Heat Sink Optimization and Design
The goal of this project was to design a heat sink which would be used to cool electronic components. Given a series of requirements, we performed basic analysis using resistance networks to estimate the maximum thermal resistance of our optimal heat sink and used this value to select a commercial heat sink. While trying to minimize cost, we performed algorithmic calculations to calculate the geometry of the heat sink. As a result of the calculations we were able to create an optimized pin finned heat sink which was extremely cheap and met all our criteria. After modeling both commercial and experimental heat sinks on SolidWorks, thermal analysis was performed on COMSOL to provide theoretical values which could be used validate our calculations.
Based on the results of the project, we learned of the importance of performing CFD analysis prior to testing heat sinks in real life. Commercial sites will often make many assumptions to the benefit of their product which allow for discrepancies in perceived and actual values. From our experiment, we learned that the commercial heat sink was not able to dissipate the required amount of heat which it had stated online, which would have caused our electronic component of over heat. This result also aligns with the CFD analysis we performed which stated that the component would exceed the specified heat criteria.
Introduction
Modern electronics contain very small processors that are capable of producing immense amounts of heat. To dissipate the heat created by these processors, most electronic devices contain a component known as a heat sink. This device is one of the most common means of thermal management in modern technology and is utilized to increase heat flow away from electronic components (“What are Heat Sinks?”, 2019). Heat sinks work by dispersing heat over a larger surface area allowing the device or heated part to cool rapidly. It is able to do this through the use of heat fins. As air flows past the fins, the heat is pulled away by the air currents, therefore, the efficiency of the heat sinks geometric and material characteristics of its fins. In this report, we discuss the calculations for fin geometry and find the optimal heat sink design for the criteria specified below:
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The heat sink base dimensions must not exceed 2 in. on a side. The heater to which it will be mounted is a 4 in square aluminum plate (a CAD model will be provided).
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The temperature of the base of the heater, in the geometric center, must be maintained at less than 80 C when the power dissipation from the heater is 15 W. This temperature is to be experimentally measured at the interface between the heat sink and the flat base.
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The height of the heat sink fins must not exceed 75 mm.
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Only natural convection is used for cooling (at room temperature).
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The heat exchanger must be made from common engineering materials.
Based on our coursework thus far, we know that heat sinks need large amounts of surface area to work effectively. We assume our heat sink might have a rectangular or pin fin design to maximize heat dissipation from the device. We will test this theory in our design of the heat sink and once we’ve designed our heat sink. Additionally, given our list of criteria, there are many feasible options that meet our constraints, but not all of the designs might be considered optimal for our purposes. The factor by which we will determine whether a heat sink will be optimal or not, is the cost.
Conceptual Design
The first step taken in the design process is to determine which type of geometries could be chosen for our optimal fin design. As stated before, because heat dissipation is directly correlated to surface area, we can assume that the straight rectangular fins and pin fins will give us the best result. However, according to a research paper by Antonios I.Zografos and J.Edward Sunderland, it was determined that, “for the same surface area, pin fins can transfer considerably more energy than straight fins”(Zografos and Edward Sunderland 1990, 440-449). According to the journal article, the authors suggest that the most important parameter that influences heat transfer in pin fins is the center-to-center spacing between the pin fins. Keeping these things in mind, we can begin with designing our pin fin heat sink.
In order to design the optimal heat sink, we start by calculating the target thermal resistance. This thermal resistance will help us determine the range of heat sinks that are suitable for our given constraints.
This equation states that the total resistance is equal to the contact resistance plus the fin resistance. Since we know that the contact resistance is 0.5*10^-4 Cm^2/W, the temperature difference is 58C, and the power dissipation is 15W, we can use these things to calculate what the fin resistance should be. To come up with an optimal design for our heat sink, we use an algorithmic approach to calculate the geometry of a single pin fin, while minimizing material costs. This approach is commonly used in the engineering industry to find solution to a problem that has a variety of constraints and a wide range of possible values. The procedure is executed iteratively by comparing solutions until a solution is found that meets all the criteria and maximizes or minimizes an objective function. For our heat sink, we will be using a Monte Carlo optimization which is a simulation technique that creates an array of randomly generated values to get a range of solutions between specified ranges of criteria.
In this optimization problem, our decision variables are the diameter and height of each pin fin, as well as the spacing between pin fins on the heat sink. Our objective function is derived from the resistances of the heat sink and the contact resistance. Since we know the power dissipation from the heater and the temperature of the heat sink, we can calculate the required maximum resistance that our heat sink must have. We can use this value to eliminate all the heat sinks which do not have a lower resistance value, giving us our feasible solutions. In order to find the most optimal of this array of solutions, we find the value with the lowest costs, and from this, we can obtain a specific set of optimal values we can use to design our optimal heat sink. The costs are determined by material weight. For our heat sink, we will be using aluminum, as the material is cheaper than copper and is commonly used in heat sinks. A graph which shows the distribution of solutions for our heat sink using the Monte Carlo method can be seen below.
From the optimization, we designed a heat sink with following characteristics: a diameter of 1.078 mm, a height of 38.351 mm, spacing of 3.9299 mm, 100 pin fins, and a cost of $0.039242.
