{"id":523,"date":"2013-02-17T16:55:32","date_gmt":"2013-02-17T22:55:32","guid":{"rendered":"http:\/\/tonykordyban.com\/?page_id=523"},"modified":"2014-04-13T20:28:39","modified_gmt":"2014-04-14T01:28:39","slug":"everything-you-know-is-wrong-september-2003","status":"publish","type":"page","link":"http:\/\/tonykordyban.com\/?page_id=523","title":{"rendered":"Everything You Know Is Wrong September 2003"},"content":{"rendered":"

 <\/p>\n

Answers to those Doggone Thermal Design Questions<\/strong><\/p>\n

By Tony Kordyban<\/strong><\/p>\n

Copyright by Tony Kordyban 2003<\/p>\n

Dear Tony,<\/em><\/p>\n

Currently I use a finite element analysis (FEA) tool for thermal design of our electronic products.\u00a0 To design a heat sink, I only need to input average Heat Transfer Coefficient, h, for the convection boundary condition on heat sink flow areas, and then the whole thermal model is numerically solved.\u00a0 I don’t have a CFD tool available, so I use empirical formulas to hand calculate h.\u00a0 But I’m not sure I’m using the right equations to do that.\u00a0 Our product design heavily relies on the thermal simulation because of the lack of experimental tools.<\/em><\/p>\n

For a pin fin heat sink I use the empirical equations for flow across tube banks from “Heat Transfer” by J.P. Holman, to take into account the effect of multiple rows of pins.\u00a0 Do you think this is good enough or you can recommend better literature for me to use?<\/em><\/p>\n

For a plate fin heat sink, I use the equation in the same book for fully developed laminar flow in rectangular ducts.\u00a0 The Heat Transfer Coefficient “h” for pin fins is several times higher than plate fins.\u00a0 I believe pin fins should perform better because pins can generate turbulence in surrounding air.\u00a0 But I’ve been told by different people that pin fin sinks always looks better in simulation but in real life a plate sink is better (of course, if air flow direction is known).\u00a0 What do you think about this?\u00a0 If it’s true, the critical thing is, should I “downgrade” pin fin results or “upgrade” plate fin result in modeling?\u00a0<\/em><\/p>\n

Pinned to the Mat in Matteson\u00a0<\/em><\/p>\n

 <\/p>\n

Dear Pinned,<\/p>\n

You don’t have CFD, and you don’t have any experimental facilities.\u00a0 You are in trouble.\u00a0 I am glad that you found your way to J. P. Holman at least.\u00a0 Unfortunately, that text will probably not do you much good in this case either.<\/p>\n

What correlation from the extensive heat transfer literature would be best from estimating convective coefficient for a pin fin heat sink?\u00a0 Maybe you will be surprised at the answer I give later.\u00a0 For now, to build up a little suspense, let’s discuss the correlations you already mentioned.<\/p>\n

Which correlation gives a more realistic value of “h” for a pin fin sink:\u00a0 the one for flow across a bundle of tubes, or the one for laminar flow in a rectangular duct?\u00a0 They give very different values, so if one is right and the other wrong, it is important to know.\u00a0 If the tube bundle correlation is valid, then you should always use pin fins, because “h” is so much higher than for a plate fin sink of the same size and surface area.<\/p>\n

When applying a correlation from literature, one very important thing to keep in mind is similarity.\u00a0 The researchers went to a lot of trouble to non-dimesionalize their equations so that you don’t have to have the same fluid, the same dimensions, or the same velocity that they used to derive the equation.\u00a0 Some people say that they write their equations using Nusselt and Reynolds numbers just to confuse the ordinary engineer and make themselves seem smarter than everybody else.\u00a0 Maybe that is true, but it does allow the correlation to be used for a much wider range of problems.\u00a0 But for the correlation to be valid, you must have similar geometry, and a similar flow pattern.\u00a0 You shouldn’t use the correlation for a flat plate to find “h” for a sphere, for example.\u00a0 And an equation for laminar flow isn’t good for a turbulent flow problem, of course.<\/i><\/p>\n

\"pinfin3\"<\/a>Flow through a pin fin sink at least superficially is similar to flow through bundles or banks of tubes.\u00a0 The bundles these correlations were developed for were the pipes carrying feedwater into coal-fired boilers.\u00a0 These tubes were very big, very long, and the temperature gradient was very large compared to pin fin sinks.\u00a0 One of the basic assumptions in tube bundle correlations is that the tubes are infinitely long in the direction perpendicular to the flow (or at least very, very long compared to the diameter and spacing of the tubes in the bundle.)\u00a0 With infinitely long tubes, the flow through them is 2-dimensional.\u00a0 The flow zig-zags around each tube, but there is no flow in the direction parallel to the tubes.<\/p>\n

