The sun is known to emit ~63 Mega Watts per meter squared from its photosphere. But what is the heat flux inside this emissive photosphere?
Heat flux formula: q = k*ΔT/L
q = k * (6600-4400 Kelvin) / (500,000 meters)
What is the thermal conductivity (k) value of hydrogen at these temperatures? 
This is actually very difficult to find, but I managed to find something:
This y-axis needs to be divided by 10 to get units (W/m*K).
The range of pressure in the photosphere is: 0.0009 atm to 0.123 atm. I think it’s safe to say that thermal conductivity of hydrogen is definitely no more than 2.5 W/m*K in our desired range. That will be our upper limit. Thus,
q = 2.5 * 2200 / 500000 = 0.011 W/m² 
As you can you can see, there is no problem with 0.011 W/m² “supporting” a 63 MW/m² output.
My critics will be quick to point out that I can’t use the conduction formula because the sun only has radiative transfers in the photosphere. But that’s just their excuse for NEVER figuring out what the internal heat flow is. Any of their attempts at doing so will be embarrassing for them, and so they will avoid it at all cost. Surely there is a heat flux, and surely it can be figured out.
My critics believe in conservation of heat flow, that is: internal heat flux => emergent radiation. There must be equality of these two things, otherwise there will be rapid cooling. Well, the sun has had 4.5 billion years to reach their “steady-state” equilibrium nonsense and it’s nowhere close. Maybe despite all their chest thumping, they have no idea what they’re talking about?
What goes for the sun here goes for my geothermal theory as well.
Just as <0.011 W/m² internal heat flux can “support” a 63 MW/m² emission from the sun, so too can a ~0.9 W/m² geothermal heat flux “support” a ~334 W/m² emission from Earth’s surface.
Think about it!
Enjoy 🙂 -Zoe
 I left out helium. I don’t care to include it, as it makes little difference. I only care about being right within an order of magnitude.
 I don’t include surface area of emission, because the difference in solar radius of top and bottom of photosphere is too small.