Rule of thumb equations for convective cooling of metal surfaces.
Rule of thumb equations for convective cooling of metal surfaces.
(OP)
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.
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





RE: Rule of thumb equations for convective cooling of metal surfaces.
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_coeffic...
http://en.wikipedia.org/wiki/Convective_heat_trans...
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RE: Rule of thumb equations for convective cooling of metal surfaces.
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
RE: Rule of thumb equations for convective cooling of metal surfaces.
Darrell Hambley P.E.
SENTEK Engineering, LLC
RE: Rule of thumb equations for convective cooling of metal surfaces.
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.
RE: Rule of thumb equations for convective cooling of metal surfaces.
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
RE: Rule of thumb equations for convective cooling of metal surfaces.
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.
RE: Rule of thumb equations for convective cooling of metal surfaces.
Tunalover