In part 1 of our 3 part series, we covered why and how natural convection works and how a heat sources geometry can affect natural convection. Part 2, addressed board orientation and its impact on natural convection cooling and useful equations that can be used for calculating initial and simplistic results based on viable assumptions. In part 3, our final part in this series, we‘ll cover the calculations in generic plate fin heat sinks and wrap up our series.
For a generic plate fin heat sink, with a fin height of H, and spacing between fins of B, there is a relative fin spacing to fin length ratio which will provide optimal heat transfer within a given volume. Where spatial constraints prevent the use of a larger sized heat sink, optimizing its design for natural convection and increasing its efficiency can be the difference between normal operation and thermal failure.
Figure 3. A Simple Plate Fin Heat Sink.
Because the heat sink has to include heat transfer from the base, an equivalent channel width needs to be determined. The equivalent channel width is solved similar to a hydraulic diameter, as seen below .
H = fin height
B = distance between fin surfaces (fin pitch minus fin thickness)
The heat extracted from the heat sink can be found using this equivalent channel width and an assumed temperature difference between the ambient and heat sink surface.
Figure 4. Heat Dissipation of a Sink for Different Configurations of Fin Spacing and Fin Height Natural Convection 
The results shown in Figure 4 highlight the effects of changing the fin height relative to fin to fin spacing. For low volumes, it may not be economical to extrude or machine a heat sink with the exact geometry to optimize heat transfer from a given control volume, but the results show that for a standard or off-the-shelf solution it is safer to pursue a design with a larger fin spacing to fin height ratio than otherwise.
In this article we have shown that many applications prevent the use of forced convective flow from fans or other sources, due to acoustics, cost or other reasons. But, optimizing heat transfer by using the natural buoyancy-induced movement of air can be effective in cooling electronics. Some techniques for optimizing airflow and heat transfer in natural convection situations involve a vertical channel. For heat-generating boards suspended in a vertical configuration, there is calculable board spacing which will lead to an optimal power density per volume. Heat sinks can also be optimized for natural convection, and while it may not be feasible to obtain a heat sink of the perfect fin height and fin pitch for a workable volume, the next best performer is a heat sink with larger fin spacing relative to fin height.
1. Hwang, P., Cheng, H., Fang, J. and Li, J., CFD-Based Thermal Characterization of Board-Level Microelectronic Devices under Natural Convection Cooling, Microsystems, Packaging, Assembly and Circuits Technology, 2007. IMPACT 2007.
2. Malhammar, A., Optimum Sized Air Channels for Natural Convection Cooling, Telecommunications Energy Conference, 1987.
3. Incropera, F., Liquid Cooling of Electronic Devices by Single Phase Convection. New York, Wiley. 1999.