Rule of thumb equations for convective cooling of metal surfaces.

[DHambley]

As an electronics engineer I have limited knowledge of heat-flow equations and theory. However, on every new design I need to get a rough estimation of the thermal resistance of a metal to air boundary so I can at least know the temperature rise to within a 10C to 15C accuracy. This analysis will typically be done after the fact by a mechanical engineer or, by simply testing it after the design is mature. Hard to get a enclosure concept design going when the thermal picture is so vague.

Long ago a mechanical engineer gave me this equation for a the temperature rise of a cube in still, sea-level air: delT = (P * 1000 / area)^0.83 where P is in Watts and area is in cm^2. Another method I've used is finding curves of basic finned heat-sink shapes and interpolating from there. Seems a little crude but, that's all I've got to work with.

Do you have a set of ballpark or rule-of-thumb equations, especially at lower air density such as for aircraft, which you can share?

Thanks for your help.



Darrell Hambley P.E.
SENTEK Engineering, LLC

 

[IRstuff]

The basic factors are, area, heat transfer coefficient, and delta temperature to the still air.

Regardless of anything else, these there are present in one form or another. A typical heat transfer coefficient for natural convection is 5-10 W/m^2-K. For electronics boxes, there are typically several layers of transfer:
> part to internal air
> air to chassis
> chassis conduction
> chassis to air

Typically, this requires a minimum of 3 unknown temperatures, part case temperature, box air temp, and chassis temp, assuming the chassis is thin and temperature drop is negligible. The heat transfer across each interface is the same, so the simultaneous equations are usually easily solved by programs like Excel, Mathcad, Matlab, etc.

Wikipedia has some reasonably usable pages:

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

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

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[Tunalover]

Dhambley,
It's often advantageous to ignore what's happening inside the enclosure and assume the surface temperature of the box is constant. Metals are so conductive that the temperature distribution is very nearly uniform. David Steinberg's book Cooling Techniques for Electronic Equipment is a great place to get the convection coefficient equations. You can do a heat balance and get a non-linear equation in one unknown (the surface temperature) which you can solve graphically or by Newton-Raphson iteration (or whatever solution technique you choose).

Tunalover

 

[DHambley]

tunalover, thanks for the book name. Have you got several "favorite" pages from that book which show these "rules of thumb" which I'm searching for? I really dislike using generalities and "rules of thumb" in engineering but, as I wrote, I'm just looking for ballpark figures to get a design started. I've been playing with the "convective heat correlation factors" equations on the wiki link which IRstuff sent. For some range of areas, the curves correlate with my simple "delT = (P * 1000 / area)^0.83" equation but, only for small ranges.

Darrell Hambley P.E.
SENTEK Engineering, LLC

 

[racookpe1978]

Think of your boundary limits for two things: Inside the box, you can cool individual components with cooling fins, radiation and convection, or by forced air cooling, right? (Think of a PC box with an internal fan(s) over the CPU and power supply.)

So, you can make a pretty good assumption that all of that "internal heat" is evenly transmitted to the box walls on way or the other. So the next assumption will be about cooling the box itself: which will (as shown above) be cooled by natural convective air currents to the room. (Or, as in the original PC boxes0 be forced cooled by fans into the room around the PC.)

If there is any forced cooling in either location (inside the box, or outside the box by blowing air around the box, or from the inside of the box to the outside-the-box environment), that forced convection will far exceed the effect of convective (natural circulation) cooling.

If the environment is itself a closed space, the environment will begin heating up and that will start affecting the convection losses. For example, you have an electronic enclosure holding a transformer and CPU, but the enclosure is not outside nor in a large open air-conditioned room , but is in a storage closet with a closed door. The room itself will get hot, which will significantly change your assumed "environmental" air temperature for the both forced air convection losses from the box and natural convection losses from the box.

 

[ione]

Darrell,

For natural convection and laminar flow you can evaluate the heat transfer coefficient htc (in W/m^2/°C) with the following correlation:

htc = K (deltaT/L)^0.25

where deltaT (in °C) is the temperature difference between the surface and the cooling fluid, and L (in m) is the characteristic length of the shape to be cooled.
K is a constant for the typical geometry involved. Yunus A. Cengel in his Heat Transfer - A practical approach reports different values of K for different geometries.
The correlation above stands for atmospheric pressure. For pressures P different from the atmospheric one, you can use:

htc (P) = htc (P=1 atm) * SQRT(P)

Once you have the heat transfer coefficient, you can express the heat transfer Q (in W) from a surface of area A (in m^2) and the cooling fluid as:

Q = htc*A*deltaT

as already mentioned by IRstuff

 

[racookpe1978]

The detailed examination of simultaneous equations from IRStuff above is the most thorough way to do the problem - if there is no forced air exchanged between internal box and room.

If there is forced air exchange going around inside the box and the box is small and made of metal inside a large room, then you can probably assume the box walls, sides, floor and top of the box are equal in temperature compared to the room air. If there is only natural convection inside the box, then the top of the box and top of the sidewalls of the box will be significantly hotter than the floor of the box and lower sides of the box. Your individual parts inside the box will be themselves significantly hotter than the "average" of anything else since the "natural" convection air flow and radiation is the only thing cooling them.

As IRstuff indicated, You have make assumptions, get the temperatures, then repeat the iterations to get final approximations.

 

[Tunalover]

The method I put forward will get you to within .5degC when working with broadband amplifiers (the kind you see on utility poles) with die cast aluminum enclosures. I did tests and proved that the method is quite accurate with enclosures that are at least 1/16" thick!


Tunalover