Shape sensitivity analysis for a microchannel cooling system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:492

Article

Blauth, Sebastian^1,2  Leithaeuser, Christian¹  Pinnau, Rene² 

[1] Fraunhofer ITWM, Kaiserslautern, Germany

[2] TU Kaiserslautern, Kaiserslautern, Germany

关键词: Shape optimization;    Adjoint approach;    Optimization with PDE constraints;    Microchannels;   

DOI  :  10.1016/j.jmaa.2020.124476

来源: Elsevier

【 摘 要 】

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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free