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arXiv · 2005.02754

Shape Sensitivity Analysis for a Microchannel Cooling System

Sebastian Blauth·Christian Leithäuser·René Pinnau
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Abstract

We analyze the theoretical framework of a shape optimization problem for a microchannel cooling system. To this end, a cost functional based on the tracking of absorbed energy by the cooler as well as some desired flow on a subdomain of the cooling system is introduced. The flow and temperature of the coolant are modeled by a Stokes system coupled to a convection diffusion equation. We prove the well-posedness of this model on a domain transformed by the speed method. Further, we rigorously prove that the cost functional of our optimization problem is shape differentiable and calculate its shape derivative by means of a recent material derivative free adjoint approach.

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Sebastian Blauth, Christian Leithäuser, René Pinnau. 2020-05-06. Shape Sensitivity Analysis for a Microchannel Cooling System. https://doi.org/10.1016/j.jmaa.2020.124476

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