Quick, Easy, and Mostly Right Heatsink Performance Estimate
I really enjoyed both of the Web Seminars on heat sinks; Heatsink 101 presented by Alexandra Francois-Saint-Cyr and Heatsink 201 presented by Dr. John Parry. I was especially interested in a couple of equations presented in Heatsink 101 that estimated h (convective heat transfer coefficient) and minimum fin spacing. The equations were derived from a Flat Plate in Parallel Flow theory but were simplified so that all of the fluid properties and unit conversions were already taken into account. This inspired me to carry it a bit further, with a few more assumptions. The idea behind these formulas aren’t really to allow the design of a heatsink but more as a preliminary sizing tool. With this in mind I wanted to come up with a single formula that would estimate the required volume to generate the desired heatsink thermal resistance for a given velocity. Enough of the work, I think, is shown below.
Aside from some simplifying assumptions on the heat sink surface area was the idea that the length, width, and height of the fin area were all equal. None of these dimensions are related to the actual fin thickness, this calculation doesn’t go into that level of granularity. Essentially it assumes that the heat sink is at a single uniform temperature where the flow between the fins never fully develops. The number of fins is based on the assumption that the flow never fully develops; The fins are spaced at 2δ apart at the distance L along the plate.
A few years back I wrote an excel vba macro to estimate heat sink performance that took into account such things as , airflow bypass, heat sink thermal conductivity, heat spreading, and fin efficiency. The problem was that when I was in a situation where it might be useful I didn’t want to populate it with all of the information it required. I have started to dust it off again though with an attempt to streamline the input. Ironically, I guess, it uses a Nusselt number based on internal flow in a rectangular channel with an infinite aspect ratio where the flow is fully developed. The approach presented here is a bit more useful, at least to me, because it requires only two inputs.Aside from checking for consistent units and producing the results in the table below, which I think look reasonable, I haven’t done any testing. For better or worse I do think this is an equation I will use for a first pass size calculator. This table shows what the estimated L,W,H needs to be “roughly” to achieve the desired heat sink thermal resistance (10→1) at various velocities (0.5→5)
I encourage you to let me know what you think of this or if you think I made a mistake. Also, if there are any other approaches that balance the required input (minimal) to accuracy/usefulness (somewhat) I would very much like to hear about it.
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