Abstract
This article describes how Computational Fluid Dynamics (CFD) can help inthe selection and/or design of a heat sink for electronics cooling applications.CFD modeling complements the other tools in the thermal tool kit: calculationsbased on approximations and correlations; and experimental work. Whether theapplication includes single or multiple heat sinks, the visualization power ofCFD can help users to make better, faster design decisions than is possibleusing traditional methods.
Introduction
The performance of any heat sink is measured by the temperature differencebetween its base and the local ambient, normalized to the dissipated power. Thisperformance is a strong function of the operating environment. Accurateknowledge of the fluid (air) flow and temperature distribution around the heatsink is necessary to calculate the heat sink performance. When the heat sink isoperating inside a populated enclosure, it is not, in general, possible toestimate the fluid velocity and temperature with a reasonable degree ofconfidence. This is where Engineers can gain the greatest benefit by using CFD.CFD provides a visual and numerical description of the flow field andtemperature distribution in and around the heat sink inside the enclosure.
Step 1: System Level Calculations
Before beginning the modeling process, it is important to identify the goalsand the scope of the proposed analysis. Generally, the objective is to selectthe best of several designs, and to determine the air flow distribution in thesystem.
The air flow, after all, is what carries the heat away from the component;the heat sink just makes that process more efficient. In order to prevent themodel from becoming too large and requiring large computing resources, it isimportant to limit the scope of each model to a tractable size. At this stagethe Engineer needs to get a good idea of the air velocity and air temperaturethroughout the cabinet.
There are several important pieces of information the Engineer will needbefore starting on the system model. He/she must know the general configurationof the system, vent locations, fan size, its location and its performance curve.A system model must include any large blockages to the flow: power supplies,cables, connectors, cards, EMI filters and similar items. Smaller obstructionsmust be omitted or combined together into an average component height or alarger object with equivalent area.
The primary objective of this phase of the work is to obtain the local airvelocity and temperature upstream of the heat sink. In order to do that, thesystem resistance must be reasonably well modeled, so that the fan pulls theright volume flow rate. If the system air flow must maneuver around baffles andobstructions, details of the heat sink should be omitted, or a combinedrepresentation of the heat sink used. When developing the component model, theEngineer should use the air flow well upstream as the flow boundary condition.If the heat sink is likely to be the dominant obstruction, as for a high powerdissipation heat sink, he/she will need to make some assumptions about it andinclude a schematic representation of it in the system model. It could, forexample, simply be modeled as a flow resistance.
The velocity and temperature distribution in the system model can bepredicted without modeling many components in detail. An example of thisapproach would be to include air flow passages and vents, and distribute thepower dissipation uniformly. It is important to include any features that wouldrestrict air motion around the heat sink. It is also necessary to include anypower sources that would preheat air, and induce motion, around the heat sink.In passively cooled systems, CFD is even more valuable on account of its powerto handle the coupling between the momentum and energy equations. It isimportant to note that there may be time dependent phenomena which could keep asteady-state model from converging.
Step 2. Heat Sink Design
The most efficient way to design a heat sink is to perform an analysis basedon fully-developed flow correlations. Although the flow is not necessarilyfully-developed, as a design strategy it is easier to make that assumption. TheCFD modeling the Engineer will do later will show exactly how the flow isbehaving around the heat sink. Fully-developed flow analysis will follow thesame general trends, and in many applications, manufacturing constraints on theheat sink will limit the extent to which its performance can be improved. For anextruded heat sink, the fins are very efficient. It is sufficient then to use anaverage fin thickness for tapered fins.
To start the design, a reasonable expected value for the velocity betweenthe fins based on the air flow boundary conditions should be chosen. A geometrybased on typical manufacturing values should be used; these can be obtained fromvendor catalogs, or from Table 1.
| feature | extruded | bonded | folded |
| fin thickness | > 2 mm | > 1.3 mm | > 0.125 mm |
| fin height | > 75 mm | not limited | < 50 mm |
| aspect ratio* | < 6-8 | not limited | varies |
| * ~ fin height divided by fin spacing Table 1. Typical heat sink manufacturing constraints |
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The heat sink should be analyzed as a straight flow through straight,continuous fins. Applicable correlations for forced convection, fully developedlaminar flow in rectangular ducts are given in White, 1991. A good source forcorrelations applying to natural convection is Guyer, 1989. Pin fins can beapproximated quite well as continuous fins, unless the flow is angled relativeto the channel direction. In practice, the performance of dense rectangular pinfins is usually within 10% of a straight fin heat sink.
