Summer 2006


	*Summer 2006*

See previous newsletters and CoolingZone articles list.

Reading List Suggestions: Here are a couple of books I've read with my book club recently. We don't particularly focus on any subject, but these have really been interesting:

Cradle to Cradle by William McDonough & Michael Braungart. This book has opened my eyes to a new way of thinking about design in everyday life, and sustainability in general. It seems pretty dense, but at least read the first half. See also their website.

Collapse by Jared Diamond. A fascinating synthesis of many different sciences (none of them thermal, I think!) to evaluate why societies succeed or fail. Interesting to see our collective shift (or lack thereof?) towards sustainability with this for background.

A summer note...on the way out the door recently, my husband mentioned that since he moved to a top-floor office at work, he's not as cold in the summertime. Why? Most likely because the ceiling temperature is warmer under the roof. Human comfort is strongly affected by thermal radiation, as well as the local air speed. There are university groups that study this topic, and the conclusions aren't surprising. For example, a flat roof painted white keeps humans more comfortable in the summertime in Arizona -- at the same room temperature -- than a black one. So actually one could save energy by turning up the thermostat, and maintain the same comfort level. My own winter experience is that radiant heat is more comfortable than forced-air heating systems, even at a lower air temperature.

The conversation reminded me of the importance of thermal radiation when convection coefficients are low. In fact, if you figure out an effective radiative heat transfer coefficient for electronics applications, it can be the same magnitude as natural convection in air.

Spreadsheet Tricks for Thermal Engineers : Radial Fin Analysis

Radial fin? What's that? Picture a flat disk, with a heat source of a certain radius in the center. There is a convection coefficient on the top and bottom surfaces of the disk.

A classic application of this is the type of baseboard radiator in the home where I grew up -- a copper tube (forced hot water from the furnace) with individual metal fins. Okay, those fins were rectangular, but we can approximate that away with some mathematical tricksmanship (equivalent radius, anyone?). The whole assembly was hidden behind a cosmetic cover with an adjustable vent. I realize that many readers will not be familiar with this system... and besides, most of us aren't going around analyzing our home radiators. (That might be fun, come to think of it...) Seriously, though, why am I bringing this up?

In an electronics cooling context, there are several places where the radial fin concept, with its associated mathematical solution, might apply. Besides the straightforward heat sink, with a center stem or heat pipe and radial fins, there is the heat source mounted on a circuit board. The circuit board always participates in the cooling, even if there is another heat path (heat sink) available. Of course, if the heat source has a really good heat sink on it, the circuit board cooling will be a minor effect. But even though some components have big heat sinks, there are often neighboring low-power components that rely on the circuit board to spread and dissipate the heat. You can think of this as a "thermal territory" (see Ake Malhammar's description), where a certain board "acreage" is needed to support the power dissipation and temperature limit for a component. Large territory? Low temperature. Territory too small (components too close together)? The component is starved for dissipation capacity, and needs to increase its temperature.

So much for the concept. How can we actually use it for analysis? Bruce Guenin wrote about the circuit board application in Electronics Cooling. In the article, among other things, he describes the heat transfer between circuit board traces and the air using the circular fin approximation. Table 3 of the article shows the exact mathematical solution; for a circuit board he approximates the effective board thickness (its conductivity isn't uniform).

The Bessel function solution looks intimidating, but Excel (and I'm sure other spreadsheets too) has them built in. To make it easier to get going, I've written up the equations for you to download. (Cells in blue text are your inputs; the black text cells are calculations. Note the units for the input cells.) Just remember that the solution given evaluates only the conductive & convective behavior of the fin -- there will be other mechanisms going on in your system. (For example, How is the heat getting to the inner radius? What is the local air temperature over the fin? What is the value of the heat transfer coefficient, anyway?)

Just one more caveat: use this idealized mathematical description to give you design guidance -- not to try for 100% accuracy. For example, you might use it to answer the question "Does this component need a heat sink or is board cooling going to be OK, given the proximity of its neighbors?" If you're unsure, design in the heat sink...you might be able to eliminate it later, when you discover that the component power estimates were high by 75%!


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