Multi-objective topology optimization of pin-fin heat exchangers using spectral and finite-element methods

Forced convective pin-fin heat exchangers, due to the high wet surface area per volume and the hindered thermal boundary layers, feature low thermal resistances. However, the considerable coolant pressure drop, particularly for densely packed fin arrays, imposes operational costs for pumping power supply. This paper develops a multi-objective topology optimization approach to optimize sink geometries in order to minimize thermal resistance and pressure loss, concurrently. In accordance to the pin-fin geometrical characteristics, a dedicated pseudo-3D conjugate heat transfer model is utilized, by assuming periodic flow and fin design pattern, to reasonably reduce the high cost of full-3D model optimization. For the solution of flow part, a pseudo-spectral scheme is used, which is intrinsically periodic and features a high spectral accuracy, and the finite element method for the non-periodic conjugate heat transfer model. Exact partial derivatives of the discrete solutions are obtained analytically by hand-differentiation. This task is rather convenient for the flow part, due to the simplicity of the pseudo-spectral implementation; however, the MATLAB symbolic toolbox is selectively utilized for the finite element code to ensure an error-free implementation. Finally, the sensitivities are computed directly or via a discrete adjoint method, for the flow and heat models, respectively. To examine the present approach, two approaches are used for optimization of a practical cooling task: constrained and unconstrained multi-objective formulations, where in all cases more emphasis is placed on thermal resistance minimization. A series of optimized heat sink geometries via constrained or unconstrained multi-objective optimizations are obtained to examine practical utility of the present approach. The optimized topologies demonstrated superior cooling performances at lower costs of pressure losses compared to conventional (circular) in-line and staggered fins, and confirmed the supremacy of topology over pure sizing optimization.