Step 3. Heat Sink Model
Once the Engineer has a general idea of the heat sink parameters design, andlocal air flow boundary conditions, he/she can build the heat sink detailedmodel. Some strategies to minimize the amount of work are to use symmetrywherever possible; to use whatever heat sink model building capabilities isoffered by the software; and to represent the heat dissipation area on the baseof the heat sink by a simple heat source.
Important areas to model are the fluid flow area near the heat sink surfacesand the approach areas. In the approach areas the Engineer needs to know whatthe flow behavior is, so it is important to model all the fluid around the heatsink, all the way to the nearest obstructions. Between the fins, or in any airspaces, the Engineer will need the velocity profiles to show the proper flowbehavior. Usually three cells are adequate for showing the correct trends forlaminar flow between surfaces.
Inside the solid material of the heat sink, one cell is usually sufficientin the fin thickness direction. At least four cells should be allowed for in thefin height direction to account for temperature difference along the fin height.For a very small source, at least three cells of approximately the same size asthe source should be allowed in the plane of the heat sink near the source. Atleast two cells should be used in the base thickness. These numbers must bemodified to ensure that the results given by the CFD software are sufficientlyindependent of the grid choice.
Now that the heat sink has been modeled in CFD, the temperature distributioncan be readily obtained. Problems to look for are areas of large temperaturegradient within the solid, indicating that the heat sink is too thin; sectionswhere the air temperature is close to the fin temperature (typically towards theback of the heat sink). This is caused by the air that may flow up and out ofthe heat sink; and cool fins, indicating that they are too far away from theheat source to have any effect. The combination of the temperature distributionand the air flow distribution will help the Engineer to decide what designchanges may be necessary in order to achieve the heat sink performance goals.The heat sink design then becomes an iterative process.
Now the process becomes iterative for the selection of the most promisingheat sink design. To understand its effect on the device junction temperature,the Engineer may then need to model the component and the interface material aswell as the surrounding board. This model will allow him/her to determine themaximum chip or junction temperature, which is, after all, the goal of the wholeexercise. When modeling the whole system, the interface resistance between thecomponent case and the heat sink should be included. Interface material vendorssupply this information typically as a resistivity, the resistance normalized tothe area. For advice on component modeling, consult the software or componentvendor. They may have ready-made models you can use to speed up the process. Tomodel the heat spreading ability of the board, the Engineer must concentrate onthe power plane layers in the plane of the board, since they usually dominate.If most of the air flow in contact with the board is on the side opposite thecomponent and heat sink, the Engineer will need to account for the thermalconductivity of the epoxy-glass layers as well.
Step 4. Verification
The next step is to verify the design experimentally by measuring the basetemperature relative to the local air temperature. It is important to ensurethat the measurement devices are in good thermal contact with the heat sink; anelectrical continuity check assures at least some thermal contact. It is alsoimportant to get an accurate value of the power being dissipated through theheat sink. Errors can be minimized by using a heater well insulated on the backside, and by taking voltage measurements as close to the heater as possible.
The Engineer should not be alarmed if the numerical results do not exactlymatch the measurements. The heat sink model was just a model. The experimentalprototype is also a model. The true performance of the heat sink is at bestbracketed by the errors inherent in both measuring and modeling. Also, the CFDmodel gives only an average temperature of a grid cell, whereas an experimentalmeasurement is really the temperature of the sensor that has been installed tomake the measurement. In the final analysis, the goal of the CFD work is to makea good design decision, and as long as the Engineer has represented the physicsof the problem correctly, the trends will be correct.
Summary
In order to use the power of CFD in the heat sink design process, it isnecessary to model the surrounding system adequately. Air flow pathconfigurations are as important as heat flow path details. Once the heat sink ismodeled, viewing the results helps to suggest effective design changes.Experimental validation provides valuable feedback on modeling. Even if theagreement between physical models and numerical models is not perfect, modelperformance trends should be represented well enough to shorten the total designcycle.
References
Guyer, E., editor, Handbook of Applied Thermal Design,McGraw-Hill, 1989. White, F. M., Heat and Mass Transfer, Addison-Wesley, 1991.
