Ali Belghith

Multiple natural convection solution in porous media under cross temperature and concentration gradients

Double-diffusive natural convection is of interest in several natural and industrial fields, for example, oceanography, nuclear waste, transformation processes, and crystal growth techniques. This work focuses on double-diffusive natural convection in a square cavity filled with porous media heated and cooled along vertical walls by uniform heat fluxes when a solutal flux is imposed vertically. The formulation of the problem is based on the Darcy?Brinkman model, and the density variation is taken into account by the Boussinesq approximation. W e found three distinct regimes. The first is a fully thermal convective regime in which the flow is essentially due to thermal buoyancy forces. The second is a diffusive one where the solutal forces are strong enough to produce a stable solutal stratification with no significant convective flows. The third is an intermediate regime where competition between the two buoyancy forces takes place. In the intermediate regime a hysterisys is observed and two different sol...Double-diffusive natural convection is of interest in several natural and industrial fields, for example, oceanography, nuclear waste, transformation processes, and crystal growth techniques. This work focuses on double-diffusive natural convection in a square cavity filled with porous media heated and cooled along vertical walls by uniform heat fluxes when a solutal flux is imposed vertically. The formulation of the problem is based on the Darcy?Brinkman model, and the density variation is taken into account by the Boussinesq approximation. W e found three distinct regimes. The first is a fully thermal convective regime in which the flow is essentially due to thermal buoyancy forces. The second is a diffusive one where the solutal forces are strong enough to produce a stable solutal stratification with no significant convective flows. The third is an intermediate regime where competition between the two buoyancy forces takes place. In the intermediate regime a hysterisys is observed and two different solutions can be obtained depending on the initial state. The effects of Rayleigh, Lewis, and Darcy numbers are analyzed.

Finite element simulation of transient natural convection of low‐Prandtl‐number fluids in heated cavity

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low‐Prandtl‐number fluids. The flow is driven by the horizontal temperature gradient between the vertical walls maintained at different temperatures. Two‐dimensional equations of conservation and energy are solved using a finite element method and a fractional step time. The discrete equations systems are solved in the lap of each element‐mesh with the aim of verifying the Boussinesq hypothesis locally. To compare our results with the earlier predictions, we have chosen the fluids for Prandtl‐numbers 0.001, 0.005 and 0.01 and with Grashof numbers up to 1 × 107. To predict the steady state solutions with an oscillary transient period, the results are reduced in terms of the time series average Nusselt‐number at the vertical walls, the velocity at the center of the cavity and near right boundary. In addition, the isotherms and the velocity field are produced with the aim of showing the main circulation and particularly the weak circulations at the corners of the cavity.

Effect of Surface Radiation on the Natural-Convection Stability in a Two-Dimensional Enclosure with Diffusely Emitting Boundary Walls

A transient interaction of natural convection with thermal radiation of gray surfaces of a square cavity filled with air is investigated numerically. The effect of radiation on the flow field, temperature distribution, and onset of oscillatory instability of flow is predicted. A complete study of stability of some value of Rayleigh number is performed for emissivity ε varying from 0 to 1. The finite-element and the fractional step time methods are used to solve the two-dimensional time-dependent Navier-Stokes and energy equations. The results are reduced in terms of the time-series averages Nusselt number and velocity component near vertical walls and at the center of the cavity. The Grashof number is varied up to 5 × 10 7 to determine the new critical values of regime flow for different values of emissivity.

Thermosolutal Convection During Melting in a Porous Medium Saturated with Aqueous Solution

The thermosolutal convection in a porous medium saturated with an aqueous solution near the temperature of the density maximum is studied. The fixed temperatures applied to vertical walls include the density maximum. The formulation of the problem is based on the Darcy-Brinkman model and the density variation is governed by a nonlinear approximation. The equations are solved by a finite-volume method. The numerical model is validated through experimental results. We show that the nonlinear variation of the density influences strongly the flow structure and the heat transfer. The structures of this flow show that the density maximum generates a complex flow structure of two contrarotating cells of unequal importance.

Simulation of mixed convection in a channel partially filled with porous media

We present a numerical study for mixed convection in a two-dimensional horizontal plan channel containing both fluid and porous layers, heated by a constant flux on the top surfaces. The finite volume method and the iterative SIMPLER algorithm are used. The thermal field, streamlines and local Nusselt numbers are analysed for a wide range of the Darcy numbers (1 < Da < 10-5), and for different values of the thermal conductivity ratio, Rk. The results identify the limit of mixed convection and the effect of porous media characteristics (permeability, conductivity) on flow structure and heat transfer.

Natural Convection in a Horizontal Cavity Partially Occupied by a Porous Media Saturated by a Coolant Liquid

The natural convection is studied in a cavity witch the lower half is filled with a porous media that is saturated with a first fluid (liquid), and the upper is filled with a second fluid (gas). The horizontal borders are heated and cooled by uniform heat fluxes and vertical ones are adiabatic. The formulation of the problem is based on the Darcy-Brinkman model. The density variation is taken into account by the Boussinesq approximation. The system of the coupled equations is resolved by the classic finite volume method. The numerical results show that the variation of the conductivity of the porous media influences strongly the flow structure and the heat transfer as well as in upper that in the lower zones. The effect of conductivity is conditioned by the porosity which plays a very significant roll on the heat transfer. The structures of this flow show that this kind of problem with specific boundary conditions generates a complex flow structure of several contra-rotating two to two cells, in the upper half of the cavity.Copyright