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A shape optimal design problem with convective and radiative thermal transfer. Analysis and implementation

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HAL Id: inria-00256545

https://hal.inria.fr/inria-00256545

Submitted on 15 Feb 2008

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A shape optimal design problem with convective and

radiative thermal transfer. Analysis and implementation

Denise Chenais, Jerome Monnier, Jean-Paul Vila

To cite this version:

Denise Chenais, Jerome Monnier, Jean-Paul Vila. A shape optimal design problem with convective and radiative thermal transfer. Analysis and implementation. Journal of Optimization Theory and Applications, Springer Verlag, 2001, 110 (1), pp.75-117. �inria-00256545�

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! 2 1 "1 "2 1 "1 "2 x x 2 1 ! 2 1 "1 "2 1 "1 "2 x x 2 1 0 0 ) #( T T-1

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! To !

$

T=I+V T

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T = I + V T-1 ! $ R y y

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Engine block

Exhaust pipe

Battery Screen

Air exit Air exit

Air entrance Hose

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.

SIMULATOR

OPTIMIZER DIRECT PB (NON LINEAR)

FLUID PDE y = ( % & w )h h h h COST FUNCTION J (h ! ) = ... ADJOINT PB (LINEAR) ADJOINT INTEGRAL EQN ADJOINT THERMAL PDE ADJOINT FLUID PDE THERMAL PDE INTEGRAL EQN p = ( P , T , q ) h h h h GRADIENT (! )

!

n +1

!

n = ...

(

)

n n G

G

LINE SEARCH: ALGORITHM DESCENT: '

!

n

;

[ j(

!

n

)

]

h OF BFGS n n+1 dn ( = ( " ' n

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zoom a b a ( (= s( ) ) ) i 1 )i-1 ) i b i+1 )

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