Three-dimensional Darcy’s reduced-order isogeometric shape optimization for cooling channels

This paper presents a shape optimization for the three-dimensional cooling channel with high Reynolds number flow and strong convection heat transfer based on isogeometric analysis (IGA). Meanwhile, the applicability conditions of Darcy’s potential flow, which is an approximate liner flow, are introduced to solve the heat-flow coupling problem. We call this method Darcy reduced-order isogeometric analysis (DRIGA). The volume parametric model is constructed by using the segmentation–mapping–merging mechanism of design features, and the model can be directly analyzed by IGA without data conversion and to eliminate discrete errors. The calculation formulas for DRIGA are derived. Then, a DRIGA-based shape optimization is achieved by applying the sensitivity analysis method with the average temperature as the objective function, the location coordinates of the fluid–solid boundary control points as the design variables, and the percentage of fluid volume and the pressure drop as the constraints. Several examples of approximate water-cooling devices show that our method can accurately describe the heat-flow coupling problem in the case of a narrow channel with a high flow velocity. The analytical results are in general agreement with those of the finite element convection–diffusion analysis, and the shape optimization results show that the average temperature is reduced, which proves the correctness of the method.