radiation & free convection to internal air temperature

[someguy79]

I have a copy of ASHRAE Handbook Fundamentals 2005. In it I've been using the relationships for sol-air temperature and heat flux. See page 30.22, equation 28.

q/A=alpha*E+h(Tambient-Tsurface)-epsilon*dR

h = coefficient of heat transfer by long wave radiation and convection on surface
E = total solar radiation incident on surface
epsilon = hemispherical emittance
alpha = absorptance for solar radiation
dR = difference between long wave radiation incident on surface and surrounings to radiation emitted by blackbody at ambient temperature

I've been using this with some success to determine heat load on a paritially insulated steel box out in the sun.

The object of this effort is to determine the internal air temperature of the box.

Unfortunately, I am having trouble figuring out how to get this temperature figured out in a particular set of conditions. There is no wind (free-convection only) and the box is raised up off the ground on a short pedistal. I haven't been able to develop a relation for heat conduction away via the pedistal. I don't think it should be much though.

This leaves me with heat transfer by radiation and convection. With the ASHRAE method mentioned above, the radiation and convection are coupled. I can figure out how to get different surface temperatures on the sides, top, and bottom of the box. I cannot figure out how to relate those back to an internal temperature.

My client is a stickler for having published references for my methods.

Does anyone have suggestions on what methods I might be able to use and obtain internal temperatures of the box?

 

[IRstuff]

It'll be pretty much the same deal internally, wouldn't it, except there's no solar absorptance, but that's replaced with your heat dissipation from your electronics...


TTFN

FAQ731-376

 

[someguy79]

There are no heat sources internal to the box.

Solar heat gain is approximately equal to convective heat loss.

It would be nice if there were some way to do this that didn't involve making a finite element or finite difference problem out of it. Still, I would do that if I could quantify the solar heat gain independently of convection.

I can find plenty of references for solar irradiance outside earth's atmosphere, but calculating the energy down on the ground is a different matter. That's what I'm looking for.

 

[IRstuff]

If there are no internal sources, then the interior of the box must equilibrate to the wall temperatures, right?

As for the solar load, what's the difficulty? MIL-HDBK-310 puts the maximum solar load at 1120 W/m^2, also see:

http://en.wikipedia.org/wiki/Insolation

TTFN

FAQ731-376

 

[someguy79]

The ASHRAE book uses a relationship that's supposed to account for diffuse irradiation. Using a single heat flux number like you are suggesting only accounts for sunlight hitting a surface directly. At least, that's my understanding of it.

Anyway, I may be making this more complicated than it should be. I'll look into MIL-HDBK-310. I haven't thought of that one in a while. Thanks for the suggestion.

 

[Hydronican]

Don't you think ASHRAE clear sky model can give you solar irradiation onto every sides of your box? Radiant Time Series Method will give you solar irradiation on every surface at every hour. ASHRAE 2005 Handbook has the basic information.

____________________
Comfort has a price.

 

[marcoh]

remember that solar radiation at your box will depend on where you are in the world, time of year, orientation, clouds, and atmospheric clarity.

There is a reason why we use heat load analysis to get accurate results.

If your manual calculations correlate fairly well to what you are measuring I would thinkg you have done very well considering the accuracy of the various inputs and assumptions.

 

[someguy79]

I've already done the calculations to get direct, diffuse, and reflected radiated heat flux during the middle of the day at the site location per ASHRAE handbook. As far as I can tell, these are what is refered to as the clear sky model. The relationships are from the Nonresidential Heating and Cooling chapter (30) and Fenestration chapter (31).

I've been multiplying radiation heat flux values (adjusted for incident angle, latitude, time of day, etc. as described above) by the areas on each side, top and bottom of the box. It's on a small column, rather than sitting on the ground. This gives me a steady state heat input.

I assume no wind, and a hot ambient temperature with very low humidity.

Then I calculate free convection heat transfer coefficients, solve for internal air temperature, and back solve for surface temperatures. The computed surface temperatures get put back in as inputs to find new convection coefficients and iterate. When the surface temperatures converge, so should inside air temperatures. Meanwhile, heat balances are computed to make sure I'm getting reasonable results.

One of the problems with the calc is that when the thermal resistance of the bottom of the box is represented realistically, (to the best of my ability) I can't get it to converge. The bottom is not insulated, while the other sides and top are insulated. I find that the output will, at some point, give a temperature below the ambient, and the heat transfer coefficients go imaginary.

Hydronican,

I would like to use the RTS procedure in ASHRAE handbook, but it seems to be tuned for buildings occupied by people. I'm dealing with box made from 2" thick A36 & A571 plate, that's insulated on 5 of 6 sides. Aside from that, I don't have a set of ambient temperatures I can use for a daily cycle. If I go that route I need a really good justification for picking a set of temperatures other than what's set forth in the engineering standards supplied. Like I said before, they're sticklers for published references and methods.

Marcoh,

This is a low production volume item. Right now it's just a on-off that isn't fielded. It will not be fielded until the client buys off on calcs, drawings, etc, etc.

 

[someguy79]

I should've said in my last post that I made some progress in getting the radiation heat load. I'm still having trouble with the model.

If my last post makes sense to you, and you think a steady-state model such as the one I described should work, I would like to know. Any greater detail beyond that would probably be asking you to do my work for me.

So, thank you all for your input.

 

[IRstuff]

The only reason for posting more detail is that someone else might be able to spot any inconsistencies in your calculations.

TTFN

FAQ731-376