Numerical computation of 3D heat transfer in complex parallel convective exchangers using generalized Graetz modes

Charles Pierre (1) , Julien Bouyssier (2) , Frédéric de Gournay (3) , Franck Plouraboué (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 IMFT - Institut de mécanique des fluides de Toulouse
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We propose and develop a variational formulation dedicated to the simulation of parallel convective heat exchangers that handles possibly complex input/output conditions as well as connection between pipes. It is based on a spectral method that allows to re-cast three-dimensional heat exchangers into a two-dimensional eigenvalue problem, named the generalized Graetz problem. Our formulation handles either convective, adiabatic, or prescribed temperature at the entrance or at the exit of the exchanger. This formulation is robust to mode truncation, offering a huge reduction in computational cost, and providing insights into the most contributing structure to exchanges and transfers. Several examples of heat exchangers are analyzed, their numerical convergence is tested and the numerical efficiency of the approach is illustrated in the case of Poiseuille flow in tubes.

Mots clés: functional minimization; Generalized Graetz mode; parallel heat exchangers; optimal weak-variational formulation

Domaines: Analyse numérique [math.NA]

Charles Pierre, Julien Bouyssier, Frédéric de Gournay, Franck Plouraboué. Numerical computation of 3D heat transfer in complex parallel convective exchangers using generalized Graetz modes. Journal of Computational Physics, 2014, 268, pp.84-105. ⟨10.1016/j.jcp.2014.02.037⟩. ⟨hal-00795038v2⟩