We needed some sort of way to test the resistance value calculated above and determine how our optimal heat sink would compete with other models in the market. Using 3.87 °C/W as our maximum thermal resistance, we looked on Digi key to find a compatible heat sink and settled on the BGAH425-125E heat sink manufactured by Ohmite which has a thermal resistance of 2.50 °C/W, with natural convection. Because the thermal resistance of this heat sink is lower than our maximum thermal resistance value, we can assume that the BGAH425-125E will be able to dissipate more heat than our optimized pin finned heat sink.
Experimental Validation
In order to test the validity of the values on the Digi key website, we purchased the BGAH425-125E heat sink and simulated the conditions of a heated chip to test the heat dissipation of the heat sink. We were able to replicate these conditions by using a temperature controller and a hot plate which was set to create a heat flux of 15W. On the hot plate, was a thermocouple that was press fit into the plate which allowed us to get the most accurate temperature reading at the heat sink and plate interface.
When performing the lab, we had to first apply thermal paste onto the bottom of the heat sink before attaching the heat sink onto the hot plate. The thermal paste is a thermal compound that is applied between the heat sink and the electronic component to eliminate the air gaps in the contact area, maximizing heat dissipation. Once the thermal paste had been applied, the heat sink is placed on the preheated hot plate and the thermocouple reads off the temperature at the interface. We allowed the heat sink to reach an equilibrium state before taking down any temperature readings and took a thermal image of the experimental setup which can be found below.
According to the temperature reading on the thermocouple, as well as on the infrared image, it was clear that our heat sink did not have the thermal resistance stated on the website. From the experimental data, we can calculate that the commercial heat sink had an actual thermal resistance of 4.427 C/W which exceeds the maximum thermal resistance we calculated above and explains why the temperature at the interface exceeded our 80 temperature criteria. As a result, our next step was to perform CFD analysis to figure out whether our issue was with heat sink or our experimental procedure.
Detailed Design
From the optimized heat sink we designed using the Monte Carlo method, we designed a CFD model to perform a thermal analysis. This model has a diameter of 1.08 mm, height of 38.35 mm, spacing of 3.93 mm, and 100 fins. The heatsink was modeled as a steady state model with a constant heat flux boundary condition of 15W on the bottom of the heat sink and natural external convection on all of the walls and pins. From the analysis we get the following results:
From the 3D plot, we can see that the heat sink is quite effective at dissipating heat. The maximum temperature at the bottom of the heat sink is 78.85 C and according to the model, the heat flux of the heat sink is 23.38 W. In order to confirm the validity of the results, a mesh independence study was performed whose results can be found in Appendix B. Thus, through this CFD analysis, we can see that the optimal heat sink meets our project criteria.
The same CFD analysis was performed with the Ohmite BGAH425-125E heat sink, which had a proposed natural thermal resistance of 2.5 C/W. The heatsink was modeled as a steady state model with a constant heat flux boundary condition of 15W on the bottom of the heat sink and natural external convection on all of the walls of the heat sink.The results of our analysis are shown below.
From the 3D plot, we can see that the commercial heat sink is not nearly as effective at dissipating heat as the optimal heat sink was. Though the heat flux of the heat sink is 25.21W, the maximum temperature at the bottom of the heat sink is 87.6 C which does not meet our project criteria. This supports our experiment which showed that the temperature of the heat sink in our given scenario would be closer to 88.4 C.
Economic Analysis
According to our monte carlo analysis, the cost of the heat sink is $0.039242. However, it is important to keep in mind that this cost only accounts for material costs and doesn’t account for other costs which might include manufacturing and processing time. Due to the geometry of pin finned heat sinks, they can be very hard to manufacture, especially when many fins are involved and the diameters or spacing of the fins are small. The calculation for the cost of our optimal heat sink was from the price per weight value of aluminum which we found to be $2.39/Kg. Our optimal heat fin had a weight of 16.42g which is only 6.18g less than the weight of the commercial heat sink. The cost of our commercial fin is $6.54, which may seem excessive, but like our optimal heat sink, this heat sink also has an extremely complicated geometry. The angles of the rectangular fins as well as their thicknesses are intricacies that might not be easily manufacturable.
Final Reccomendations and Conclusions
The results of this lab show us the importance of theoretical models, prior to purchasing commercial thermal management components. The use of CFD programs like COMSOL help to provide accurate models which give us insight as to how commercial components may perform in real life. Our algorithmic modeling on MATLAB resulted in a heat sink that proved to be more effective, and possibly cheaper, than the model which we purchased online. This also supports Antonios I.Zografos and J.Edward Sunderland’s article which describes the efficiency of pin finned and straight rectangular finned heat sinks. Moving forward, it may be interesting to perform similar analyses on heat sinks which use parabolic fins or triangular fins, which may improve efficiency and reduce costs. Another analysis we could perform, is to find out what the optimal height of our pin fins should be. The 3D plot of our optimized pin finned heat sink shows that the pins reach ambient temperatures relatively quickly. By decreasing the length of our pins, we could dramatically reduce the cost of our fins and also improve fin efficiency.