Wednesday, October 19, 2011

Atmospheric Phonons - RHC and the Greenhouse Effect

Modeling heat flux exchange between atmospheric boundary layers

The interaction of conductive, convective and radiant heat flux change with density in the atmosphere. That complicates making a simple model that best illustrates the heat exchange between layers. Ideally, the basic model could be used for as many layers as possible so that the changes in the impact of one flux relative to the others would be most apparent.

Using the surface and Tropopause as an example, Flat plates for the surface opposed by a flat plate Tropopause would be a simple illustration for radiant flux, opposing triangles with a broad base at the surface decreasing to a point below the tropopause opposed by a potential energy triangle with the broad base at the potential temperature of the conductive energy transferred to the atmosphere, and the convective with latent would be a column with its width equal to the energy transferred from the surface to the point of condensation which then tapers to a point where water vapor is negligible.

For a RHC model, the three flux models would be combined into what appears to be a cone opposed by a cone, more accurately, a Bucky-mid opposed by a Bucky-mid. A Bucky-mid being a cone with its base shaped like a segment of a Bucky ball. Two dimensionally, a triangle would have to do.

Because of the interaction, the flat plates would not be very descriptive. The three dimensional model would be a Bucky ball core centered in a Bucky ball sphere. The surface base for each flux would be the same, but the area of the Tropopause Bucky segment would vary for each flux.

The drawing attempts to show in two dimensions, how the sum of the three energy fluxes shift from mixed flux to nearly pure radiant flux. The area of each flux showing the amount of work performed to create the potential energy of the atmosphere, the atmospheric effect.

Deftly erasing the individual flux representations  The opposing triangles represent the surface net flux which is opposed by the atmospheric effect.

Energy is converted from kinetic to potential with the typical loss of efficiency expected when work is performed, Thermo 101.

Visualizing the net effect with efficiency loss is easy. Understanding why radiant energy flux has to obey the basic laws of thermodynamics appears to not be so easy for many of my readers. This explanation starts with, “Nearly perfect does not equal perfection.”

The inverse square law of wave propagation is alive and well in physics. The concave shape of the atmosphere relative the convex shape of the surface does not indicate that infrared radiant heat flux can be focused. Visualizing the radiant energy of the atmosphere as a point source of energy at the average altitude of its origin is a more representative expression of how its impact on the surface decreases with distance from the source of the energy and the target or sink for that energy. If we could focus infrared radiation, our energy worries would be over. That difference between short wave and long wave electromagnetic radiation should be a clue to some misinterpreting the atmospheric effect.

This partially illustrates why the assumption of perfect energy transfer from the upper troposphere to the surface is incorrect. Unfortunately, that is a common assumption in the Greenhouse Effect Theory.

The much more interesting part is the interaction of the three flux members. At the surface, opacity is very high, there is little if any direct radiant transfer from the surface to the top of the atmosphere. GHG molecules can absorb surface energy, but the timing for pure emission is much too long, so collisional transfer dominates the cooling of the GHG molecules.

This is well known, what appears to be new, is that this transfer also involves work with enough loss of efficiency to not be negligible. Simple stated, that Kirchoff’s law needs a little tweaking in a gray body application. i.e. energy in to a layer is equal to the energy out minus plus entropy, since work is performed at less than 100% efficiency.

Very simple concept, there is no free lunch in energy transfer. The fun part is figuring out the entropy for radiant heat transfer in a mixed gas environment with changing density and composition of the gases.

In modern physics, quantum mechanics would be used to describe the probability density of the photons by their relative motions and energies. a touch complex, but doable. I classic physics, relativity would be used to simplify the complexities addressed by quantum physics. That is where the Relativistic Heat Conduction comes into the picture.
From Wikipedia, since that is one of the few sources I have at my disposal,

. The main features of RHC are:

1. It admits a finite speed of heat propagation, and allows for relativistic effects when heat flux transients approach that speed.
2. It removes the possibility of paradoxical situations that may violate the second law of thermodynamics.
3. It, implicitly, admits the wave–particle duality of the heat-carrying “phonon”.

The phonon distinction, is interesting. While it applies to solids and some liquids, the results of the Kimoto equation suggest that it may also apply to gases. I find that interesting. One of the criticisms of RHC is that, “4.The equivalence of relativity and the second law is shocking, because it implies that one of them can be a derivative of the other.” Imagine that?

Note: What I thought was a simple explaination is turning into a book. There has been a great deal of research done on RHC and I am sure I am wasting time describing what has been much more effectively communicated by others. I am a little curious how well my simple observations jive with current research that I do not have access to at the moment.

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