Nice sunny day here, so did the test with surface mount thermocouple to measure actual temperature of the roof below the PV panel.
I did several runs, but this one is representative:
- Ambient temperature: 73F
- Full sun: 790 watts/sqmeter on PV panel surface
- Inside van temperature: 78F
- Wind speed: 0 to 4 mph (near calm)
- PV panel top surface temperature: 157F
- Roof temperature under the PV panel: 136F
- Roof temperature outside the PV panel: 119F
So, the roof is about 17 F warmer under the PV panel than away from it. If you were trying to maintain them temperature inside the van at 70F, then the heat gain for the part of the roof under the PV panel would be about 35% greater per sqft than the gain from rest of roof.
This is with a white roof van, as RD pointed out, the difference would likely be less with a dark roof as the roof runs hotter.
The roof temperature under the PV panel ends up being about half way between the PV panel temperature and the roof temperature.
Surface mount thermocouple on roof under PV panel (PV panel edge unscrewed and raised up a bit to allow placement of the thermocouple)
surface mount thermocouple on top surface of PV panel
Measuring solar radiation
Measuring wind velocity
A little more on the web page for this test: https://www.buildagreenrv.com/design...-on-heat-gain/
JH -- on your comments...
"The predominant mode of heat transfer from back of PV panel to roof surface is radiation. Convection in between is nearly zero due to the open space in even the slightest of breezes.
Conduction is non-existent as these surfaces are _NOT_ in contact."
There is contact and conduction between the two surfaces and the air and then heat transfer from convection currents. You don't have to have contact between the two final surface to have heat transfer that is in part conduction -- almost all heat exchangers use conduction/convection to a heat exchange media (like water) with no contact between the final surfaces.
"You seem to be forgetting that the roof, and the entire van body, is in fact a huge steel heat sink. A radiator if you will. Any spot anywhere on the surface being heated (by whatever source and heat transfer mode) rapidly conducts this heat to the rest of the steel body of the van, and thus its locally increased temperature quickly reaches an equilibrium with its vicinity, as heat conduction in steel works extremely well.
Meaning that the roof surface under the PV panel will read just about the same temperature as the one exhibited over the rest of the roof."
The thin sheet metal of the (0.036 inch) does not hold much heat and is not really that effective in conducting heat away.
The whole roof weights about 145 lbs and with a specific heat of 0.122 BTU/lb-F, it only holds/sinks about 18 BTU per deg F of temperature increase -- almost nothing compared solar heat flux coming onto the van.
Its also not that effective in conducting heat away from the hotter PV panel area - its just to thin to provide an effective heat transfer area. The perimeter of the panel is 19.5 ft, and this whole perimeter has a heat transfer area of only (19.5ft)(0.036 inch/12 in/ft) = 0.059 sqft. If you consider the heat transfer through a 6 inch wide strip of sheet metal all the way around the perimeter of the PV panel for a 1F temperature difference, it comes out:
Q = (k/S)(A) (dT) = ((25 BTU/hr-F-ft)/(0.5ft)) (0.059ft^2)(1F) = 3 BTU/hr --- pretty darn small compared to the more 5400 BTU/hr coming onto the PV panel.
If the van roof/skin were such an effective at transferring and equalizing temperature differences as you suggest, you would not see such large differences in skin temperature around the van. In the test this morning, walking around the van and measuring skin temperatures, they ranged from 72F to 120F -- sometimes with only small distances between markedly different temperatures.
It would be nice if you provided some numbers to go with the strong assertions you make.