How to Underestimate Geothermal
Many people believe that because the geothermal heat flux is ~91 milliwatts/m², this would imply that, without the sun, the Earth’s surface would be ~36 Kelvin.
This is calculated the following way:
The math is correct, but there are two problems. First, this is for the top-of-the-atmosphere, not for the surface. But I will not address this today. The second problem, I will address today, is that this flux is wrong for this type of calculation.
Imagine an internally heated object is radiating to space. It’s very warm on the inside, but it very rapidly cools as you approach the exterior surface. Then a much hotter object joins in and starts to heat the exterior surface. What happens? The surface is now much warmer then it would be, and the flux going from inside to outside is … reduced!
The famous [small] geothermal heat flux is already a product of this reduction! The question now becomes … what would the flux be without the sun?
This question is extremely difficult to answer given all the variable parameters, and as far as I can tell … NO ONE has attempted it. But I’ll give it a small shot 🙂
I made a very simplistic 1-dimensional heat transfer program (code below) to help me out. First let me tell you its shortcomings:
No Albedo. No emissivity. No seasons. One latitude. No accounting of variation of specific heat or k-value as a function of depth. m*Cp = 222 and k=1, for all depths.
The sun simulation: Sun rises at 6am and goes to a full 1360 W/m² (no albedo) at high noon and disappears again at 6pm (like equator on equinox). This is repeated for 10 years (3650 days).
Despite these limitations, my central point is correct and will become obvious.
Not knowing where to start, I chose 273.15 K (0 °C) as the inherent geothermal temperature at 200m depth. The result becomes:
T @ depth of 200m = 273.15 K
$ cat plot.csv
0 253.63
2 253.82
4 254.02 …
196 272.76
198 272.95
200 273.15
The geothermal flux here is:
That is very close to the measured geothermal flux. Now let’s see what happens when we turn off the solar influence:
This result can also be achieved via a simple equation:
The geothermal heat flux now is 0.9462 W/m². That is … nearly 10 TIMES the flux when the sun is included. 9.695x to be more exact.
So the actual geothermal flux without the sun is very different than the flux with the sun. And this is not surprising.
Before my critics complain that I arbitrarily kept the temperature at 200m depth constant, they should be reminded that this doesn’t matter to my central point. The top (surface) cools much faster than the interior, and that this immediately raises the flux.
Either way, the famous geothermal heat flux is irrelevant for no-sun calculations as the REAL “steady state” tendency [without the sun] is to cool from top to bottom to the external temperature from distant space objects (2.725K).
Given infinite time … the heat flux goes to ZERO, and the surface temperature is obviously driven much colder than the 35.65 K figure calculated simply from today’s current geothermal heat flux with solar influence.
The 91 milliWatts/m² geothermal heat flux is worthless for no-sun predictions of surface termperature. QED
See more here: phzoe.com
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Alan
| #
Look at the moon to see the surface temperature that the earth would have without an atmosphere. Surely, it is the cooling effect of the atmosphere is far more important that geothermal heat flux.
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Lit
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From Planck´s Theory of Heat Radiation, page 6:
“But the empirical law that the emission of any volumeelement depends entirely on what takes place inside of this element holds true in all cases (Prevost s principle).”
https://ia904508.us.archive.org/26/items/theheatradiation00planrich/theheatradiation00planrich.pdf
So, as you see, the surface emission at 390W/m^2 all depends only on the internal state. This means that the geothermal heat flow is 390W/m^2, not 90 mW.
90mW is what you get when you measure two points at different shallow depths in the crust. This is similar to measuring two points inside a boiling pot of water on the stove. You´ll have practically no heat flow between those two points in the boiling water, but this doesn´t mean there´s no heat flow -THROUGH- the water from the stove plate. The heat flow from the heating element through the water is massive, but between the measuring points INSIDE the water it´s nothing. The same principle applies to the earth crust, you have massive flow of heat THROUGH the crust, but measuring between two (relatively) shallow points inside the crust will show negligible heat flow.
All of the 390W/m^2 surface emission comes from within, of course. Because that´s what Planck and Prevost say. Solar radiation and surface emission is related only through the internal state of the earth, they´re not cause and effect. We´re walking on a red hot ball with a crust that´s less than 1% of the volume. Of course the heat comes from the red hot ball inside.
If you don´t agree, talk to Planck. There´s no room for doubt in his statement. Trust him.
Here´s Prevost´s conclusion:
“Prevost also showed that the emission from a body is logically determined solely by its own internal state.”
https://en.wikipedia.org/wiki/Black-body_radiation
The surface emission depends ENTIRELY on the internal state. All 390W/m^2. It´s all geothermal. What did everyone think, that surface emission is bouncing solar radiation and that the Earth crust only emits 90mW?
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Robert Beatty
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“We’re walking on a red hot ball with a crust that’s less than 1% of the volume. Of course the heat comes from the red hot ball inside.”
The most likely place for that heat to emerge is through the oceans – which leads to an understanding of Henry’s Gas Law – and a complete refutation of the IPCC and the AGW scare campaign.
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Alcheminister
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I can’t believe that, sorry.
I thought the Sun kinda constantly provides energy/matter to the earth (meaning it contributes to whatever is considered geothermal) and without it shit would die and get cold real quick. I’m not so sure about it, but how much energy does the Earth constantly get from the Sun? That seems to be absorbed and equalized through what seems to effectively be a kinda spherical density gradient (presumably most dense at the center).
It’s like a porno suggestion, as if the sun is cooking some egg and in doing so, growing it.
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Robert Beatty
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Hi Zoe,
I noted “Imagine an internally heated object is radiating to space. It’s very warm on the inside, but it very rapidly cools as you approach the exterior surface. Then a much hotter object joins in and starts to heat the exterior surface. What happens? The surface is now much warmer then it would be, and the flux going from inside to outside is … reduced!”
This correctly assumes the earth is rotating. If we go back to the primordial start, there is no reason to think the earth was not in tidal lock with the sun? Under these circumstances, one spot on the surface gets to heat, and eventually meets the growing internally generated radio active heat. This is a formula for a massive explosion which could launch a goodly sized chunk of the surface into space. My supposition of where this all leads to is at https://bosmin.com/PSL/PlanetsSatellitesLandforms.pdf pages 10 to 18.
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