Shape Sensitivity Analysis for a Microchannel Cooling System
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912642781675520 |
|---|---|
| author | Blauth, Sebastian Leithäuser, Christian Pinnau, René |
| author_facet | Blauth, Sebastian Leithäuser, Christian Pinnau, René |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_02754 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Shape Sensitivity Analysis for a Microchannel Cooling System Blauth, Sebastian Leithäuser, Christian Pinnau, René Optimization and Control Analysis of PDEs 49Q10, 49Q12, 35Q35, 76D55 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. |
| title | Shape Sensitivity Analysis for a Microchannel Cooling System |
| topic | Optimization and Control Analysis of PDEs 49Q10, 49Q12, 35Q35, 76D55 |
| url | https://arxiv.org/abs/2005.02754 |