The effects of hydrodynamic anisotropy on the mixed-convection in a vertical porous channel heated on its plates with a thermal radiation are investigated analytically for fully developed flow regime. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is oblique to the gravity. The generalized Brinkman-extended Darcy model which allows the no-slip boundary-condition on solid wall is used in the formulation of the problem. The flow reversal, the thermal radiation influence for natural, and forced convection are considered in the limiting cases for low and high porosity media. It was found that the anisotropic permeability ratio, the orientation angle of the principal axes of permeability and the radiation parameter affected significantly the flow regime and the heat transfer.
An integral method based on Lighthill's analysis (Q J Mech Appl Math 6 (1953) 398-439) is carried out to study the similarity regime for penetration of convective heat transfer in a vertical cylindrical well filled with an anisotropic porous medium. The porous medium is anisotropic in permeability with its principal axes oriented in a direction that is oblique to the gravity vector. In the limit of the slenderness of the porous matrix, the penetration length of the convective flow and the heat-transfer rate are expressed in terms of the anisotropic properties of the porous medium, the modified Darcy-Rayleigh number and the aspect ratio of the geometrical configuration. A scale analysis is applied to predict the order of magnitudes involved in the similarity regime of the phenomenon. The conditions of existence of the similarity pattern is found to be dependent on the anisotropic parameters. It is demonstrated that both the anisotropic permeability ratio and the orientation angle of the principal axes have a strong influence on the heat-transfer rate and on the vertical penetration length into the well.
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.
Rapid population growth and major trends of world economy growth have led to significant energy needs in our country. Benin, Gulf of Guinea country, although with a significant coastal network powered by potential energy from breaking waves, has experienced a deficit and a critical energy instability, marked by recurrent power cuts and disruption of the national economy. To ensure the integration of this source of renewable energy in the Benin energy mix and sustainably reduce the energy deficit in progress, this work has aimed to study the dissipation of wave energy at the bathymetric breaking in the breakers zone of Cotonou coast. Sea conditions and the statistics parameters of the breaking waves under perturbation effect of the seabed were evaluated to predict the beginning of the breaking. The modeling is based on the Navier-Stokes equation in which the viscosity and the interactions between the molecules of the oceanic fluid are neglected. The nonlinear wave dispersion relation is also used. The results obtained for this purpose showed that water particles have an almost parabolic motion during their fall; their velocity is higher than those of the early breaking. In this area, the waves dissipate about 80% of their energy: it generates turbulence which leads to a strong setting in motion of sediments.
In the present study, both anisotropy and magnetic field effects on bi-diffusive natural convection in a rectangular cavity filled with a porous medium saturated by a binary fluid are investigated analytically for fully developed flow regime. The cavity is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted. The porous medium is anisotropic in permeability whose principal axes are oriented in a direction that is arbitrary to the gravity field. On the basis of the generalized Brinkman-extended Darcy model of newtonian fluids on steady flow through porous media, analytical expressions were obtained for the flow and thermal fields, the concentration of speaces, the average Nusselt and Sherwood numbers in terms of the Darcy number, the anisotropic permeability ratio, the orientation angle of the principal axes and the Hartmann number. The limiting case corresponding to pure porous media (Da→0) and pure fluid media (Da→∞) for the thermal conditions mentioned on the cavity completed these results in order to compare them to those obtained in the literature. It is found that, Nusselt and Sherwood numbers increase by increasing anisotropic parameters of the porous medium while increasing magnetic field magnitude greatly reduces the intensity of the flow and thus affects significantly heat and mass transfer.
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