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Shape sensitivities in a Navier‐Stokes flow with convective and grey bodies radiative thermal transfer
Author(s) -
Monnier J.
Publication year - 2003
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.728
Subject(s) - differentiable function , radiative transfer , mathematics , domain (mathematical analysis) , mathematical analysis , inverse problem , differential equation , convection , flow (mathematics) , thermal radiation , partial differential equation , mechanics , physics , thermodynamics , geometry , quantum mechanics
We study a shape optimal design problem for a forced convection flow: the steady‐state Navier–Stokes equations coupled with an integro‐differential thermal model. The thermal transfers are convective, diffusive and radiative with multiple reflections (model of grey bodies, radiosity equation). The inverse problem consists in minimizing a smooth cost function which depends on the solution, with respect to the domain of the equations. We prove the differentiability of the solution with respect to the domain. It follows the cost function differentiability. We introduce the adjoint state equation and obtain the exact differential of the cost function. The computational method of shape sensitivities and the optimization process are presented too. Copyright © 2003 John Wiley & Sons, Ltd.