Parametric solution of the Rayleigh-Benard convection model by using the PGD Application to nanofluids

Abstract

Purpose – The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time. Design/methodology/approach – In this paper both parameters are introduced as model extracoordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily. Findings – Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters. Originality/value – Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.