3D analytical modelling of plate fin heat sink on forced convection

Abstract

With the development of embedded systems, it is crucial to reduce weight of equipments. In power converter, heat sink is a heavy part that often can be reduced in volume and weight. There are several models and methods to calculate a heat sink thermal resistance. However the more precise these methods are, the more time consuming they are and thus they can be hardly integrated in a weight optimization routine. Using analytical models to calculate heat sink thermal resistance is a good compromise between execution time and precision of results. They are usually one-dimensional models which are simple but do not take into account heat spreading effects, which is important when power electronic heat sources are small compared to their heat sink. This paper describes a three-dimensional analytical model of forced convection plate fin heat sink, which will be compared with numerical simulation. A maximum difference of 1.4°C has been observed between the mean $\Delta$T of the models. This analytical model will be used in an optimization routine to reduce the weight of an existing heat sink in order to show that fast and precise optimization of cooling system is possible with analytical models.

Introduction

Real development of more electrical aircraft is only possible if high level of equipment integration is achieved, i.e. if one can reduce at most the system’s mass and increase power density. One of the most important equipments that must be optimized is a static power converter, which can be found in many applications inside an aircraft.

Designing a power converter always implies on finding the best trade-off between cost, mass, efficiency and reliability applied to different elements such as capacitors, inductors, switches, cooling system (heat sinks), and control boards. Most of the times, the heat sink, which is one of the heaviest elements, is only evaluated at the end of the design process and is often oversized.

Heat sinks are generally made of aluminium and sometimes of copper and other materials. Thus, heat sink is a heavy element, which significantly contributes to the converter weight. For that reason increasing power density of a power converter implies on reducing at maximum the heat sink weight.

Moreover, since reliability is a major aspect in any aircraft application, liquid cooling heat sink should be avoided. The use of pumps and fluid circulation circuits requires regular maintenance and decreases system reliability. For that reason, it is essential to use fin heat sinks in natural or forced convection.

Weight optimization of fin heat sinks can be only achieved by the use of adapted models, which are precise enough to design a valid device but fast enough to be executed in a reasonable time. Calculation of heat sink thermal resistances and temperatures is possible either by very precise 3D Finite Element Method (FEM) simulations or by analytical models. FEM simulations are very time consuming and are hardly integrated in optimization routines. On the other hand, analytical modelling is usually fast but inaccurate. Our goal is to then develop a heat sink analytical model, which is fast enough to take part of a power converter optimization routine, and at the same time fairly precise (maximum 5% difference between analytical calculation and FEM simulation).

Modelling presented in [2] and shown in this paper concerns forced convection heat sinks with plate fins which is one of the most robust, cheap and thus common types of cooling systems. Analytical model to describe a plate fin heat sink will be developed in this paper. The goal of this model is to give the mean heat source(s) temperature(s) for any source and heat sink dimensions, source position on the heat sink baseplate, and fan associated to the heat sink. A state of art of an existing model will be first presented before we develop the model used in our optimization routines. After that, a comparison between FEM and the developed analytical model will be shown in order to confirm that it is precise enough to be used for fast design.

Finally, this model will be integrated in an optimization routine so a thermal system design can be performed. An example of heat sink design for a power converter used in aircraft applications will be shown. This example illustrates how fast the developed optimization routines are and also the importance of taking into account heat spreading in the baseplate of the heat sink.