如何计算散热器的散热功率

如何计算散热器的散热功率

Calculati on Corner

Estimati ng Parallel Plate-Fi n Heat Si nk Thermal Resista nee

Robert E. Simons , Associate Editor, IBM Corporation

As no ted previously in this colu mn, the trend of in creas ing electro nic module power is maki ng it more and more difficult to cool electro nic packages with air. As a result there are an in creas ing nu mber of applicati ons that require the use of forced con vect ion air-cooled heat sinks to con trol module temperature. An example of a widely used type of heat si nk is the parallel plate con figurati on show n in Figure 1.

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Figure 1. Parallel plate fin heat sink configuration.

In order to select the appropriate heat sink, the thermal designer must first determ ine the maximumallowable heat sink thermal resista nee. To do this it is necessary to know the maximum allowable module case

temperature, T case, the module power dissipation, P resista nee at the module-to-heat si nk in terface, R allowable temperature at the heat sink attachment by moq and the thermal int. The maximum

surface, T base, is

given

where T air-in , is the temperature of the cooli ng air at the in let to the heat sink

passages. At this point many thermal engineers will start looking at heat sink ven dor catalogs (or more likely today start searchi ng ven dors on the in ternet) to find a heat sink that will fit in the allowable space and provide a heat sink thermal resista nee, R hs , less tha n R max at some specified flow rate. In some cases, it may be useful to do a sizing to estimate R hs for various plate-fi n heat sink desig ns to determ ine if a feasible desig n con figurati on is possible. The rema in der of this article will provide the basic equations to do this. The thermal resistance of the heat sink is give n by

where h is the conv ective heat tran sfer coefficie nt, A base is the exposed base surface area between fins, N fin is the number of fins, 丨仙 is the fin efficie ncy, and A fin is the surface area per fin tak ing into acco unt both sides of the fin.

To proceed further it is n ecessary to establish the maximum allowable heat sink volume in terms of width, W, height, H, and len gth in the flow direct ion, L. It is also n ecessary to specify a fin thick ness, t fin . Using these parameters the gap, b, between the fins maybe determined from

The exposed base surface area may the n be determ ined from

r ba ^nmd R m t

The maximum allowable heat si nk resista nee, R ma 马

is the n give n by h 门

' bdse + tin r lfin 八 fin

and the heat tran sfer area per fin from

At this point it is necessary to specify the air flow rate either in terms of the average velocity, V, between the fins or a volumetric flow rate,

G. If a volumetric flow rate is used, the corresp onding air velocity betwee n the fins is

To determine the heat transfer coefficient acting upon the fins, an

equation developed by Teertstra et al. [1] relating Nusselt number, Nu, to Reyno Ids nu mber, Re, and Pr nu mber, Pr, maybe employed. This equatio n is

The Pran dtl nu mber is

where - is the dynamic viscosity of air, c P the specific heat of air at

con sta nt pressure, and k is the thermal con ductivity of air. The Reyno Ids nu mber used in (8) is a modified cha nnel Reyno Ids nu mber defi ned as

Rc ? P V「b上(HO

p L

where 1 is the density of air. Equation (8) is based upon a composite model spanning the developing to fully developed laminar flow regimes and was

For purposes of illustrati on these equati ons were used to estimate heat sink

thermal resistance for a 50 x 50 mm aluminum heat sink. The effect of increasing the fin height and the number of fins is shown in Figure 2 for a con sta nt air velocity and in Figure 3 for a con sta nt volumetric flow rate. In both cases it maybe seen that there are limits to how much heat sink thermal resistance may be reduced by either increasing fin len gth or addi ng more fins. Of course to determ ine how a heat sink

will actually perform in a specific application it is necessary to determine validated by the authors [1] by comparing with numerical simulations over a broad range of the modified cha nnel Reyno Ids nu mber (0.26 < Re < 175) and with someexperimental data as well. Using the Nusselt number obtained in (8) the heat transfer coefficient is given by

Note: Kfin should be K. 20051017

where k 仙 is the thermal conductivity of the heat sink material. The

efficie ncy of the fins may be calculated using

"tin ianh(m + Hf)

where m is give n by ini

Using these equations it is possible to estimate heat sink thermal performa nee in terms of the thermal resista nee from the temperature at the base of the fins to the temperature of the air entering the fin passages. It maybe no ted that the relati on ship for Nusselt nu mber (8) in cludes the effect of the temperature rise in the air as it flows through the fin passages. To obta in the total thermal resista nee, R °t , to the base of the heat si nk it is n ecessary to add in the thermal con duct ion resista nce across the base of the heat sink. For uniform heat flow into the base R tot is give n by

(14)

the air velocity or volumetric flow rate that can be delivered through

the heat sink. To do this it is necessary to estimate the heat sink pressure drop characteristics and match them to the fan or blower to be used. This is a topic for con sideratio n in a future article.

20

IttlS

Figure 3. Effect of fin height and number of fins on heat sink thermal

3 resista nee at a volumetric air flow rate of 0.002

4 m /s (

5 CFM).

References 1. Teertstra, P., Yovanovich, M.M., and Culham, J.R., "Analytical

Forced Convection Modeling of Plate Fin Heat Sinks," Proceedings of 15th IEEE :n Hi IU 2 0 Number of fins o Figure 2. Effect of fin height and number of fins on heat sink thermal

resista nee at an air velocity of 2.5 m/s (492 fpm).

tin tnnii t ..1■

§ ■ 5 #

Semi-Therm Symposium, pp. 34-41, 1999.

如何计算散热器的散热功率计算角

估计平行板翅式散热器的热阻罗伯特 E 西蒙斯，副主编，IBM 公司正如以前在本专栏中，增加电力电子模块的趋势正在使越来越多的困难与空气冷却电子封装。结果有一个应用程序，需要强制对流风冷散热器来控制模块的温度越来越多。的一个广泛使用的散热器类型的例子是平行板的配置如图 1 所示。

图1。平行板翅式散热器的配置。

为了选择合适的散热器，热设计者必须首先确定最大允许散热器热阻。要做到这一点，要知道最大允许模块外壳温度，TCASE ，模块的功耗，PMOD ，并在模块到散热片接口，RINT 热阻。最大的散热片附着在表面，TBASE ，允许温度由下式给出允许的最大散热片电阻，R 最大，然后给出

在新台的，是冷却空气入口温度对散热器的通道。在这一点上许多热工程师将开始在散热器供应商目录（或更可能今天开始在互联网上搜索供应商）希望找到一个散热器，将适合在允许的空间，并提供一个散热器热阻，RHS，小于R最大在某些特定的流量。在某些情况下，

它可能是有用的做大小来估计各种板翅式散热器设计RHS，以确定是否一个可行的设计配

置是可能的。本文的其余部分将提供基本方程来做到这一点。该散热器的热阻由下式给出

其中h 是对流换热系数，侮是裸露的基地面积鳍片之间，Nfin 是数量的鳍，鳍鳍效率，AFIN 是每鳍表面积考虑到双方的鳍。

要继续进一步就必须建立在宽度，W，高度H,并在流动方向上所允许的最大长度散

热器体积，L.还必须指定一个翅片厚度，tfin。使用这些参数的差距，B之间的鳍，可确定

从

基面的暴露面积，然后确定可能从

和每翅片换热面积从

使用，相应的鳍之间的空气流速是

要确定传热系数后，鳍，由Teertstra 等人开发一个公式行事。［1］与努塞尔数，怒族，以雷诺数，重，和Pr 数，镨，可受聘。这个方程

普朗特数