Temperature rise of object in the sun 1

[Dan68c]

Hi,
I have been trying for ages to work out the temperature rise of an object in the sun. Such as a roof of a house.
What i have done so far is used the constant on 1200W/m2 delivered from the sun.
From here i use the reflectivity value to reduce the amount absorbed and then the maximum temperature will occur during at steady state when the heat added is equal to the heat loss.
The heat loss i have done is from radiation and convection and as the temperature rises so does the heat loss.
However doing all this i get a huge temperature rise which doesnt seem real. I am using the correct constants and the temperature in kelvin.
Any help would be much appreciated.

 

[IRstuff]

For your values, I got ~55°C rise as well; the model you posted is identical to the one I'm using. That's a plausible value for this worst-case scenario, since that would put it just above boiling point of water; 325K+55K = 380K (boiling point is ~373). One caution is that an ambient temperature of 325K = 52°C is above the 99-percentile high temperature per MIL-HDBK-310.

Since I had a lower convection coefficient and lower ambient temperature, the rise in my original model is 84.5°C. Note that the lower ambient temperature actually worsens the temperature rise, because the radiated cooling is less effective due to the 4th power of the absolute temperature.

Overally, such values are not implausible. Solar cookers can take objects above boiling, even on overcast days. A parabolic mirror can collect sufficient heat in a small enough area to ignite paper or wood, which requires a temperature well in excess of 200°C.

TTFN

FAQ731-376

 

[mrpi]

I had not thought about the reduced radiation loss at lower temp, that's good point.

I just picked those numbers as what I thought would produce the worst case based on operating conditions spec'd by a couple military-based projects I've seen.

I'm not very familiar with solar loading and I couldn't find much info on the topic. IR, have you done any testing? What sorts of emissivity and convection numbers are realistic?

A parabolic mirror will concentrate 1120W/m2 down into significantly less m2, so the heat flux goes way up. But yes, solar radiation has a lot of energy, especially when you consider that the source is 93 million miles away!

Beat to fit, paint to match.

 

[IRstuff]

No real testing, all analysis. No one can afford to design a system for this worst-case, so the general rule is to assume 55°C ambient when considering solar load.

TTFN

FAQ731-376

 

[ione]

To athomas236,

The equation is written for a thermal equilibrium, and as per the Kirchoff’s law the body emissivity equals its absorpitivity. On the first member (left) of the equation you can’t consider the whole thermal power radiation, but only the part really absorbed: so epsilon has to be there.

 

[athomas236]

ione,

Thanks for info, much appreciated.

Regards,

athomas236