Gérard Degan

Influence of anisotropy on convection in porous media with nonuniform thermal gradient

Abstract Effect of anisotropy on the onset of natural convection heat transfer in a fluid saturated porous horizontal cavity subjected to nonuniform thermal gradients is investigated analytically. The porous layer is heated from the bottom by a constant heat flux while the other surfaces are being insulated. The horizontal boundaries are either rigid/rigid or stress-free/stress-free. The hydrodynamic anisotropy of the porous matrix is considered. The principal directions of the permeability are oriented in a direction that is oblique to the gravity. Based on a parallel flow assumption, closed-form solution for the flow and heat transfer variables, valid for the onset of convection corresponding to vanishingly small wave number, is obtained in terms of the Darcy–Rayleigh number Ra , the Darcy number Da , and the anisotropic parameters K * and θ . The critical Rayleigh number for the onset of convection arising from sudden heating and cooling at the boundaries is also predicted. The limiting cases Da →∞ (for a viscous pure fluid) and Da →0 (for anisotropic porous media) completed all results. It is demonstrated that effects of anisotropic parameters are strongly significant.

Forced convection in horizontal porous channels with hydrodynamic anisotropy

Abstract This paper presents an exact solution for fully developing forced convective flow in parallel-plate horizontal porous channels with an anisotropic permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. A constant heat flux is applied on the channel side walls. Basing this analysis on the generalized Brinkman-extended Darcy model which allows the satisfaction of the no-slip boundary condition on solid wall, it is found that anisotropic parameters K* and ϕ have a strong influence on the flow fields and heat transfer rate, in the limiting case of low porosity media (Da→0). The results indicate that a maximum (minimum) heat transfer rate is reached when the orientation of the principal axis with higher permeability of the anisotropic porous matrix is parallel (perpendicular) to the vertical direction.

Liquid film condensation along a vertical surface in a thin porous medium with large anisotropic permeability.

The problems of steady film condensation on a vertical surface embedded in a thin porous medium with anisotropic permeability filled with pure saturated vapour are studied analytically by using the Brinkman-Darcy flow model. The principal axes of anisotropic permeability are oriented in a direction that non-coincident with the gravity force. On the basis of the flow permeability tensor due to the anisotropic properties and the Brinkman-Darcy flow model adopted by considering negligible macroscopic and microscopic inertial terms, boundary-layer approximations in the porous liquid film momentum equation is solved analytically. Scale analysis is applied to predict the order-of-magnitudes involved in the boundary layer regime. The first novel contribution in the mathematics consists in the use of the anisotropic permeability tensor inside the expression of the mathematical formulation of the film condensation problem along a vertical surface embedded in a porous medium. The present analytical study reveals that the anisotropic permeability properties have a strong influence on the liquid film thickness, condensate mass flow rate and surface heat transfer rate. The comparison between thin and thick porous media is also presented.

Effect of anisotropy in permeability on thermal convection of viscoelastic fluids in rotating porous layer heated from below

ABSTRACT In this work, we studied the linear stability analyses of thermal convection, in a viscoelastic fluid saturated rotating anisotropic porous layer heated from below. The influence of hydrodynamic anisotropy and of rotation on the convective phenomenon are considered and investigated by extending the modified Darcy-Maxwell-Jeffrey model to include the Coriolis force term. It is shown that the anisotropic permeability ratio , the inclination angle of the principal axes ( ) of the porous medium, the relaxation time ( ), the retardation time ( ) and the Taylor Darcy number ( ) have a strong influence on the convective flow.

PRE-DESIGN AND MODELLING OF A QUALITY CONTROL DEVICE TO TEST TILES MECHANICAL CHARACTERISTICS

Toukourou Chakirou Akanho, Ph.D. (Engineering), Master – Assistant, Laboratory of Thermophysical Characterization of Materials and Energy Appropriation (Laboratoire de Caractérisation Thermophysique des Matériaux et d’Appropriation Energétique, LABO – C. T. M. A. E.), Laboratory of Energetics and Applied Mechanics (LEMA), University of Abomey-Calavi, 01 BP 2009 Cotonou, Benin, e-mail: potemat@yahoo.fr Semassou Guy Clarence, Ph.D. (Engineering), Master – Assistant, Laboratory of Energetics and Applied Mechanics (LEMA), University of Abomey-Calavi, 01 BP 2009 Cotonou, Benin, e-mail: seclar2001@yahoo.fr Chegnimonhan Kouamy Victorin, Ph.D. (Engineering), Associate professor, Teacher in the department of Thermal Engineering and Energetics, Polytechnic school of the University of Nantes, Laboratory of Thermokinetics BP 50609, 44306 Nantes, France; (LTN) – CNRS UMR 6607, e-mail: victorin.chegnimonhan@univ-nantes.fr Guidi Tognon Clotilde, Ph.D. (Engineering), Associate Professor, Laboratory Processes and Technology Innovation (LaPIT), University Institute of Technology Lokossa, Lokossa University, BP 133 Lokossa, Benin, e-mail: iut.lokossa@yahoo.fr, guidi65@mail.ru Assogba Zéphérine, Engineer, Laboratory of Thermophysical Characterization of Materials and Energy Appropriation (Laboratoire de Caractérisation Thermophysique des Matériaux et d’Appropriation Energétique, LABO – C. T. M. A. E.), University of Abomey-Calavi, 01 BP 2009 Cotonou, Benin, e-mail: potemat@yahoo.fr Vianou Antoine, Ph.D. (Engineering), Professor, Laboratory of Thermophysical Characterization of Materials and Energy Appropriation (Laboratoire de Caractérisation Thermophysique des Matériaux et d’Appropriation Energétique, LABO – C. T. M. A. E.), University of Abomey-Calavi, 01 BP 2009 Cotonou, Benin, 01 BP 2009 Cotonou, Benin, e-mail: avianou@yahoo.fr Degan Gérard, Ph.D. (Engineering), Professor, Laboratory of Energetics and Applied Mechanics (LEMA), University of Abomey-Calavi, 01 BP 2009 Cotonou, Benin, e-mail: ger_degan@yahoo.fr