# Evaluating performance of heat sink designs without finite element simulation

I have the opportunity to do a few metal 3D prints for just the material cost, and would like to experiment with the performance of heat sink designs (mostly for fun).

Since I have no experience designing heat sinks, I would say that the expected failure rate when just printing what I have in mind and testing it will be quite high, so I need a good way to evaluate the performance of a design before creating a prototype.

Now since this is just for my fun, I do not want to invest in pricey finite element simulation tools. I could not find anything free that is useful, since I think it has to take into account airflow and thermal radiation. How can I get an idea of how my design will perform before printing a prototype and without using finite element simulation?

I am planning on a 4 cm by 4 cm 120 W Peltier element (ceramic surface), the heat sink should be stainless steel, though I am hoping the relative performance of two heatsinks doesn't change with a different material (one day I hope I can use copper).

I am not so sure about temperature differential here but I am assuming 25 °C ambient temperature.

• Not an expert but just my ideas about your interesting project: Stainless conducts about $16\,[W/m\cdot k]$ whereas for example aluminium conducts $210$ and convection dynamics (to get it to the surrounding medium) depend more on geometry. I think optimizing for a relatively low conducting material will result different (more compact?) result that will likely not transfer to an other material. – Walter Feb 26 '15 at 17:11
• I'm not really sure about details but I'm afraid 3d-printed metal, which is in fact thermally fused metallic powder will have vastly different thermal properties from solid, machined metal. – SF. Feb 26 '15 at 18:30
• @SF: I have my doubts here, after all afaik they create titanalloy turbine blade parts because that process has less potential for structural defects – PlasmaHH Feb 26 '15 at 18:38
• @PlasmaHH But SF was not refering to structural, but to thermal properties! – Volker Siegel Feb 27 '15 at 5:23
• If Rth(Shape_A,Material_X) < Rth(Shape_B,Material_X) then almost always Rth(Shape_A,Material_Y) still_< Rth(Shape_B,Material_Y) ie shape dominates the general behaviour but material may fine tune it. | Exceptions (maybe not the only ones) will occur if eg design B is suboptimal in material X due to having long thermal paths from the heat input point to substantial radiating surfaces. Changing to material Y with higher thermal conductivity reduces the resistance out to the good radiator and allows it to perform better. A real world example may be adding a heat pipe as a "spreader" on a ... – Russell McMahon Feb 28 '15 at 1:03

First, to counter what some people are saying about printed metals, selective laser sintering can produce parts that are as thermally conductive as their base metals. They are limited only by porosity, and state of the art machines can produce fully-dense (zero porosity) metal parts.

Second, you probably don't need to take radiation into account because you are at low temperature and airflow is going to make a much bigger contribution than radiation.

Third, traditional heat sink design uses equations that calculate the temperature distribution along the fin from the root to the tip in order to come up with an "effective area" upon which an average convection coefficient can be imposed. This means that you aren't calculating the exact airflow, but rather using an average over the whole surface.

Any good heat transfer textbook will have formulas for many different fin shapes, including fins with a non-constant fin area. I personally like Incropera and DeWitt.

Nevertheless, if you design sufficiently complicated fins, the standard equations will break down. You then have three choices:

1. Approximate your fins with similar fins. This can lead to results that are close enough.
2. Simplify your design to make it fit an established pattern
3. Go to a full finite element simulation.

I would advise using number 1 or number 2 because they might be more accurate. It is easy to make subtle mistakes in finite element models that completely invalidate your results1, however if you do choose to go that route, you should know that there are free open-source FEM solvers (Elmer comes to mind).

And now some general tips:

• As others have noted, stainless steel is a bad conductor of heat. Aluminum is probably a much better choice, but unless you decide not to 3D print it, you probably can't use aluminum. This is the reason that I probably would print something else if I had access to a 3D printer
• The Coefficient of Performance of Peltier coolers is often less than one, so in order to get e.g. 20W of cooling power, you will need to put in more than 20W of electrical power. Your heat sink needs to dissipate the sum of the cooling power and the electrical power.

tl;dr: You can model heat sink designs without using FEM and as long as your designs are not too crazy, you will probably get good results. Traditional "by-hand" calculations don't take into account radiation and assume an average airflow over the whole surface, which is usually good enough. I personally would avoid making heat sinks at all and use your time on the 3D printer for better things.

1 Trust me, I'm a graduate student in Mechanical Engineering, and I've screwed up so many models.

• Great answer. I know about steel beeing bad, but it comes for me at a really low cost, for all other materials I would have to pay more than just the material. It would be nice if you could add a word to if one model performs better than another with steel, if this will be the same for e.g. copper. I did look at quite some FEM programs, but as I am not familiar with it, it seemed that many would not be able to properly model the airflow and heat flow at once. Can Elmer do this? – PlasmaHH Feb 26 '15 at 21:04
• If you aren't familiar with FEM programs, I would advise avoiding FEM entirely. (In fact, my advisor often recommends avoiding FEM even if you are familiar, and he did molecular dynamics in his grad work). Probably your best bet would be to use a simple fin design equation to get a good estimate, and then just give your actual design more surface area so that you know it will work. Fin design equations take material properties into account, so you should be fine there. – regdoug Feb 26 '15 at 21:47
• I take that as a "no it can't" then – PlasmaHH Feb 27 '15 at 0:09
• Actually, Elmer can model the heat transfer in the solid and the airflow around it simultaneously, but I don't know if you'll be able to get it to do what you want. FEM, CFD, and the like are very tricky. – regdoug Feb 27 '15 at 14:29
• It is something for fun and learning, and I have an excuse to play with FEM, something that was fascinating me for decades. There is no deadline, and producing something that performs well in FEM and fails miserably in real life is a learning experience too ;) – PlasmaHH Feb 27 '15 at 14:32

Some pointers:

1. It's first about surface area! But don't put the fins too close together or there is not enough space for natural convection to start... I read somewhere that ~0.25" (~6 mm) is a reasonable spacing.

2. Stainless steel is not a good choice. You want a metal with good thermal conductivity. Aluminum is just about perfect since it is also light. Copper would also work.

3. Heat sink design seems fairly mature to me, I'd copy other designs for a start.

• I know about point 2, but that is what I have available to play with. – PlasmaHH Feb 26 '15 at 20:59