε*σ*TS4)
where TS is the temperature of the surface. That is, the amount of energy flowing as heat from the solar insolation to the surface is given by a function of the difference between the temperature of the absorbed solar insolation and the temperature of the surface. Now the heat flow equation makes physical and logical sense in the context of solar heating on a surface, and there are no superfluous illogical terms. An obvious result is that, if the absorbed solar insolation is equal in strength to the thermal emission from the surface, that is, equilibrium, then there will be no heat flow, i.e. Q = 0 and so
I*(1-α) = ε*σ*TS4
which gives us back
TS = (I*(1-α)/ε/σ)1/4
for the temperature of the surface when in equilibrium with the insolation input. So now we’ve made the Stefan-Boltzmann equation method for determining the temperature of a surface absorbing radiation in equilibrium, totally consistent with the heat flow equation, by deriving it from the heat flow equation. It always was there in the first place of course, it just hadn’t been required to demonstrate it until the IPCC greenhouse effect believers reinterpreted (incorrectly) some of the maths.
Note that there is an interesting logical condition to consider when the temperature of the surface is independently warmer than the temperature forcing from the insolation. In this case, as was stated, the insolation will not increase the temperature of the surface because the heat flow direction will be away from the surface, rather than toward it. Does that then mean that a surface at 1500C, when faced with solar insolation forcing of 1210C, sends heat to and thus warms the Sun which is already at 60510C? Don’t you love logical opportunities to learn logical physics? The answer is logically important in how it is essential to the meaning and situational understanding of the heat flow equation.
In the heat flow equation for the solar insolation on the surface,
Q = A*(I*(1-α) – ε*σ*TS4),
all of the terms are in-situ, that is they correspond to a specific locality. First, consider Q; where is the heat flow that it denotes? It doesn’t provide its own answer, so get to the next term, I*(1-α). Aha! That term definitely defines a location. Why? Because solar insolation is a function of distance from the Sun, and so whatever value that we’ve been using for ‘I’ is the value that it has at the surface with temperature TS. That is, the equation denotes the heat flow directly at the surface’s location.
So now, if you want to know the heat flow at the surface of the Sun, given that the other TSsurface was warmer than the local solar insolation upon it which therefore indicated a heat flow away from it, you need to use the insolation of solar energy at the solar surface and the insolation provided by the surface and temperature from TS at the distance it is away from the Sun.
Well you should be able to imagine in your mind’s eye what happens: the surface of the Sun will be way hotter than the temperature of the insolation from TS, and so the TS surface will not heat the surface of the Sun, because it is too cool at that distance. The laws of thermodynamics are obeyed.
Note the final conditions of this scenario, then. The surface was warmer than the solar insolation forcing temperature, and so the solar energy couldn’t raise the temperature of the surface. The direction of heat flow was in fact, and obviously, from the warmer surface, towards the Sun. However, the radiant heat from the surface doesn’t actually “make it” to the Sun because by the time it gets there, it has been diluted so much that it is too weak to do anything. Locally, heat is flowing outward from the surface TS, but it is also flowing outward from the surface of the Sun. In between, the heat seems to just get “lost”, and so where does it go? To the heat and entropy of the space between the surface and the Sun, to the growing heat and entropy of the universe. Locally, radiant heat flow can be “outward”; at the other location, however, it might not actually cause any heating, because of the local conditions there, and the heat flow can be outward at that location as well.
I mean just think of if it always did cause heating: then you’d have situations where as a hotter source heated something up, the radiation from the thing which got heated up would cause the source of heat to heat up further, which would then heat up the other thing some more… Well this obviously quickly runs away and is a simple exponential positive-feedback, and that’s not how thermodynamics or reality works.
For those with the memory, that’s the heart of the error with Eschenbach’s steel greenhouse; he merely stopped the mutual-heating feedback cycle at the value he desired as if conservation of energy is a force that can suddenly stop the backradiation heating he used to amplify the temperature in the first place. That is, as his outer shell warmed up, its “backradiation” continuously came back to warm up the interior sphere some more, which then warmed the outer shell some more, thus setting up a mutual heating cycle. This cycle can’t stop just because it is convenient to stop it at a pre-desired value…the backradiation from the shell can’t just suddenly cut off its heating of the interior sphere at 240 W/m2. The 240 W/m2 still needs to come back to the sphere from the shell which will still cause the sphere to continue heating up some more – it doesn’t matter what happens on the outside because it is the established conditions on the inside which set up the heating cycle in the first place. That it indicates that more than 240 W/m2 would begin to be emitted to the outside if we naturally continued the heating cycle which was set up is the point! That point indicates the entire logical error of the whole thought experiment!
Energy Conservation
Stating the heat flow equation once again,
Q = A*σ*(Th4 – Tc4)
we often find this reinterpreted by climate science greenhouse effect believers as if it represents conservation of energy. Typically the statement will be: “Since Q needs to be conserved, because it is the energy from the Sun, then if the atmosphere Tc warms up, the surface Th needs to warm up also in order to conserve Q, and this is the atmospheric radiative greenhouse effect.” Of course as we’ve seen, that absolutely makes no sense. Q is not the energy from the Sun, and the energy from the Sun is not dependent upon the difference in temperature between the surface and the atmosphere on the right hand side of the equation. Q is simply the quantity of energy which flows as heat between two sources, it doesn’t specify the solar energy or relate to energy conservation.
Of course, the correct application of the heat flow equation with the solar insolation and radiant energy from a surface is
Q = A*(I*(1-α) – ε*σ*TS4)
which when in equilibrium results in
I*(1-α) = ε*σ*TS4,
which is just the Stefan-Boltzmann Law
F = ε*σ*TS4
Thus we have seen how the Stefan-Boltzmann Law for radiation and the heat flow equation for radiation can be directly related to each other, and we have shown that these do not lend any interpretation towards the alternative version of the greenhouse effect of climate science, the radiative greenhouse effect, which of course as we know failed the empirical and propositional test long ago.
Read more from Joe Postma at climateofsophistry.com
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