S. Bouabdallah^1,2, R. Bessaïh¹

FDMP-Fluid Dynamics & Materials Processing, Vol.6, No.3, pp. 251-276, 2010, DOI:10.3970/fdmp.2010.006.251

Abstract In this paper, a numerical study of magnetohydrodynamics stability during phase change of a pure metal (liquid Gallium) in a cubical enclosure is presented. An external magnetic field is applied in X-, Y-, and Z-directions separately. Two electric potential boundary conditions are considered: electrically conducting and insulating walls. The finite-volume method with enthalpy formulation is used to solve the mathematical model in the solid and liquid phases. The Grashof number is fixed at Gr =105and the Hartmann number is varied from Ha= 0 to 200. The effect of magnetic field on the flow field and heat transfer, and on the… More >

O.M.Lavrenteva, Yu. Holenbergand A.Nir¹

FDMP-Fluid Dynamics & Materials Processing, Vol.6, No.1, pp. 41-74, 2010, DOI:10.3970/fdmp.2010.006.041

Abstract A variety of exact analytical solutions describing natural and thermocapillary convection in a horizontal double layer system consisting of Newtonian and Herschel-Bulkley fluids subjected to longitudinal temperature and concentration gradients is constructed. The lower boundary of the system is a solid wall with no-slip, while the upper ones if either a solid wall or a free surface. It was demonstrated that, depending on the governing parameters of the system, viscoplastic layer is entirely yielded or unyielded, or it can be yielded partially, exhibiting up to 5 flowing and quasi-solid layers. The dependence of the flow patterns (appearance and position of… More >

Ahmed Mezrhab¹, Hassan Naji²

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.3, pp. 283-296, 2009, DOI:10.3970/fdmp.2009.005.283

Abstract The objective of this paper is to assess the effectiveness of the coupled Lattice Boltzmann Equation (LBE) and finite volume method strategy for the simulation of the interaction between thermal radiation and laminar natural convection in a differentially heated square cavity. The vertical walls of the cavity are adiabatic, while its top and bottom walls are cold and hot, respectively. The air velocity is determined by the lattice Boltzmann equation and the energy equation is discretized by using a finite volume method. The resulting systems of discretized equations have been solved by an iterative procedure based on a preconditioned conjugate… More >

R. Djebali^1,2, M. El Ganaoui^2,3, H. Sammouda¹, R. Bennacer⁴

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.3, pp. 261-282, 2009, DOI:10.3970/fdmp.2009.005.261

Abstract The simplified thermal lattice Boltzmann model (STLBM) developed by Peng, Shu and Chew (2003) is used in this work to simulate low-Rayleigh-number natural convection in a heated rectangular cavity on a uniform grid. It is shown how by resorting to the double populations approach both hydrodynamic and thermal fields can be effectively simulated. Furthermore, a general benchmark is carried out to account for the effect of different parameters in relatively wide ranges. Results are compared with previous works available in the literature. More >

Aouachria Z¹

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.2, pp. 137-148, 2009, DOI:10.3970/fdmp.2009.005.137

Abstract This work treats heat and mass transfer by natural convection along a vertical wall in porous media imbibed by fluid, using an integral method. The problem governing parameters are the buoyancy ratio,N, and the Lewis number, Le The results for the local Nusselt and Sherwood numbers are presented for a large range of these parameters. The concentration and thermal boundary layer thickness are also determined. We observe that our results are in good agreement with those obtained by Bejan and Khair (1985). More >

Edoardo Bucchignani¹

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.1, pp. 37-60, 2009, DOI:10.3970/fdmp.2009.005.037

Abstract This article describes an implicit method for the solution of time dependent Navier-Stokes equations written in terms of vorticity and velocity. The field equations are discretized using a finite volume technique over quadrilateral meshes.
The numerical code has been applied to the classical window cavity test, employing a fine stretched non-uniform grid, in order to provide an accurate steady solution for a high value of the Rayleigh number (10⁸). It has also been performed a simulation for a value of Rayleigh larger than the critical value, in order to show the capabilities of the proposed method to properly simulate… More >

M. El Alami¹, E. A. Semma^2,3, M. Najam¹, R. Boutarfa²

FDMP-Fluid Dynamics & Materials Processing, Vol.5, No.1, pp. 23-36, 2009, DOI:10.3970/fdmp.2009.005.023

Abstract This study is devoted to the investigation of natural convection in a two dimensional horizontal channel with rectangular heated blocks at the bottom. The aspect ratio of the channel is A = L'/H' = 5. The blocks are heated with a constant temperature while the upper plane of the channel is cold. The governing equations are solved using a finite volumes method and the SIMPLEC algorithm is used for the treatment of the pressure-velocity coupling. Special emphasis is given to detail the effect of the Rayleigh number and blocks height on the heat transfer and the mass flow rate generated… More >

Ahmed Mahmoudi^1,2, Imen Mejri¹, Mohamed Ammar Abbassi¹, Ahmed Omri¹

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.4, pp. 353-388, 2013, DOI:10.3970/fdmp.2013.009.353

Abstract A double-population Lattice Boltzmann Method (LBM) is applied to solve the steady-state laminar natural convective heat-transfer problem in a triangular cavity filled with air (Pr = 0.71). Two different boundary conditions are implemented for the vertical and inclined boundaries: Case I) adiabatic vertical wall and inclined isothermal wall, Case II) isothermal vertical wall and adiabatic inclined wall. The bottom wall is assumed to be at a constant temperature (isothermal) for both cases. The buoyancy effect is modeled in the framework of the well-known Boussinesq approximation. The velocity and temperature fields are determined by a D2Q9 LBM and a D2Q4 LBM,… More >

A. Rtibi¹, M. Hasnaoui¹, A. Amahmid¹

FDMP-Fluid Dynamics & Materials Processing, Vol.9, No.2, pp. 183-207, 2013, DOI:10.3970/fdmp.2013.009.183

Abstract In this paper we present an analytical and numerical study of Soret convection in an inclined rectangular porous layer saturated with a binary fluid and subject to uniform heat fluxes. In the problem formulation, the Darcy model is considered and the results are presented for wide ranges of R_T (50 ≤ R_T ≤ 1000), θ(0°≤θ≤180°) and φ(-1 ≤ φ ≤ 1) for Le = 10, where R_T, θ, φ, and Le are the thermal Darcy-Rayleigh number, the cavity inclination, the separation parameter, and the Lewis number, respectively. An analytical solution, derived on the basis of the parallel flow approximation, is… More >

Nadia Dihmani¹, Samir Amraqui¹, Ahmed Mezrhab^1,2, Najib Laraqi³

FDMP-Fluid Dynamics & Materials Processing, Vol.8, No.3, pp. 311-322, 2012, DOI:10.3970/fdmp.2012.008.311

Abstract Natural convection with surface radiation heat transfer is investigated numerically in a vented vertical channel heated asymmetrically. The numerical solution is obtained using a finite volume method based on the SIMPLER algorithm for the treatment of velocity-pressure coupling. Concerning the radiation exchange, in particular, the working fluid is assumed to be transparent, so that only the solid surfaces (assumed diffuse-grey) give a contribute to such exchange. The effect of Rayleigh numbers and rib width (for Pr=0.7 air fluid) on the heat transfer and flow structure in the channel is examined in detail. Results are presented in terms of isotherms, streamlines,… More >