Mathematical Analysis of parallel convective exchangers

Julien Bouyssier (1) , Charles Pierre (2) , Franck Plouraboué (1)

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

We propose a mathematical analysis of parallel convective exchangers for any general but longitudinally invariant domains. We analyse general Dirichlet or Neumann prescribed boundary conditions at the outer solid domain. Our study provides general mathematical expressions for the solution of convection/diffusion problems. Explicit form of generalised solutions along longitudinal coordinate are found from convoluting elementary base exponential Graetz mode with the applied sources at the boundary. In the case of adiabatic zero flux counter-current configuration we find a new longitudinally linearly varying solution associated with the zeroth eigenmode which can be considered as the fully developed asymptotic behaviour for heat-exchangers. We also provide general expression for the infinite asymptotic behaviour of the solutions which depends on simple parameters such as total convective flux, outer domain perimeter and the applied boundary conditions. Practical considerations associated with the numerical precision of the truncated mode decomposition is also analysed in various configurations for illustrating the versatility of the proposed formalism. Numerical quantities of interest are carefully investigated, such as fluid/solid internal and external fluxes.

Mots clés: Heat and mass transfer; convection diffusion; variational formulation; Graetz mode decomposition; mixed formulation; convective exchangers

Domaines: Analyse numérique [math.NA]

Julien Bouyssier, Charles Pierre, Franck Plouraboué. Mathematical Analysis of parallel convective exchangers. 2012. ⟨hal-00667657v1⟩