In this paper, the bioconvective flow in a Porous square cavity containing oxytactic microorganism in the presence of chemical reaction is investigated. The bioconvection flow and heat transfer in Porous media are formulated based on the Darcy model of Boussinesq approximation. The governing partial differential equations are solved using the Galerkin finite element method. The computational numerical results are exhibited by the streamlines, isotherms, isoconcentrations of oxygen, isoconcentrations of microorganisms, average Nusselt number, average Sherwood numbers of oxygen concentration and microorganisms. The effects of key parameters such as bioconvection Rayleigh number (Rb), chemical reaction parameter (Kr) and thermal Rayleigh number (Ra) are presented and analyzed. It can be deduced that the chemical reaction reduces the strength of isoconcentrations of both oxygen and microorganisms. It has been revealed that the chemical reaction has a greater effect on the swimming of the microorganisms, average Nusselt number, and average density number.

In present paper, a numerical analysis for a rectangular cavity filled with a anisotrop Porous media has been studied. It is assumed that the horizontal walls are adiabatic and impermeable, while the side walls of the cavity are maintained at constant temperatures and concentrations. The buoyancy force that induced the fluid motion are assumed to be cooperative. In the two extreme cases of heat-driven (N£1) and solute-driven (N³1) natural convection, scale analysis is applied to predict the order of magnitudes involved in the boundary layer regime. Especially, the effects of anisotropic properties on heat and mass transfer have been considered. The variation of Nusselt and Sherwood numbers for values of permeability ratio for a wide range of thermal Rayleigh number, buoyancy ratio, and Lewis number are presented. It is demonstrated that the anisotropic properties of the Porous medium considerably modify the heat and mass transfer rates from that expected under isotropic conditions.

This paper introduces dimensional and numerical investigation of the problem of solute transport within the two-phase flow in a Porous cavity. The model consists of momentum equations (Darcy’ s law), mass (saturation) equation, and solute transport equation. The cavity boundaries are constituted by mixed Dirichlet-Neumann boundary conditions. The governing equations have been converted into a dimensionless form such that a group of dimensionless physical numbers appear including Lewis, Reynolds, Bond, capillary, and Darcy numbers. A time-splitting multiscale scheme has been developed to treat the time derivative discretization. Also, we use the Courant-Friedrichs-Lewy (CFL) stability condition to adapt the time step size. The pressure is calculated implicitly by coupling Darcy’ s law and the continuity equation, then, the concentration equation is solved implicitly. Numerical experiments have been conducted and the effects of the dimensionless numbers have been on the saturation, concentration, pressure, velocity, and Sherwood number have been investigated.

In this study natural convection heat transfer fluid flow and entropy generation in a Porous inclined cavity in the presence of uniform magnetic field is studied numerically. For control of heat transfer and entropy generation, one or two partitions are attached to horizontal walls. The left wall of enclosure is heated with a sinusoidal function and right wall is cooled isothermally. Horizontal walls of the enclosure are adiabatic. The governing equations are numerically solved in the domain by the control volume approach based on the SIMPLE technique. The influence of Hartmann number, inclination angle, partition height, irreversibility distribution ratio, and partition location is investigated on the flow and heat transfer characteristics and the entropy generation. The obtained results indicated that the partition, magnetic field and rotation of enclosure can be used as control elements for heat transfer, fluid flow and entropy generation in Porous medium.

This research deals with the numerical analysis of the heat transfer characteristics of the unsteady combination of alumina-kerosene nanofluid enclosed in a Porous cavity with a moving lid. The governing equations of fluid flow and conjugate heat transfer along with the relevant boundary conditions are applied to express the physical problem mathematically. First, the boundary conditions and governing equations are converted into non-dimensional forms by suitable transformation series. In the next step, the finite element method based on Galerkin residue was used to solve the transformed non-dimensional equations. The evaluation is shown by previous studies and found to be excellent in resolution. Numerical solutions are obtained in a wide range of governing variables. In this study, Solid volume fraction ( ), Richardson number (Ri), Reynolds number (Re), etc. are the governing variables. The numerical results of thermal fields and flow are graphically shown according to the average Nusselt number, streamlines, and isotherms on the cavity’s hot surface. It is found that Ri has a wide influence on the streamlines and isotherms in the cavity as well as in specifying the average rate of heat transfer.

Steady state natural convection of Al2O3-water nanofluid inside a square cavity filled with a Porous medium is investigated numerically. The temperatures of the two side walls of the cavity are maintained at TH and TC, where TC has been considered as the reference condition. The top and the bottom horizontal walls have been considered to be insulated i.e., non-conducting and impermeable to mass transfer. Darcy–Forchheimer model is used to simulate the momentum transfer in the Porous medium. The transport equations are solved numerically with finite volume approach using SIMPLER algorithm. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number, Ra, 104£Ra£106, Darcy number, Da, 10-5£Da£10-3, and solid volume fraction, j, 0.0£ j£0.1). Numerical results are presented in terms of streamlines, isotherms and average Nusselt number. It was found that heat transfer increases with increasing of both Rayleigh number and Darcy number. It is further observed that the heat transfer in the cavity is improved with the increasing of solid volume fraction parameter of nanofluids.