An active fluid heat exchanger can be controlled effectively using Peltier elements to condition the temperature of the fluid flowing through the heat exchanger. The thermal resistance of the heat exchanger can be reduced to increase the speed of controlling the fluid's temperature. Topology optimization is used in this study to find the geometry of a heat exchanger with reduced thermal resistance.
The design of a heat exchanger using topology optimization requires the coupling of the fluid flow equations and the energy equation in a finite element model with a continuous design variable. The existing optimization models perform well when the goal of the optimization problem is to minimize viscous dissipation. A weighted sum multi-objective function is however necessary to optimize the thermal performance of a design, and the correct choice of weights to meet design specifications is difficult to arrive at.
The drawback in the existing model is that the conductivity distribution is defined as a function of the design variable of the optimization problem. This results in infeasible designs when the goal of the optimization problem is to minimize only thermal resistance, and this is demonstrated with several numerical examples along with a motivation for a new formulation.
A new formulation for conductivity distribution is proposed in this thesis. The new formulation defines the conductivity distribution in terms of the velocity field in the design domain. The new formulation is capable of significantly reducing the thermal resistance of the heat exchanger, and this is demonstrated with a numerical example. Finally, a 3d design case is implemented, the results of the optimization routine are post-processed and the performance of the baseline design from ASML is compared with the topology optimized design.