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Driving the motors on cars, trains, and other electric transportation systems, power modules operate at high voltage and high current — so they get hot. Keeping these modules cool might mean that their case temperature doesn't exceed 150°F, to avoid system failure or semiconductor performance degradation. Understanding the total cooling system is critical to the overall proper design. As IGBTs and Power MOSFETS increase in power capabilities, the heat generated by these components also increases. The overall target is to create the smallest heat exchanger with the lowest R_{θJA} value. The total system includes the total heat to be removed, the system flow impedance model, and the thermal resistance schematics.
The objective here is to describe the effects of heat exchanger variables on the overall heat transfer coefficient of the design. In the heat exchanger design, there are many factors to consider such as the fin thickness, fin width, fin length, and fin pitch. All these variables contribute to the overall heat transfer ability of the component when supplied with a forced air system. The compact heat exchanger is a significant component to design when coupled to an air delivery system.
Prior to starting the calculations, you should generate a table listing necessary data and design considerations (Table 1). In this table, the foremost requirement is “How much TOTAL power must be removed?” You can accomplish this by taking the system bill of materials and supplying each component with a heat dissipated value. If we simplify the condition to only three IGBTs mounted on the heat exchanger, we can proceed with the development process. This simplification ignores the contribution the other components make and should be examined on an individual basis. Additional information required includes:
 What is the maximum temperature rise of the air?
 What is the maximum inlet temperature?
 Are there any dimensional constraints for the heat exchanger in the system?
 Is there a size and location restriction on the fans?
 Is there a noise restriction on the fans?
Answers to these questions will indicate the advantages to making a tradeoff between fin thickness, fin height, and fan size and performance.
The mass flow rate of air needed to remove the given amount of heat is:
Where: m_{dot} = Mass flow rate of air
P_{total} = Dissipated power in watts
ΔT_{air} = Allowable rise in temperature of the incoming air; typically 10°C.
Cp = Specific heat of air; 0.24 BTU/(lb × °F)
Given 1250W of heat are to be removed and a limit to 10°C temperature rise, with the worst case inlet temperature of 55°C, the required air flow rate is calculated to be 235 cfm. From Equation (1), on page 15, if more air is supplied, increased m_{dot}, the required temperature rise is lower, and if less air is supplied, decreased m_{dot}, the required temperature rise is higher.
Select a fan with a free flow rate of 450 cfm, based on the required flow rate and knowledge that the fan performance plotted against the system flow impedance curves dictate the system operating point. Fans in series have different performance curves than fans in parallel. Housing geometry and fan controller cards and increasing complexity are added with the addition of multiple fan systems. You can make the final selection after completing the system flow impedance model.
You can calculate the total system flow impedance by the changing geometry sections of airflow path dimension, duct turns, and component interference. Fig. 1 shows the system flow impedance model. Once you establish the layout, the question becomes “how does the different compact heat exchanger variables effect the overall system thermal resistance?”
Let's focus only on the heat exchanger and see how the overall system performs as some variables are iterated. As you increase the number of fins, you increase the heat transfer surface area; however, you also increase the system flow impedance. With the increased flow impedance, you have less air to absorb the heat and higher pressure drops across the core of the heat exchanger. The following equation governs the pressure drop for a compact heat exchanger from W.M. Kays & A.L. London ^{[1]}.
Where:
ΔP = Change in pressure across core
G = Mass velocity
gc = Gravitational constant = 32.174 ft. lb/lbf × sec^{2}
v1, v2 = Specific volume at points 1 and 2
vm = Mean specific volume = (v1 + v2)/2
kc = Contraction loss coefficient ^{[1]}
ke = Expansion loss coefficient
f = Mean friction loss
A = Heat exchanger total heat transfer area
Ac = Heat exchanger minimum free flow area
Afr = Heat exchanger total frontal area
σ = Ratio of free flow area to the total frontal area = Ac/Afr
w = mass flow rate
Using fin thickness, pitch, height, and length as variables, you can review heat exchanger designs. Placing the variables into an equation where you calculate the pressure drop, you can generate the following plots.
Fig. 2 illustrates the effect of increasing the number of fins per inch (fin pitch) on the pressure drop of the system. The arrow indicates the increasing fin thickness variable on the overall system flow impedance curve. As the fin thickness increases for a given fin pitch, the pressure drop increases. Increasing the fin thickness increases the frontal area and blocks the air passage for a unit width.
The arrow in Fig. 3, on page 18, indicates the increasing fin length variable on the overall system flow impedance curve. Increase in length increases the surface area for heat transfer, which increases the skin friction flow impedance.
In Fig. 4, the arrow indicates the increasing fin height variable on the overall system flow impedance curve. As the height opens up, more air can flow down each channel of the heat exchanger, which lowers the flow impedance.
With the system flow impedance calculations plotted against a specific fan curve, you can obtain the system operating point:
Where:
ΔP = Pressure change
R = Flow impedance
CFM = Cubic feet/minute
