Summer 2004
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Coming up soon: CoolingZone Business and Technology Summit on Thermal Management of Electronics, Aug 25-26 2004 There are a couple of good short courses planned in conjunction with this great learning experience, and you don't need to go to the summit to attend the courses. See for more information.

If you're making longer range plans, ASME's big yearly conference, the IMECE, will be held in November in Anaheim, CA. There will be several sessions in the heat transfer track, with many interesting topics beyond electronics cooling. Check the conference web site for more information.

New seminar! Optical Systems Cooling -- See seminars page for more info on cooling (and heating) mechanisms in optical systems.

See previous newsletters and CoolingZone articles list.

Neat Spreadsheet Feature : Matrix Inversion

Matrix inversion is one of those things that you hoped you would never see again after your linear algebra course (if you had one ... I never did). But it's a fast path to solving for node temperatures in a thermal network. Here's how:

First, write the governing equations in the form Q=XT, where Q is a vector of applied power, X is a matrix of coefficients describing the resistances in the network, and T is a vector of node temperature rises. (You get the matrix by writing heat balances at each node; treat ambient temperature as zero to reduce the number of nodes.) Set up the X matrix in the spreadsheet with values at each position. For n temperature nodes, you should have n heat balances, so the matrix will be n x n. Also set up the forcing-function vector Q, which should have n terms -- some of which will be zero for the nodes at which there are no heat sources.

Then, let the spreadsheet solve for the temperature rise vector. T=(XtX)-1X tQ is written in Excel using the built-in linear algebra functions: MMULT(matrix1,matrix2), MINVERSE(matrix1), and TRANSPOSE(matrix1).

To implement this, you'll need to use an array formula. Select a vector range that is one column wide and n rows tall. Then type =MMULT(MMULT(MINVERSE(MMULT(TRANSPOSE(Xmatrix),Xmatrix)),TRAN SPOSE(Xmatrix)),Qvector) (I hope that's right!). Instead of hitting Enter, use CTRL+SHIFT+Enter to make it an array formula. The same formula gets entered in each cell of the vector you originally selected. Voila! A vector of temperature rises. Then, add the ambient temperature to each to get a node temperature.

If you've done everything right, the heat flows at each node should sum to zero, a good sanity check in any case.

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