The pins in a pin fin sink are not very infinite.\u00a0 One end of the pins terminate in the base of the sink.\u00a0 At the other end of the pins, the flow is open to the atmosphere.\u00a0 Air is free to flow parallel to the pins and leak out the top of the heat sink.\u00a0 Nothing forces the flow to stay inside the field of pins if the flow restriction is too high.\u00a0 For that reason, I think there is not enough similarity in the flow pattern to use the correlation for bundles of tubes.<\/p>\n

What about the correlation for flow in a duct?\u00a0 If the pin fins are in-line, the channels between the fins might act like ducts.\u00a0 Obviously this wouldn’t work if the pins were staggered so that the flow is not in a straight line.\u00a0 The pin fin sink seems to be more like duct flow than flow through bundles of infinitely long tubes.\u00a0 But there are still some problems with similarity, which you have probably noticed.\u00a0 The “walls” of the ducts, or flow channels, are not continuous, but are regularly broken by the gaps between the pins in the flow direction.\u00a0 So the boundary layer doesn’t build up along those “walls” the way it would in a smooth duct.<\/p>\n

And even though we don’t need the duct to be infinite in any direction for its correlation to apply, we still have the problem of the open “top” of the heat sink.\u00a0 Flow is not confined to the duct, and can leak out.\u00a0 For those two reasons, the flow pattern through a pin fin sink is probably not similar to duct flow.\u00a0 Not similar enough to justify using laminar flow duct correlations.<\/p>\n

\"pinfin1\"<\/a>The same problem exists for the correlations for flat plates.\u00a0 The flow pattern is likely not similar enough.\u00a0 Once you have eliminated flow over cylinders, tube bundles, flat plates, and through ducts, you have exhausted the classical literature.\u00a0 I don’t think you are going to find any papers giving correlations for “flow through stubby cylinders with a closed wall on one side and open leakage path on the other, with flow bypass allowed”.<\/p>\n

Let’s take a look at how much variation there is between the different correlations that you might try with a heat sink.\u00a0 I picked a pin fin sink from a vendor catalog, one that had an \"pinfin4\"<\/a>equivalent plate fin version for comparison.\u00a0 (In reality, the pin fin sink is made by machining cross-cuts into the extruded plate fin sink.)<\/span><\/p>\n

I have plotted the heat sink thermal resistance as a function of the approaching air velocity.\u00a0 For a change, I have not given the equations and the values of air properties that were used in the calculations.\u00a0 If you are interested, look in Chapter 5 of Holman.\u00a0 I know we were talking about “h”, but I have plotted thermal resistance R, which is 1\/(h A).\u00a0 I did that because the vendor gave the thermal resistance curves for the heat sinks, not “h”.\u00a0 This brings up the question, “What is the surface area of a pin fin sink?”\u00a0 Should you count all the area of all the pins, or only the “effective” area, that which is in contact with the air flow?\u00a0 That all depends on how the correlation was derived.\u00a0 If you are using tube bundles, you should use all the pin surface area.\u00a0 For duct flow, probably only the duct “wall area”.\u00a0 Or maybe not.\u00a0 It is all debatable.<\/p>\n

Anyway, notice the huge range of thermal resistance.\u00a0 The tube bundle prediction is very different from the results for flat plate or duct flow.\u00a0 And they are all way off from the published values for thermal resistance from the vendor.\u00a0 We can’t blame this on the vendor trying to exaggerate the performance of their products, because they give much higher thermal resistance values than the correlations predict.<\/i><\/p>\n

 <\/p>\n

\"pinfin5\"<\/a>I made the same calculations for a different heat sink.\u00a0 It has the same number of pins, but they are much shorter, and the base is larger.<\/p>\n

Note the correlations are still off, although the duct flow correlation comes closer for this design.\u00a0 The most interesting thing I notice is that the vendor thinks that pin fin and plate fin<\/p>\n

sinks of the same geometry have very similar thermal resistances.\u00a0 The pin fin sink is slightly better in both cases.\u00a0 But at least in these graphs, there does not seem to be a very strong reason to use a pin fin in place of a plate fin sink, unless the flow direction is not known.<\/p>\n

\"pinfin6\"<\/a>The vendor data does not support the idea that “h” for pin fins is many times higher than the equivalent plate fins, as the tube bundle correlation suggests.<\/p>\n

Here are some lessons learned, admittedly from a very small number of examples:<\/p>\n