Richard, this is quite an odd angle of attack if your goal is to discredit anthropogenic global warming. The greenhouse effect was demonstrated in the 19th century well before the “guys-n-gals at Quantumville” produced any proper climate models of the Earth, and can be observed in action just as well on other planets like Venus and Mercury.
Are you really complaining that they didn’t write out and evaluate the surface integral over the daylit hemisphere ∫∫S Isuncos θincidencedS? I assure you that it simplifies to Isunπr²
In the physical world no externally heated substance can raise the temperature of its heat-source.
I assume you are referring to the second law of thermodynamics? The greenhouse effect doesn’t violate the second law. The net heat flow is still surface>atmosphere>space. The fact that infrared-absorbing gasses reflect some of this heat back to the surface would not cause the surface to “heat up” in the absence of external solar radiation. The net effect is to slow down the rate of energy emission from the surface out into space. Net heat flows from hot to cold in every step.
You may be confused by how the locally-valid rule I = Isuncos θincidence can give rise to the much simpler rule PEarth = Isunπr² when summed over all localities. The way to resolve such confusion is to evaluate the integral yourself and see that it all cancels out.
tl;dr: there is no “greenhouse effect” in reality (nor “greenhouse gases” either).
The greenhouse effect is so trivially shown experimentally that it’s a fairly standard activity for 6th grade kids to do.
I’m wondering where you got this rather interesting sequence of thoughts from. There are a whole bunch of various obvious errors that jump out - for example you seem to be confused as to what is actually warming, as you seem to think the Earth itself is a single system (like when you say no substance can raise the temperature of its heat source).
PS.: Can you link to a source for the supposedly-erroneous models?