Study on the topology optimization of heat sinks in natural convection with various shapes of physical domain

Abstract

In this thesis, topology of heat sinks with various shapes of physical domain is thermally optimized in natural convection. Depending on the existence of constraints for array types, two different approaches are adopted. In the first technical chapter, heat sinks with a given array type are optimized. In this case, the purpose of the optimization is to find the optimum values of typical design variables, e.g. channel spacing and fin thickness. For such problems, the correlations of convective heat transfer coefficient that is expressed in the design variables are developed. By using these correlations, the optimum designs and their thermal resistances are obtained through varying the design variables. For the rectangular-shaped physical domain, a new correlation of heat transfer coefficient for pin-fin heat sinks is developed by the asymptotic method. By using this correlation, pin-fin heat sinks with vertically oriented based are optimized, and their thermal performances are compared to those of optimized plate-fin heat sinks. For the cylinder-shaped physical domain, a new correlation for internally finned tubes is developed. By using this correlation, optimum fin geometries at various domain sizes are proposed using closed-form equations. In the second technical chapter, heat sinks without a given array type are optimized by using the topology optimization. When there is no given array type, it is hard to define the design variables because of the complexity of shape. To manage these difficulties, the topology optimization method is applied. In this method, computational domain is divided into a number of elements and each element has its own density variable that ranges from 0 to 1. Therefore, density distribution determines the shape of the structure, and density variables play role as design variables for optimization. Based on the finite element formulation for heat transfer problems, shape-dependent variation of heat transfer coefficient is considered by developing a new local heat transfer coefficient model for natural convection in a complex structure. For a simple, rectangular-shaped physical domain where the configuration of the optimum plate-fin heat sink was known, topology optimization with the proposed local heat transfer coefficient model reproduces the optimal channel spacing of the plate-fin heat sink. Therefore, the validity of the local heat transfer coefficient model is confirmed. With the validated local heat transfer coefficient model, a new conceptual design for a heat sink is obtained in the 2-D computational domain for which a conventional heat sink has been designed. Through the numerical simulation, it is found that the topology-optimized heat sink has 15% lower thermal resistance and 26% less material mass than the conventional heat sink. Finally, the methodologies in the 2-D topology optimization are extended to 3-D. A new local heat transfer coefficient model which is applicable to 3-D computational domain is proposed. By using this model, a 3-D topology-optimized heat sink is obtained under a computational domain for radial plate-fin heat sink. This 3-D topology-optimized heat sink has 15% lower thermal resistance and 46% less mass than the optimum radial plate-fin heat sink.