Solar Gain Calculation 3

[EngAP]

Hi all.

I need to determine the temperature rise in a sealed enclosure due to solar radiation gain, with and without a sunshield. If anyone knows of a simple way of achieving this or any texts or links that may help then I would be grateful for any information.

I would like to be able to calculate this analytically to compare to CFD results.

Thanks.

 

[Flareman]

The solar radiation at any location on the Earth's surface is a rather complex calculation involving scattering, water content and a lot of other stuff (look up Bird calculation). However, you can get a pretty good idea about your value from the formula
Is = 410 * cos(latitude - degrees)
That's going to be a good average (top end) summer value for a clear day wherever you are [+/- 30] and applies when the sun is around its highest elevation during the day
The value will be Btu/sq.ft per hour.

If you have overcast conditions the values drop, when the day is new or old, the values drop, (no sun at night !!!)

From there on, it's just heat transfer.
You will need to do the calculation iteratively so it's better with spreadsheet than a slide rule (showing my age)

Radiant transfer in from the sun as a function of the solar exposed surface, and the surface color and sheen,
Radiant transfer out to atmospheric temperature as a function of deltaT^4 etc,
Convective transfer out as a function of either natural or wind forced convection and temperature difference.
Then you have to look at the shape, and (sort of) integrate around the box.
Thats just the heat in and out on the outside.
What's the internal condition? What mass of what is available to absorb the heat which is radiated from the inside surface (it's a contained black body)
Look at the overall thermal mass of the entire unit against the initial rate of net heat transfer and estimate a time constant (say 5 x the thermal mass divided by the heat flux) That gives you a time to equilibrium from which you can extrapolate any intermediate using a naperian log rate of growth.

With a sunshield its much easier. There's no solar input. It's only going to get the ambient temperature (whatever that is) - cheating a little because you could argue that the shield transmits some radiant heat, but it's going to be small -

You could also cheat with the box by assuming its all exposed the maximum amount and just treat it like a single plate at 90 deg to the Sun. If you do that and you're in the Sahara desert, your ambient temperature goes up around 120 degF and the metal temperature might go up to between 180 degF and 225 degF

Good luck
David

 

[kjoiner]

EngAP,

You might want to try NEMA enclosure manufacturers such as Hoffman. They have some formulas and simple programs that provide temperature rise due to internal components and also due to solar exposure.

Kyle

 

[EngAP]

Flareman - thanks for the comprehensive answer. Once I have estimates for solar radation (W/m^2) that is hitting my enclosure would I be correct in assuming that the amount transmitted into the enclosure could be calculated by multiplying by (1-reflective index)?

So if 40% of 500W (say) is reflected, 60% is transmitted into the enclosure and the internal temperature rise (purely from transmitted solar radiation) would be calculated by re-arranging the standard Q = m.Cp.deltaT (m and Cp refer to the internal air) to get the deltaT?

I could then ESTIMATE the actual internal temperature by iterating as you suggested above. The answer I need is to quantify the effect of a sunshield on reducing the internal temeprature rise due to solar radiation.

Thanks again.

kjoiner - thanks also - I will check out the manufacturers.

 

[IRstuff]

You should start with what the unloaded internal temperature is, based on power dissipation inside the box. Then you can just add the absorbed solar load as a first order approximation to determine the new delta temperature.

Note, however, hot surface do emit substantial amounts of infrared energy, so you should include radiative heat loss as well.

TTFN

FAQ731-376

 

[dcasto]

According to the GPSA databook as taken from API 520, solar radiation should be look at at between 250 to 330 BTU/(hr-ft^2).

 

[IRstuff]

Maximum value listed in MIL-HDBK-310 is 355 BTU/ft^2-hr

TTFN

FAQ731-376