Optimal Finned Heat Sinks

In a multi-board computer system, the volume allocated for heat removal is often a significant fraction of the total system volume. Cooling requirements can thus impact performance, reliability, cost, acoustic noise, and floorspace. This work addresses the volume costs or space requirements for removing heat with optimally designed finned heat sinks. Simple formulas applicable to both gas and liquid cooling problems provide upper bounds on the thermal resistance of an optimal heat sink, without explicitly designing the part. Conservative junction temperature estimates can thus be made without detailed design. The design of electronic circuits is usually limited by one or more limited fundamental resources. For example, the area of a circuit board or the area of an integrated circuit is a fundamental resource. In multi-board processors, volume is a fundamental resource. Volume is needed to remove heat from circuits as well as to store the components. Volume is often the most important limit: cooling requirements typically force larger module-to-module spacings than would be otherwise desired. The longer signal paths that result from this increased spacing can reduce computational speed. Even in systems where there is no direct performance penalty, the volume used for cooling affects costs, reliability, noise levels, and floorspace, and thus influences customer acceptance. This report describes research work into the volume costs or space requirements for removing heat with optimally-designed finned heat sinks. The solutions presented are very general in nature, and can be applied to both gas and liquid cooling problems. The general approach is to assume a fluid at some velocity flowing through a heat sink of a given material and specified outline dimensions (Figure 1). It evaluates both non-ducted or open-finned heat sinks (as shown) and the more complicated capped or ducted heat sinks. For the system designer, there are simple formulas that give conservative upper bounds on the thermal resistance of optimal heat sinks, without the necessity of individually designing them (see example in Section 3.8). fluid velocity u heat flow q W H L Figure 1: Heat Sink of Specified Outline Dimensions This information is useful both to system designers and to thermal engineers. Each will appreciate the closed-form optimizations that permit the comparisons of possible systems without requiring detailed heat sink design and analysis. The thermal engineer ii will additionally benefit from the the lossless-fin analysis, the non-ducted fin-spacing optimization, and the Nusselt number substitution that permits a unified approach to …