3D topology optimization of heat sinks for liquid cooling

This paper conducts topology optimization of three dimensional heat sinks for liquid cooling. The forced cooling system is modeled with weakly coupled steady-state incompressible Navier-Stokes equation and the energy equation. We study the distribution of the conductive solid components in order to minimize the average temperature on the heat source surface. A set of consistent adjoint equations are derived from the weak forms of the state equations in order to obtain the sensitivity. We discretize the simulation domain with six million tetrahedral elements. Iterative solvers with preconditioners are used to solve the partial differential equations. We present three examples with different geometries and boundary conditions as benchmarks for topology optimization of forced cooling problems. Detailed numerical validations on one design from topology optimization show that the optimized parallel plate fin heat sink could consume up to 450% more pumping power than the topology optimization design while achieving the same thermal performance, or the temperature of the optimized parallel plate fin heat sink is 10-40% higher than the design from topology optimization when the pumping power is same. The superior performance of the design from topology optimization is achieved with a flow split effect due to the heat sink geometry. This geometry sends the hot flow to the top layer and the cold flow to the bottom layer further in the downstream region in an aerodynamically efficient manner.