Topology optimization of planar heat sinks considering out-of-plane design-dependent deformation problems

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With the increasing development of topology optimization theory in thermal-fluid problems, it has been widely applied in design problems of cooling structures. However, little researches have concurrently considered the design-dependent mechanical problems of optimized structures. This paper deals with porosity-based topology optimization of forced convection planar heat sinks considering out-of-plane design-dependent deformation problems. The optimization is performed on the middle cross-section and the mechanical behaviors of the upper cover plate are considered. Governing equations of fluid flow, heat transfer, and structural mechanic fields are constructed. Particularly, to concurrently model design-dependent loads and boundary conditions, a spring term with design-dependent stiffnesses and a design-dependent pressure term are introduced into the out-of-plane mechanical model. Numerical examples in fluid-mechanical decoupled and weakly-coupled cases are given to demonstrate the validity and potential of the present approach. Additionally, the presented scheme is also evaluated in cases considering the global mechanical behavior and cases considering the local mechanical behavior. Comparisons and verifications show that the proposed approach is effective in yielding planar heat sinks with optimized heat transfer capabilities and well-controlled out-of-plane mechanical behaviors.