Thermal wake models for forced air cooling of electronic components

Analytical solutions are presented for the temperature field which arises from the application of a source of heat on an adiabatic plate or board when the fluid is represented as a uniform flow with an effective turbulent diffusivity, the so-called UFED flow model. Solutions are summarized for a point source, a one-dimensional strip source, and a rectangular source of heat. The ability to superpose the individual kernel solutions to obtain the temperature field due to multiple sources is demonstrated. The point source solution reveals that the N^-1 law commonly observed for the centerline thermal wake decay for three-dimensional arrays is predicted by the point source solution for the UFED model. The thermal wake approaches the point source behavior downstream from the source, suggesting a new scaling for the far thermal wake that successfully collapses the thermal wake for several sizes of components and provides a fundamental basis for experimental observations previously made for arrays of three-dimensional components. Preliminary experimental results using a thermochromic liquid crystal thermal mapping technique are presented