Solar panels as Attic insulation - check my math!

One interesting side effect of mounting solar panels on the roof has been looking at attic temperatures.

Measuring the underside of the deck it seems like there's a pretty clear difference between underneath the panels, and roof that's exposed to the sun.
Just measuring right now (outside temperature 64degF, sunny, 2:30PM).

Underneath the panels, I'm seeing (depending on how you squint) ~83degF. Under exposed roof, I'm seeing ~98degF. That's a +15degF delta!

Assuming I remember my thermo equations correctly:

• Thermal Conductivity (k): 0.15 W/m·K (wood)
• Thickness of the roof deck (d): 3/4 inch = 0.019 meters
• Area (A): heat flow per square meter for simplicity.

ΔTC=95×(83°F−80°F)=95×3°F=1.67°C (with panels)
ΔTC=95×(98°F−80°F)=95×18°F=10°C (without panels)

Q=(k⋅A⋅ΔT)/d
where 𝑘=0.15k=0.15 W/m·K, 𝐴=1A=1 m², Δ𝑇𝐶=1.67 or 10°C, and 𝑑=0.01905.

Q=(0.15W/m×K×1m2×10°C)/0.019m = ~79 W/sq m of roof (without panels)
and for ΔTC = 1.67°C --> ~13 W/sq m of roof (without panels)

That's a difference of 79W - 13W = 66W / sq meter.

For my 30 panels (.990m * 1.67m) * 30 = ~50 sq meters.

50 sq meters * 66W = 3.3kW of extra heat without panels in place -- that's like having two space heaters running in the attic!

What this means in terms of actual house temperatures is a bit unclear, but I'm sure it's probably measurable.


Has anyone measured attic temperature and house temperatures before / after installing solar panels and seen any difference? Very curious to see a year's worth of data.

Here's a thermal camera video in my attic showing the difference in temperature between underneath the panels vs exposed deck.

hex4def6 said:

Has anyone measured attic temperature and house temperatures before / after installing solar panels and seen any difference? Very curious to see a year's worth of data.

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I see roof iron temps of 63c with no solar or insulation, great for baking myself in summer....

Not sure I'd agree that it's insulation, but more of a heat sink. I wonder, given enough time, would the roof equalize. The panels are absorbing ~ 80% of the solar energy (20% efficient panels), and then radiating it out - some of that energy is presumably radiating down towards the roof as well. The heat transfer from the panels through the air gap would be really inefficient, so maybe not much of that radiated heat would make it to the roof.

I'd love to see a plot of ambient air temp, both covered and uncovered temps, and indoor attic temp over time. See what happens after 7 days of 90+ degree ambient temps (long enough to soak it).

Get a few of these for the experiment? The one with the external probe could be mounted under a panel and the thermocouple put on the exposed roof.


Regardless, that's pretty awesome! Makes me hopeful it'll lower the temps in my garage this summer.

Your math might be right, but your physics probably isn't.

You have to account for the fact the 98 F surface has air around it that isn't taking that heat away. Your flow equations assumed flow into an 80 F sink, which doesn't really exist in this setup.

Now if you had 80 F to 83 F and 80 F to 98 F through the plywood, then yes, you would have that much difference in heat flow.

I doubt you did.

Mike C.

mciholas said:

Your math might be right, but your physics probably isn't.

You have to account for the fact the 98 F surface has air around it that isn't taking that heat away. Your flow equations assumed flow into an 80 F sink, which doesn't really exist in this setup.

Now if you had 80 F to 83 F and 80 F to 98 F through the plywood, then yes, you would have that much difference in heat flow.

I doubt you did.

Mike C.

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I was assuming heat flow into the ambient air in the attic which I guestimated at ~80degF right now. In both cases that would be the heat sink. The outside roof temperature I think is immaterial (eg, the temperature of the shingles themselves).

I definitely should measure that properly, and I think it would vary in both situation -- no panels vs completely paneled. The no-panel situation would have a hotter ambient temperature, which would proportionally slow down the heat flow. Eg, no panel ambient = 85degF, deck = 98degF, whereas panelled might be 80degF / 83degF.

This doesn't take into account convection vs stagnant air, etc etc. Although I think that would result in a higher deck temperature, resulting in a higher heat flow, so maybe that evens out?

hex4def6 said:

I was assuming heat flow into the ambient air in the attic which I guestimated at ~80degF right now.

