Laboratory 3 Part II: Heat Sink Design Beauty Is Only Fin Deep: Bobby Edwards, Ian Garcia­Doty, Mack Montgomery

Abstract: Our motivation in this lab was to take the step from heat sink analysis to heat sink design and production. In part 1 of the lab, we learned basics about heat sink design and were able to create a model of a single pin fin. For this part of the lab, we created a more advanced model that took the whole banks of pins into consideration. This model was made in Excel, and we were able to maximize pin size and spacing to make the best heat sink possible. Our main findings were that changing the dependent variables (i.e. pin height, number of pins in a row, etc.) had diminishing returns on lowering the thermal resistance of the heat sink. Heat Sink Design Process

Our first instinct was to look online and see what leading industrial heat sinks looked like. We perused a number of academic papers analyzing heat sink design. From this, we set our eyes on a splayed fin design with many tall pins. Because it was ambiguous whether staggered or inline spacing would be better, we left this in line in our original proposal but were open to change based on what our model said. With our original design paradigm set, we then turned to our model to decide the specifics.

We originally based our model design off the banked tube correlations given in Incropera & Dewitt, modeling each row as a separate bank and the exposed base plate area as a simple flat plate. Because we knew it would be difficult to precisely fit the pins we initially decided the pins would be in an evenly spaced square grid. Holding temperature and air speed constant, and setting the spacing as a function of the number of pins, we then optimized the number of rows, pins per row, and length of the pins. More pins would allow for more conduction but would lead to decreased airflow due to the tighter spacing and shorter pin lengths. Conversely fewer pins spaced farther apart would increase airflow around each pin, but overall there would be less surface area to convect heat away from the heat sink. Using Excel’s Solver function with the size of the baseplate and the length of the metal rods we were given were used as constraints we concluded that 6 rows of 5 pins each was the best solution, with the pins cut as long as possible. While our model assumed uniform temperature we knew that the center of base would likely be the hottest, so we arranged the pins in decreasing thickness away from the centerline of the heat sink.

However, while trying to optimize the pin spacing we realized that the textbook correlations do not correctly account for the decrease in mass flow when pins were placed closer together, resulting in wildly inaccurate predictions as the spacing became smaller. This made it impossible to use the model to optimize spacing so we reverted to the model used in the first part of lab 3,where the pins were assumed to be adiabatic and the heat transfer coefficient of each pin was calculated individually. We had already cut the pins to size at this point so we kept the arrangement of rows of five and used Solver once again to optimize the spacing, with appropriate constraints so that the pins neither overlapped nor went beyond the bounds of the base plate.

Manufacturing led to two more necessary design changes. One was to forgo splaying our pins. This would have been intensely challenging to implement given our time and tooling resources. The other was to shorten the length of our smallest diameter pins, because we had challenges with them buckling during press fitting.

Modeling Assumptions ­Air velocity remains constant throughout heat sink. ­Steady state, incompressible flow. ­The temperature over the entire heat sink is the same as the temperature measured by the thermocouple. ­Contact resistances are negligible. ­Radiation effects are negligible. ­Negligible differences in air properties between inlet and outlet temperature. ­No heat escapes from the side of the baseplate. ­All heat from the heater conducts upwards through the baseplate. Predicted and Actual Results Plots of predicted results

This plot extends the preceding graph to show how, in our model, thermal resistance eventually increases if too many pins are placed in a row

Both models significantly underestimated the thermal resistance of the heat sink. This is likely due to an errant assumption in our models. For example our less than ideal manufacturing process likely introduced significant contact resistance. Additionally, determining the heat transfer row by row for both models ignored the more complex airflow that probably occurred in real life. One curious result is that the Lab 3 prediction for just 6 pins in crossflow was within 1% of the actual value for our heat sink, as seen in the last graph. Further tests could determine if and when this approximation could be used to evaluate a heat sink design. Manufacturing Process and Design Evolution: Originally, we planned to create a splayed fin design (shown below) so that we could fit more fin surface area into the design constraints.

