Gray Body Radiation Equation applicability 1

[KENAT]

Sorry if this is a real dumb question but it's not in my normal field so wanted to get a second opinion.

I've been asked to help update a small electronics device. Basically they're adding a few components one of which will act as a 5W heat source. We want to do a rough ball park to check if the shell of the device will be an adequate heat sink/how much we need to increase the exposed surface area.

We're assuming thermal radiation for the primary heat transfer mechanism as there's no fan and sometimes the device may be used in a workstation which will limit airflow for convection.

Can I reasonably use the Gray Body Net Radiation Loss equation to get a ballpark figure for if/how much I need to increase the surface area?

q = ? ? (Th4 - Tc4) Ac

q = heat transfer per unit time (W)

? = 5.6703 10-8 (W/m2K4) - The Stefan-Boltzmann Constant

Th = hot body absolute temperature (K)

Tc = cold surroundings absolute temperature (K)

Ac = area of the object (m2)

? = emissivity of the object (one for a black body)

I plan on trying to convince them to let the body be flat black anodized - probably Al 6061-T6 (it's a machined housing - is an ? of .77 realistic for this? Or is it low as I found figures as high as .85 for hard anodized aluminum?

I appreciate the help.

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[IRstuff]

Sure, you can still assume about 2.5 W/m^2-K even with only natural convection. This is a very conservative value, there are sources that put the coefficient as high as 8 W/m^2-K.

Either value of emissivity is probably adequate, since it will only marginally change the area calculation. If you really want to get fancy, you could assume different emissivities for the influx and outflux.

TTFN

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[KENAT]

Thanks IRstuff. I've been thinking about it some more and for this modified unit apparently it's unlikely to be enclosed so I can take natural convective heat transfer into account - which is a good thing because based just on existing surface area I get temperatures of around 350K° using just radiation.

Can you give me some ideas of where to find values for natural convection heat transfer coefficient (W/m2 K) aluminum heat sink in air? The few values I've managed to find tend to be a little higher than you give above, though of course you did say 2.5 is conservative.

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[IRstuff]

Unfortunately, there is no single value, and there's a rather large spread in the numbers. See: thread391-277062 for a link suggested by Ione for convection equations for different geometries. All the equations from that link are supposedly from Incropera's book, which can be found on the web, but I won't say where.

The reference to Holman is possibly another approach, and likewise can be found.

TTFN

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[KENAT]

Thanks, I was trying to find a value for a flat plate or something, as my item is fairly tall and wide but not very deep, so the front face is the main area and approximates a flat plate.

I'll probably use the lower value you give, or maybe '5' that I found elsewhere. Looks like we're going to do a test on an existing unit, just adding a suitable heat source externally, to verify my calcs.

Thanks again.

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[KENAT]

Well, thanks for your help, my figures, combined with our lead systems guys gut feel and marketing's aesthetic concerns have led to abandoning passive cooling, enlarging the enclosure and adding a fan.

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