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Mathematical analysis of parallel convective exchangers with general lateral boundary conditions using generalized graetz modes

Bouyssier, Julien and Pierre, Charles and Plouraboué, Franck Mathematical analysis of parallel convective exchangers with general lateral boundary conditions using generalized graetz modes. (2013) Mathematical Models and Methods in Applied Sciences. 1-39. ISSN 0218-2025

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Official URL: http://dx.doi.org/10.1142/S0218202513500620


We propose a mathematical analysis of parallel convective exchangers for any general but longitudinally invariant domains. We analyze 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 generalized solutions along longitudinal coordinate are found from convoluting elementary base Graetz mode with the applied sources at the boundary. In the case of adiabatic zero flux counter-current configuration, we recover the longitudinally linearly varying solution associated with the zeroth eigenmode which can be considered as the fully developed behavior for heat-exchangers. We also provide general expression for the infinite asymptotic behavior 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 truncated mode decomposition is also analyzed in various configurations for illustrating the versatility of the formalism. Numerical quantities of interest are investigated, such as fluid/solid internal and external fluxes.

Item Type:Article
Additional Information:Thanks to World Scientific Publishing. The original PDF of the article can be found at Mathematical Models and Methods in Applied Sciences website : http://www.worldscientific.com/worldscinet/m3as
HAL Id:hal-03526369
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Université de Pau et des Pays de l'Adour - UPPA (FRANCE)
Laboratory name:
Deposited On:09 Sep 2013 08:43

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