Splayed design that we initially had decided to build

However, when we started the manufacturing stage, it was apparent that this wouldn’t be possible given the limitations of our tools. Thus, we decided to simply build our optimized design with straight pins. As for the actual manufacturing, we first drilled holes through the base plate, then had to turn the pins using a lathe in order to match a pin to a hole. We then attempted to press fit the fins, but started having trouble with the thinnest pins. We couldn’t

get a nice tight fit without the pins buckling which caused us to make the decision to shorten the pins to an arbitrary length of around ¾ their original size, which helped with the buckling for the most part (a couple pins were mangled). Although our heat sink wasn’t as pretty as others, we attributed our fairly strong performance to our tight press­fitting job, which limited contact resistances between the pins and the base plate. Design Features:

There are a number of components to our design. Our spacing and number of pins were

determined by our model, and consist of a 6x5 pattern with interesting offset spacing.

The model also encouraged us to use the maximum length of pin as we could by the design constraints, which we did, except for an impromptu shortening of the 3/16” diameter pins due to the high risk of buckling them by press fitting when they were full length. As is, we still did buckle some. We used a variety of pin diameters. While we felt this gave us a good variety of surface area/volume ratios, and in the end was helpful, it was partly out of necessity because of the strict limit on material usage to what we were given. We placed the larger fins toward the middle on the intuition that the middle of the heat sink base would convect less, and thus we need the enhanced conduction that a larger volume pin would provide. Our base and pins were largely unmodified outside of work to get them to fit together; while we did roughen the top of the base and smooth out the bottom, we felt that we didn’t have sufficient time or

machining skill to attempt much more. Our focus was to optimize the main factors of number, location, and size of pins, and let the design matter more than machining. Experimental Setup: Testing took place in a wind chamber. We placed our heat sink on a thermal pad covered in thermal grease to reduce contact resistance and connected a thermocouple to the backside of the base plate to read the temperature. An anemometer was used to help set the wind speed to 4.5 m/s, which blew perpendicular to the heat sink. After turning everything on, we allowed the system to come to equilibrium, which was determined when the temperature reading hadn’t changed in 45 seconds. This lab setup guaranteed a few sources of uncertainty in our readings. Mainly, we weren’t exactly sure if all of the heat was being transferred directly to the base plate (i.e. some of the heat could’ve escaped through the sides of the heat sink or there could’ve been some air between the thermal pad and the heat sink). However, I think that these errors are very small due to the even spreading of thermal grease and the accurate placing of the heat sink. After all, heat sinks that operate in computers have to overcome these same issues. Conclusion: From a manufacturing standpoint, we can conclude that a human should never be trusted to build a heat sink; the heat sink is much more efficient when we entrust production to a machine. Press­fitting by hand seriously affects the contact resistance between the pins and the base plate. Additionally, human error is always a factor. One mistake we made that could have seriously affected our testing outcome is to have put our thermocouple hole in the wrong face, making air flow during testing perpendicular to our design intention. Looking at it purely through analysis, our biggest conclusion was our idea of diminishing returns. We had limited materials and spots to place materials, so we had to choose a number of pins per row and pin length that would place us on the portion of our analytical graphs where we could get large marginal gains. This is important in design of computer heat sinks because the volume in which engineers must fit these heat sinks is so small. There a number of changes which we could potentially make to future designs for testing. In this iteration, we assumed the highest temperature of the base would be towards the middle of the base (in the x­direction, if the y­direction is parallel to airflow and z­direction is the direction the pins are pointing). Because of this assumption, we chose to put our largest diameter pins in the middle of the base. However, perhaps they would have been more efficient in reducing thermal resistance toward the outsides of the base, as shown in the model below. (Note the thermocouple is in the correct location in this picture, as well).

One other change the below model incorporates is using inline spacing between pins, rather than the odd offset pattern in our original as dictated by our spacing calculations. We read a number of academic papers on heat sink design before creating our design, but in the end we relied on our model. One paper we read suggested that staggered heat sinks had a higher heat transfer coefficient, while another we read suggested that staggered heat sinks had higher entropy generation than inline heat sinks (and were thus less efficient). Because of the confusion here, and the very odd, interesting pattern of pins our spacing calculations led to, it would informative to try an alternative. In the future, it would also be informative to try to calculate the fluid mechanics of flow around our original heat sink to see how fin spacing may have affected the airflow, from which we could draw conclusions about how it might be affecting thermal resistance. Lastly, as mentioned previously modeling each row as a single pin in crossflow led to a result very similar to our experimental value. The Incropera & Dewitt model uses a similar approximation for cases with small Reynolds numbers, however our result suggests that there might be other situations where this model is applicable, which would be worth exploring in further testing.