Optimal Sizing of Planar Thermal Spreaders

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Abstract
Two-dimensional cylindrical and three-dimensional Cartesian thermal spreaders are studied. One of the surfaces is convectively coupled to a uniform environmental temperature while the opposite surface is subjected to a uniform heat flux distribution over a portion of its boundary. The problem is generalized through the introduction of appropriate dimensionless variables, and analytical solutions for the temperature field are presented for each coordinate system. The solutions depend on the usual geometric and heat transfer groups. It is found that, for a range of realistic Biot numbers and a given ratio of the spreader to heater dimensions, a dimensionless spreader thickness exists for which the temperature of the heater reaches a minimum value. Optimal thickness curves are presented for these ranges.

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