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The air right next to the plywood is not 80 F. That boundary layer air is basically the same temperature as the plywood.

Air heated rises, so there will be little to no convective heat flow upwards since the air is already there.

The heat flow in the air totally dominates this system.

Mike C.

mciholas said:

The air right next to the plywood is not 80 F. That boundary layer air is basically the same temperature as the plywood.

Air heated rises, so there will be little to no convective heat flow upwards since the air is already there.

The heat flow in the air totally dominates this system.

Mike C.

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First, I think you're assuming a sealed attic -- wouldn't that boundary layer still be hotter than the bulk ambient, and thus want to move up (to the ridge vent)? This would result in a convective movement, increasing effective thermal conductivity / transfer to the air.

Regardless, however: Even if the boundary layer was static, hotter plywood would result in a hotter boundary layer, which would increase the boundary layer - bulk ambient delta-T, resulting in increased heat flow.

I don't think I'm actually disagreeing with you; it would be interesting to know exactly how much of an effect this has, and whether modelling it as two heat flows (deck-boundary) and (boundary-ambient) would improve the accuracy.

I guess also the contribution of radiation vs. convection would be good to calculate.

Q_rad=ϵσA(Ts^4−Ta^4) (Stefan-boltzmann radiative effect)
vs
Q_conv=hAΔT

• ϵ = emissivity of the surface (0.9??)
• 𝜎 = constant (5.67×10−8 W/m2K45.67×10−8 W/m2K4),
• A = surface area,
• Ts = surface temperature
• Ta = ambient temperature
• h = heat transfer coefficient (10 W/sq-mK convection??),

Playing around with numbers, it seems like they're pretty close to each other in terms of contribution.


This is all making me wish I'd got a year's worth of attic temperature data before panel install....

plympton said:

Not sure I'd agree that it's insulation, but more of a heat sink. I wonder, given enough time, would the roof equalize. The panels are absorbing ~ 80% of the solar energy (20% efficient panels), and then radiating it out - some of that energy is presumably radiating down towards the roof as well. The heat transfer from the panels through the air gap would be really inefficient, so maybe not much of that radiated heat would make it to the roof.

I'd love to see a plot of ambient air temp, both covered and uncovered temps, and indoor attic temp over time. See what happens after 7 days of 90+ degree ambient temps (long enough to soak it).

Get a few of these for the experiment? The one with the external probe could be mounted under a panel and the thermocouple put on the exposed roof.


Regardless, that's pretty awesome! Makes me hopeful it'll lower the temps in my garage this summer.

Click to expand...

I agree its reducing the actual energy as well - that 20% panel efficiency is stopping that energy from becoming heat. That's worth 200W/sq meter alone, which is substantial!

I think what also would help is that the back of the solar panel is white (PVF is 0.8-0.9), whereas shingles are probably closer to 1.0.

This means that even as the solar panel heats up, it's going to want to preferentially emit heat out the front side of the panel rather than the backside.

This emissivity effect is much smaller I think -- that's going to be worth 10% or so, maybe(?).

In terms of equalization -- yes, I assume the whole system would equalize at some value. But in terms of living area -> living area interface, and the idea that someone would be using HVAC to maintain a set living temperature, the hotter the attic, the higher the heat flow into the living area.

hex4def6 said:

This is all making me wish I'd got a year's worth of attic temperature data before panel install....

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I've always believed captured data >> model output.

It's a mixed treat. The panels may be providing some shading for the attic but the hotter sun of a California summer will reduce the efficiency of the panels in producing electricity.
Edit: So be sure to leave space for air circulation under the panels so they don't overheat.

45North said:

It's a mixed treat. The panels may be providing some shading for the attic but the hotter sun of a California summer will reduce the efficiency of the panels in producing electricity.
Edit: So be sure to leave space for air circulation under the panels so they don't overheat.

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For sure.

That brings up another question of mine -- I've noticed a lot of installs use those "solar skirts". I question how good they are for panel efficiency. Seems like they would severely cut down on air circulation.

I expect you're right. What are they for, actually? Aesthetics? I suppose it does look neater, more finished. But at what cost?
(Oops! I think I've derailed this thread)

hex4def6 said:

For sure.

That brings up another question of mine -- I've noticed a lot of installs use those "solar skirts". I question how good they are for panel efficiency. Seems like they would severely cut down on air circulation.

View attachment 213716

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That's a nice photo and a good and relevant question. I suggest you start a new thread for it and see what people think