In Fig. 5, the system flow impedance curves are plotted over the selected fan performance curve. The intersection of the two curves gives the system operating point. From the initial requirement of 235 cfm of air to cool the IGBTs, some heat exchangers don't meet the flow requirement. This results in an increased temperature rise for the lower amount of air and an increased temperature for the junction of the IGBT die. Increasing the height of the heat exchanger reduces the flow impedance as seen from Fig. 4.
You can obtain the convective heat transfer coefficient from the operating point. This makes it possible to calculate the thermal impedance of the compact heat exchanger from basetobulk temperature of the air.
Where:
η = fin efficiency
h = convective heat transfer coefficient
A_{core} = heat exchanger core heat transfer area.
Fig. 6 is the system's thermal impedance model showing R_{θ} junction to case, case to grease, grease to plate, plate to base, base to core, and core to bulk air. These are general values used to calculate the overall thermal impedance.
Fin efficiency is a function of the convective heat transfer coefficient, fin perimeter, fin height, thermal conductivity of the material, and fin cross sectional area. The convective heat transfer coefficient is a function of the Prandtl Number, Stanton Number, specific heat of the air, and the mass airflow through the heat exchanger core. These variables are constant and don't significantly affect the plots. Fig. 7 indicates how the overall thermal impedance varies with increasing fin pitch as the fin thickness increases.
Thinner fins are necessary at finer pitches, which allow needed air through to cool the electronics. At the wider fin spaces, 20 fins per inch, thicker fins have lower R_{θ} values. Conduction helps get the heat to the extreme ends of the fins. The arrow indicates increasing fin thickness. The area of interest is at 60 fins per inch.
Fig. 8 indicates how increasing the fin length changes the overall values. Increasing the length helps lower the values by increasing the heat transfer surface area. Fig. 9 plots the thermal impedance curves for increasing fin height.
Table 2 shows how the thermal impedance values change as each variable increases. Increasing the length has the most significant advantage. Once the length is maximized in a design, you can ask this tradeoff question: Which is better, fin thickness or fin pitch for a fixed heat exchanger width? The second tradeoff is between baseplate thickness and maximum fin height.
After selecting fin pitch, thickness, and length, the final problem is that the resulting flow impedance value dictates the mass air flow rate. This relates back to the ability of the air to remove the heat — specifically the rise in temperature due to the velocity of the air. Fig. 10 shows that for a given fin pitch changing the fin thickness increases the rise in temperature due to the increased flow impedance blocking the fan's capacity to push air through the design.
Increasing the length (Fig. 11) doesn't significantly affect the flow impedance, therefore the temperature doesn't vary much between length comparisons when based on the mass flow rate of the air through the system.
Fig. 12 demonstrates how increasing fin height increases mass airflow and reduces the temperature rise of the air.
Looking at the graphs, you'll find possible solutions for the system. To optimize the heat exchanger, include all system variables — since they combine to affect the results in different magnitudes. From a fan performance perspective, the fan should operate at low pressure, high cubic feet per minute (CFM). One question to ask would be “Is the fan properly sized for the problem at hand?” From Figs. 7 to 9, on pages 20 and 22, the observation of “more fins is better” results in the higher flow impedance tradeoff for lower R_{θ} values. One possible solution is to add a second fan in series for high flow impedance heat exchangers. With the increased pressures, some increased flow rates are due to the intercept of the two curves at new ordinates. Fig. 13 plots the characteristics of two fans in series, and Fig. 14 is the curve for a single fan.
The R_{θja} (junction to air) is a nice value to have, but the lowest value may not necessarily be the best. This would require a very large fan to overcome the pressures of the packed heat exchanger. The next step is to ask what is an acceptable value by evenly dividing the temperature increases at each step of the thermal model as best as possible — where Fig. 15, on page 24, illustrates the temperatures at different locations from junction temperature T_{j} to the air temperature T_{a}. Charting the increasing temperatures will help display the way heat is transferred from the IGBT to the cooling air. Each system will need to be evaluated on the individual basis. The graphs give the designer the advantage of trading off critical system space for better heat exchanger results.
For individual cases, such as electric vehicles or UPSs for computer network stations, forced air convection compact heat exchangers offer efficient transfer of heat from the baseplate to the bulk air, as noted by the low R_{θ} platetoair values indicated in Table 2, on page 22. All heat exchanger designs must be followed up to actual system testing and validation. This tool offers insight as to where to trade off critical system volume, specifically fin length, height, and thickness. Increasing the heat exchanger width, and therefore the total number of fins is always a benefit. Fig. 16 illustrates the dimensions of the heatsink.
Using the calculations discussed in this article to correctly design a heatsink for power modules is essential for the life of your cooling system.
You can contact Joseph Ufnal by calling (508) 8543686.
References

Kays & London, “Compact Heat Exchangers.” 3^{rd} Edition.

J.P. Holman,” Heat Transfer,” 5^{th} Edition McGraw Hill.

I.E. Idelchik, “Handbook of Hydraulic Resistance,” 3^{rd} Edition.

Michael R. Lindeburg P.E., “EIT Reference Manual for Mechanical Engineer,” 8^{th} Edition.
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