G. Allaire, Shape optimization by the homogenization method, Applied Math Sciences, vol.146, 2002.

G. Allaire, F. Jouve, and . Van-goethem, A level set method for the numerical simulation of damage evolution, ICIAM 07?6th international congress on industrial and applied mathematics, pp.3-2210, 2009.
DOI : 10.4171/056-1/1

G. Allaire, F. Jouve, and A. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004.
DOI : 10.1016/j.jcp.2003.09.032

H. Bau, Optimization of conduits shape in microheat exchangers, Int J Heat Mass Trans, vol.41, pp.2117-2723, 1998.

C. Bernardi and O. Pironneau, SENSITIVITY OF DARCY'S LAW TO DISCONTINUITIES, Chinese Annals of Mathematics, vol.24, issue.02, pp.205-214, 2003.
DOI : 10.1142/S0252959903000189

T. Bruns, Topology optimization of convection-dominated, steady-state heat transfer problems, International Journal of Heat and Mass Transfer, vol.50, issue.15-16, pp.2859-2873, 2007.
DOI : 10.1016/j.ijheatmasstransfer.2007.01.039

D. Bucur and J. Zolesio, Optimisation de forme sous contrainte capacitaire, CR Acad Sci Math, vol.319, issue.1, pp.57-60, 1994.

P. Canhoto and A. Reis, Optimization of fluid flow and internal geometric structure of volumes cooled by forced convection in an array of parallel tubes, International Journal of Heat and Mass Transfer, vol.54, issue.19-20, pp.4288-4299, 2011.
DOI : 10.1016/j.ijheatmasstransfer.2011.05.016

J. Céa and R. Kohn, Conception optimale ou identification de formes, calcul rapide de la d??riv??e directionnelle de la fonction co??t, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, issue.3, pp.371-402, 1975.
DOI : 10.1051/m2an/1986200303711

F. Clarke, C. Conca, R. Mahadevan, and L. Sanz, Optimization and nonsmooth analysis Shape derivative for a twophase eigenvalue problem and optimal configurations in a ball, CANUM 2008, ESAIM Proceedings, pp.311-321, 1990.

R. Dautray and J. Lions, Mathematical analysis and numerical methods for science and technology Velocity extension for the level-set method and multiple eigenvalues in shape optimization, SIAM J Control Optim, vol.2, issue.451, pp.343-367, 1988.

G. Fabbri, Heat transfer optimization in internally finned tubes under laminar flow conditions, International Journal of Heat and Mass Transfer, vol.41, issue.10, pp.1243-1253, 1998.
DOI : 10.1016/S0017-9310(97)00209-3

A. Fedorov and R. Viskanta, Three-dimensional conjugate heat transfer in the microchannel heat sink for electronic packaging, International Journal of Heat and Mass Transfer, vol.43, issue.3, pp.399-415, 2000.
DOI : 10.1016/S0017-9310(99)00151-9

J. Fehrenbach, F. De-gournay, C. Pierre, and F. Plouraboué, The Generalized Graetz Problem in Finite Domains, SIAM Journal on Applied Mathematics, vol.72, issue.1, pp.99-123, 2012.
DOI : 10.1137/11082542X

URL : https://hal.archives-ouvertes.fr/hal-00574293

K. Foli, T. Okabe, M. Olhofer, Y. Jin, and B. Sendho, Optimization of micro heat exchanger: CFD, analytical approach and multi-objective evolutionary algorithms, International Journal of Heat and Mass Transfer, vol.49, issue.5-6, pp.1090-1099, 2006.
DOI : 10.1016/j.ijheatmasstransfer.2005.08.032

L. Graetz, Ueber die W??rmeleitungsf??higkeit von Fl??ssigkeiten, Annalen der Physik, vol.14, issue.7, pp.337-357, 1885.
DOI : 10.1002/andp.18852610702

E. Haug and B. Rousselet, Design Sensitivity Analysis in Structural Mechanics.II. Eigenvalue Variations, Journal of Structural Mechanics, vol.281, issue.1, pp.161-186, 1980.
DOI : 10.1080/03601218008907358

F. Hecht and . Bamg, Variation et optimisation de formes The determination of a discontinuity in a conductivity from a single boundary measurement, Mathématiques et Applications, p.67, 1998.

A. Iga, S. Nishiwaki, K. Izui, and M. Yoshimura, Topology optimization for thermal conductors considering design-dependent effects, including heat conduction and convection, International Journal of Heat and Mass Transfer, vol.52, issue.11-12, pp.2721-2732, 2009.
DOI : 10.1016/j.ijheatmasstransfer.2008.12.013

L. Leal, F. Murat, and J. Simon, Laminar flow and convective transport processes. Butterworth-Heinemann Series in Chemical Engineering Sur le contrôle par un domaine géométrique, Thèse d'Etat, 1976.
DOI : 10.1080/07373939308916891

F. Murat, T. Lalger-neittaanmäki, P. Sprekels, J. Tiba, and D. , Séminaire d'analyse fonctionnelle et numérique de l'université d Optimization of elliptic systems. Springer monographs in mathematics D (2012) Fixed domain approaches in shape optimization problems, Theory and applications Inverse Problems, vol.28289, issue.9, pp.93-94, 1978.

S. Osher and F. Santosa, Level Set Methods for Optimization Problems Involving Geometry and Constraints, Journal of Computational Physics, vol.171, issue.1, pp.272-288, 2001.
DOI : 10.1006/jcph.2001.6789

O. Pantz, Sensibilit?? de l'??quation de la chaleur aux sauts de conductivit??, Comptes Rendus Mathematique, vol.341, issue.5, pp.333-337, 2005.
DOI : 10.1016/j.crma.2005.07.005

E. Papoutsakis, D. Ramkrishna, and H. Lim, The extended Graetz problem with Dirichlet wall boundary conditions, J Comput Phys, vol.36, pp.13-34, 1980.

C. Pierre and F. Plouraboué, Numerical Analysis of a New Mixed Formulation for Eigenvalue Convection-Diffusion Problems, SIAM Journal on Applied Mathematics, vol.70, issue.3, pp.658-676, 2009.
DOI : 10.1137/080736442

URL : https://hal.archives-ouvertes.fr/hal-00865817

O. Pironneau, Optimal shape design for elliptic systems In: System modeling and optimization, pp.42-66, 1982.

J. Pommier, Y. Renard, and . Getfem++, An open-source finite element library http://home.gna.org/getfem Seyranian AP Multiple eigenvalues in structural optimization problems, Struct Optim, vol.8, issue.4, pp.207-227, 1994.

V. Sverak, On optimal shape design, J Math Pure Appl, vol.72, issue.6, pp.537-551, 1993.