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Natural convection with Soret effect in a binary fluid saturating a shallow horizontal porous layer is studied both numerically and analytically. The vertical walls of the enclosure are heated and cooled by uniform heat fluxes and a solutal gradient is imposed vertically. In the formulation of the problem, we use the Darcy model and the density variation is taken into account by the Boussinesq approximation. The governing parameters of the problem are the aspect ratio, A, the thermal Rayleigh number, R_T, the buoyancy ratio, N, the Lewis number, Le and the Soret coefficient, N_S. The analytical solution, based on the parallel flow approximation, is found to be in good agreement with a numerical solution of the full governing equations. In the presence of a vertical destabilizing concentration gradient, the existence of both natural and antinatural flows is demonstrated. When the vertical concentration gradient is stabilizing, multiple steady state solutions are possible in a range of buoyancy ratio, N, that depends strongly on the Soret coefficient, N_S.

A computational model is developed to describe convection in volatile liquids evaporating in capillary tubes. Experimental work has demonstrated the existence of such convective structures. The correlation between this convection and the phase change process has been experimentally established. Temperature distribution on the liquid‐vapour interface is considered in order to characterise the minimum of radial temperature gradient required to initiate and orientate Marangoni convection. Direct numerical simulation using finite volume approximation is used to investigate the heat and mass transfer in the liquid phase. The case of a capillary tube filled with a volatile liquid is investigated for various Marangoni numbers, to characterise heat and mass transfers under conditions close to realistic operating parameters. The simulation shows that a minimum irregularity in evaporative flux along the liquid‐vapour interface is necessary to trigger thermocapillary convection. The enhancement of heat and mass transfer by Marangoni convection is also investigated.

The purpose of this paper is to apply the lattice Boltzmann method (LBM) to simulate mixed flow, which combines natural convection for temperature difference and forced convection for lid driven, in a two‐dimensional rectangular cavity over a wide range of aspect ratios (A), Rayleigh numbers (Ra) and Reynolds numbers (Re).

The LBM is applied to simulate the mixed flow. A multi‐relaxation technique was used successfully. A scale order analysis helped the understanding and predicting the overall heat transfer.

In the considered lid driven cavity, the Richardson number emerges as a measure of relative importance of natural and forced convection modes on the heat transfer. An expression of the overall heat transfer depending on the cavity slender (A) is deduced. The validity of the obtained expression was checked in mixed convection under the condition of low Richardson number (Ri) and the limitation condition was deduced.

This paper has implications for cooling system optimization and LBM technique development.

This paper presents a new cooling configuration, avoiding critical situation where the opposing effect induce weak heat transfer; and a stable and fast LBM approach allowing complex geometry treatment.

The use of natural ventilation by large openings to maintain thermal comfort conditions in the premises is a concept that is perfectly integrated into the traditional architecture of countries in the Mediterranean region or in tropical climates. In a temperate climate where the architecture is not usually designed to respond to the use of natural ventilation is seasonal and is done at the initiative of the occupants by making changes in the design of their doors. The European interest in natural ventilation, as a passive building air-conditioning technology, is increasing and has been the subject of a research program commissioned by the European Community. In this work, the authors consider a part of a housing compound as a refreshing floor. This floor is maintained at a constant cold temperature, the one vertical wall at hot temperature and other surfaces are adiabatic. Various scenarios are considered for this work. Mixed convection for different boundary conditions and different configurations is carried out. In addition, an airflow is injected through a window and extracted on the opposite window. Classical conclusion and transitional value on Richardson number have been completed by the new thermal configuration with nonsymmetric thermal conditions. The complex 3D flow structure is more obvious when one of the two flows (ventilation or natural convection) dominates. However, the induced heat transfer is less sensitive to the added ventilation. In this study, the authors consider a part of a housing compound as a refreshing floor. This floor is maintained at a constant cold temperature, the one vertical wall at hot temperature and other surfaces are adiabatic.

This is a qualitative preliminary study of a 2D–3D flow. The authors examine the competition between the natural convective flow and the added airflow on the flow structure and indoor air quality. The numerical model shows a good agreement with that obtained by researchers analytically and experimentally. To deal with turbulence, the RNG k-ε model has been adopted in this study.

