Bounding relations for natural convection heat transfer from vertical printed circuit boards

The simplicity and convenience of direct cooling with freely circulating air, as well as the ubiquity of such systems in the marketplace, make this the technique of choice for many thermal packaging tasks. While standard heat transfer correlations are generally unsuitable for determining the detailed thermal behavior of individual components, the maximum surface temperature of integrated circuit packages mounted on PCBs can often be shown to lie between two analytical bounds: an upper, "asymmetric isoflux," bound based on heat transfer from just one side of the PCB and a lower, "symmetric isoflux," bound based on identical thermal transport from both sides of each PCB. Following a brief review of the development and validation of the theoretical symmetric and asymmetric isoflux relations for smooth-plate channels, this study focuses on the application of the proposed bounding relations to widely and closely spaced component-carrying PCBs. Successful comparison with much of the available data demonstrates the acceptable accuracy of these analytical expressions, for all except the narrowest spacings, and their utility to the thermal designer of air-cooled PCBs.