Academic involved : Franck Plouraboué Collaborators : Charles Pierre (http://web.univ-pau.fr/ cpierre1/) LMA UMR CNRS 5142, Jérome Fehrenbach, Frédéric de Gournay, Institut de mathématique de Toulouse (IMT UMR 5219) (http://www.math.univ-toulouse.fr/).
Convecto-diffusive transfers in tubular configurations are relevant in various contexts such as tissue exchanges (e.g. in muscles), heat exchangers, hemodyalisers, etc..
We have developed theoretical and numerical analysis of these transfer problems by the generalization of Graetz modes In finite or infinite domains. These works have shown that 3D parallel convective transport problems can be mapped onto solving 2D transverse eigen-modes problems, whose longitudinal variations can be found analytically.
In the case of Dirichlet lateral boundary conditions all the modes display longitudinal exponential variations, whereas for homogeneous Neumann lateral conditions, one supplementary mode having a linear longitudinal variation can be found for equilibrated counter-current configuration.
This work have permit to propose a very efficient method using variational formulation and finite element resolution for the computation of complex exchangers (such as those illustrated in the figure above which represent a longitudinal cut of the 3D heat solution) where the idea of fully developed regime can also be applied.
Our interest in the future is to use those ideas to design and predict optimal configurations in this context.
- C. Pierre & F. Plouraboué, Numerical analysis of a new mixed-formulation for eigenvalue convection-diffusion problems, SIAM J. App. Math, 70, 3, pp. 658-676, 2009.
- Jérôme Fehrenbach, Frédéric de Gournay, Charles Pierre, Franck Plouraboué, Generalized Graetz problem infinite domains, SIAM J. App. Math, 72, pp. 99-123, 2011.
- J. Bouyssier, C. Pierre, & F. Plouraboué, Mathematical Analysis of Parallel Convective Exchangers with General Lateral Boundary Conditions Using Generalized Graetz Modes, Math. Models Methods Appl. Sci., 24, 4:627-667, 2014.
- Jérôme Fehrenbach, Frédéric de Gournay & F. Plouraboué, Shape optimization for the generalized Graetz problem, to appear in Structural and Multidisciplinary Optimization, 2014 .
- C. Pierre, J. Bouyssier, F. de Gournay , F. Plouraboué, Numerical computation of 3D heat transfer in complex parallel heat exchangers using generalized Graetz modes, J. Comp. Phys., 268 pp.84-105, 2014.
- D. Polezhaev, P. Duru, F. Plouraboué, Enhanced evaporation from an oscillating liquid in a capillary tube, Int. J. Heat Mass Transfer, 95, 288–295, 2016.
- J. Dichamp, F. De Gournay& F. Plouraboué, Theoretical and numerical analysis of counter-flow parallel convective exchangers considering axial diffusion, Int. J. Heat Mass Trans., 107, 154—167, 2017.
Analyse mathématique et numérique des échangeurs convectifs parallèles
Julien Bouyssier, Jérôme Fehrenbach, Frédéric de Gournay, Charles Pierre, Franck Plouraboué, acte du congrès Français de mécanique, 2012, Besançon.