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This paper reports an analytical and numerical study of mixed convection heat and mass transfer of a binary fluid in a vertical parallel plate channel filled with a porous medium. The thermal conditions applied on the walls of the system are uniform heat fluxes. Both the cases of double-diffusion and Soret-induced convection are considered. The governing equations for the porous medium rely on Darcy's model. The governing parameters for the problem are the Rayleigh number, Ra, Peclet number, Pe, Lewis number, Le, buoyancy ratio, φ, aspect ratio of the channel $A = L'/H'$ and the constant a ( a = 0 for double diffusive convection and a = 1 for Soret induced convection). The resulting problem, in the limit of fully developed mixed convection, is solved analytically in closed form. A numerical solution of the full governing equations is demonstrated to be in good agreement with the analytical model. The temperature and velocity fields and the Nusselt and Sherwood numbers are obtained in terms of the governing parameters. The possible existence of reversed flows in the channel is discussed. © 2011 Canadian Society for Chemical Engineering [ABSTRACT FROM AUTHOR]

This article reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with nanofluids. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure while the two horizontal ones are assumed insulated. Three types of nanoparticles are taken into consideration: Cu, Al2O3 and TiO2. Various models are used for calculating the effective viscosity and thermal conductivity of nanofluids. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number Pr, the aspect ratio of the cavity, A and the solid volume fraction of nanoparticles, Φ. In the first part of the analytical study a scale analysis of the present problem is made. In the second part analytical solutions are obtained, in the limit of an infinite layer ( $A\gg 1$), for the stream function and temperature fields. The analytical model relies on the assumption of a parallel flow approximation in the core region of the cavity and an integral form of the energy equation in the end regions. In the high Rayleigh number regime a good agreement is obtained between the predictions of the scale analysis and those of the analytical solution. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations based on the lattice Boltzmann method. Cet article présente une étude analytique et numérique de la convection naturelle dans une cavité rectangulaire peu profonde remplie de nanofluides. Les conditions aux limites de Neumann pour la température sont appliquées sur les parois verticales de l'enceinte tandis que les deux parois horizontales sont supposées isolées. Trois types de nanoparticules sont pris en considération: Cu, Al2O3 et TiO2. Divers modèles sont utilisés pour le calcul de la viscosité et la conductivité thermique effective du nanofluide. Les paramètres régissant le problème sont le nombre de Rayleigh thermique, Ra, le nombre de Prandtl Pr, le facteur de forme de la cavité, A et la fraction volumique de nanoparticules solides, phi. Dans la première partie de l'étude analytique une analyse d'échelle du problème est réalisée. Dans la deuxième partie les solutions analytiques sont obtenues, dans la limite d'une couche infinie, pour la fonction de courant et les champs de température. Le modèle de la solution repose sur l'hypothèse de l'écoulement parallèle dans la région centrale de la cavité et sur un bilan de conservation d'énergie dans les extrémités. Pour des nombres de Rayleigh assez élevés un bon accord est obtenu entre les prédictions de l'analyse d'échelle et ceux de la solution analytique. Des solutions numériques des équations complètes sont obtenues pour une large gamme des paramètres de contrôle. Un bon accord est observé entre le modèle analytique et les simulations numériques basées sur la méthode de Lattice Boltzmann. © 2011 Canadian Society for Chemical Engineering [ABSTRACT FROM AUTHOR]

Abstract: The present work is concerned with the effect of a uniform magnetic field on the onset of convection in an electrically conducting micropolar fluid. A flat fluid layer bounded by horizontal rigid boundaries, subjected to thermal boundary conditions of the Neumann type, is considered. The parallel flow approximation is used to predict analytically the critical Rayleigh number for the onset of convection. The onset of motion is found to depend on the Hartmann number Ha, materials parameters K, B, , and the micro-rotation boundary condition n. A linear stability analysis is carried out to study numerically the onset of convection. The predictions of the analytical model are found to be in good agreement with the numerical solution. The above results are also compared with those obtained numerically for the case of a system subject to Dirichlet thermal boundary conditions. [Copyright &y& Elsevier]

This investigation reports on a linear stability analysis of the quiescent state within a horizontal porous cavity subject to vertical gradients of temperature and solute. The fluid motion is modeled using the Brinkman extension of Darcy's law, coupled with energy and species conservation equations. The horizontal boundaries are considered rigid-rigid, rigid-free, or free-free. Mixed thermal and solutal boundary conditions, of Dirichlet and Neumann types, are considered. The thresholds for monotonic and oscillatory convection instabilities are determined explicitly in terms of the governing parameters of the problem. The results for a viscous fluid and the Darcy porous medium emerge from the present analysis as limiting cases. [ABSTRACT FROM AUTHOR]