如何计算散热器的散热功率
如何计算散热器的散热功率
Calculation Corner
Estimating Parallel Plate-Fin Heat Sink Thermal Resistance
Robert E. Simons, Associate Editor, IBM Corporation
As noted previously in this column, the trend of increasing electronic module power is making it more and more difficult to cool electronic packages with air. As a result there are an increasing number of
applications that require the use of forced convection air-cooled heat sinks to control module temperature. An example of a widely used type of
heat sink is the parallel plate configuration shown in Figure 1.
Figure 1. Parallel plate fin heat sink configuration.
In order to select the appropriate heat sink, the thermal designer must first determine the maximum allowable heat sink thermal resistance. To do this it is necessary to know the maximum allowable module case temperature, Tcase , the module power dissipation, Pmod , and the thermal
resistance at the module-to-heat sink interface, Rint . The maximum
allowable temperature at the heat sink attachment surface, T base , is given
by
The maximum allowable heat sink resistance, Rmax
, is then given by
where T air-in , is the temperature of the cooling air at the inlet to the heat
sink passages. At this point many thermal engineers will start looking at heat sink vendor catalogs (or more likely today start searching vendors on the internet) to find a heat sink that will fit in the allowable space and provide a heat sink thermal resistance, Rhs , less than Rmax at some
specified flow rate. In some cases, it may be useful to do a sizing to estimate Rhs for various plate-fin heat sink designs to determine if a
feasible design configuration is possible. The remainder of this article will provide the basic equations to do this. The thermal resistance of
the heat sink is given by
where h is the convective heat transfer coefficient, Abase is the exposed
base surface area between fins, N fin is the number of
fins, fin is the fin
efficiency, and Afin is the surface area per fin taking into account both
sides of the fin.
To proceed further it is necessary to establish the maximum
allowable heat sink volume in terms of width, W, height, H, and length in the flow direction, L. It is also necessary to specify a fin thickness, t fin . Using these parameters the gap, b, between the fins may be determined
from
The exposed base surface area may then be determined from
and the heat transfer 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 corresponding air velocity
between 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 Reynolds number, Re, and Pr number, Pr, may be employed. This equation
is
The Prandtl number is
where is the dynamic viscosity of air, cp the specific heat of air at
constant pressure, and k is the thermal conductivity of air. The Reynolds
number used in (8) is a modified channel Reynolds number defined as
where is the density of air. Equation (8) is based upon a composite model spanning the developing to fully developed laminar flow regimes and was
validated by the authors [1] by comparing with numerical simulations over a broad range of the modified channel Reynolds number (0.26
and with some experimental data as well. Using the Nusselt number obtained in (8) the heat transfer coefficient is given by
Note: Kfin should be K. 20051017
where kfin is the thermal conductivity of the heat sink material. The
efficiency of the fins may be calculated using
where m is given by
Using these equations it is possible to estimate heat sink thermal performance in terms of the thermal resistance from the temperature at the base of the fins to the temperature of the air entering the fin passages. It may be noted that the relationship for Nusselt number (8) includes the effect of the temperature rise in the air as it flows through the fin passages. To obtain the total thermal resistance, R tot , to the base of the
heat sink it is necessary to add in the thermal conduction resistance across the base of the heat sink. For uniform heat flow into the base Rtot
is given by
For purposes of illustration these equations 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 constant air velocity and in Figure 3 for a constant volumetric flow rate. In both cases it may be seen that there are limits to how much heat sink thermal resistance may be reduced by either increasing fin length or adding more fins. Of course to determine how a heat sink will actually perform in a specific application it is necessary to determine
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 consideration in a future article.
Figure 2. Effect of fin height and number of fins on heat sink thermal
resistance at an air velocity of 2.5 m/s (492 fpm).
Figure 3. Effect of fin height and number of fins on heat sink thermal resistance at a volumetric air flow rate of 0.0024 m3/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 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
此时有必要指定的平均速度，V 之间的鳍或体积流量，G. ，条款空气流速或者如果体积流量
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
其中是空气动力粘度，CP 的空气定压比热，k 是空气的导热系数。雷诺数使用（8）修改后的通道雷诺数定义为
其中是空气密度。方程（8）是基于一个复合跨越发展，充分发展层流制度，由作者验证模型[1]与数值模拟比较多的修改后的通道雷诺数（0.26
注：Kfin 应K. 20051017
其中kfin 是散热器材料的热导率。翅片效率的计算可使用
其中m 是给予
利用这些方程的估计是可能的散热片从热电阻的温度在鳍基地的通道，进入空气温度条件鳍的散热性能。这可能是注意到，努塞尔数（8）关系包括空气中的温度升高的影响，因为它通过翅片通道流动。要获得总热阻，Rtot ，对散热器有必要在热传导阻力增加整个散热器的基地群。对于进入基地Rtot 均匀热流由下式给出
为了便于说明这些公式被用于估计为50 × 50毫米铝质散热片散热片的热阻。在增加翅片高度和翅片数的影响如图所示为一个恒定风速2和图恒定的体积流量3。在这两种情况下，可以看出有多少散热器的热阻可减少或增加鳍鳍长度或增加更多的限制。当然，以确定如何将散热片实际执行中的具体应用，有必要确定风速或体积流量，可以通过散热片传递。为此，有必要估计散热器压降特性和匹配给风扇或鼓风机使用。这是在以后的文章中审议的议题。
图2。翅片高度和散热器上以2.5米/秒（492 FPM）空气流速热阻鳍数的影响。
图3。翅片高度和容积在0.0024空气流速对散热器热阻鳍数的影响立方米/秒（5 CFM）。