The transfer is more sensitive between the 2D and 3D cases for the present analyzed case.

The study of ventilation efficiency has shown the competition between the big and small structures and the induced discomfort.

The purpose of this paper is to study analytically and numerically the effect of a transverse magnetic field on the separation of species induced in an inclined rectangular porous cavity saturated with an electrically conducting mixture.

The porous layer is assumed homogeneous and submitted from its long sides to uniform heat fluxes and to a magnetic field of strength B. The Darcy model combined with the Boussinesq approximation are used to study the heat and solute transfer in the medium. An analytical solution is developed on the basis of the parallel flow approximation. Numerical simulations are also performed in order to validate the analytical solution. The controlling parameters of this problem are the thermal Rayleigh number, the inclination of the enclosure, the separation parameter, the Hartmann number and the Lewis number.

For given values of the thermal Rayleigh number, the inclination of the enclosure, the separation parameter and the Lewis number, there is an optimal magnetic field which leads to a maximum of separation. At relatively high Rayleigh numbers, where convection destroys the separation process, it is possible, with an optimal choice of the Hartman number, to recover a good level of separation.

Since the problem is governed by several parameters (five parameters), only the Darcy model was used in this study instead of the Darcy-Brinkman extended model even if the latter model allows to cover the pure fluid and Darcy porous media as limiting cases.

In separation experiments, it is very difficult technically to work with small Rayleigh numbers due to technical difficulties. However, the process of separations is canceled at high Rayleigh number by the strength of convection which causes a mixing in the binary mixture. This study shows that, by using adequate combinations of the controlling parameters, it becomes possible to reach a good level of separation even at relatively high Rayleigh numbers.

Optimum choice of the magnetic field and the inclination of the cavity may lead to a good level of the separation process. For large Lewis numbers, the separation vanishes far above and far below the optimal Ha. However, for small Lewis numbers, an important level of separation is maintained for any Ha located below the optimal value of the latter parameter.

The purpose of this paper is to numerically study the double-diffusive natural convection within an eccentric horizontal cylindrical annulus filled with a Newtonian fluid. The annulus walls are maintained at uniform temperatures and concentrations so as to induce aiding thermal and mass buoyancy forces within the fluid. For that, this simulation span a moderate range of thermal Rayleigh number (100Ra_T100,000), Lewis (0.1Le10), buoyancy ratio (0N5) and Prandtl number (Pr=0.71) to examine their effects on flow motion and heat and mass transfers.

A finite volume method in conjunction with the successive under-relaxation algorithm has been developed to solve the bipolar equations. These are written in dimensionless form in terms of vorticity, stream function, temperature and concentration. Beforehand, the implemented computer code has been validated through already published findings in the literature. The isotherms, streamlines and iso-concentrations are exhibited for various values of Rayleigh and Lewis numbers, and buoyancy ratio. In addition, heat and mass transfer rates in the annulus are translated in terms of Nusslet and Sherwood numbers along the enclosure’s sides.

It is observed that, for the range of parameters considered here, the results show that the average Sherwood number increases with, while the average Nusselt number slightly dips as the Lewis number increases. It is also found that, under the convective mode, the local Nusselt number (or Sherwood) increases with the buoyancy ratio. Likewise, according to Lewis number’s value, the flow pattern is either symmetric and stable or asymmetric and random. Besides that, the heat transfer is transiting from a conductive mode to a convective mode with increasing the thermal Rayleigh number, and the flow structure and the rates of heat and mass transfer are significantly influenced by this parameter.

The range of the Rayleigh number considered here covers only the laminar case, with some constant parameters, namely the Prandtl number (Pr = 0.71), and the tilt angle (α=90°). The analysis here is only valid for steady, two-dimensional, laminar and aiding flow within an eccentric horizontal cylindrical annulus. This motivates further investigations involving other relevant parameters as N (opposite flows), Ra, Pr, Le, the eccentricity, the tilt angle, etc.

An original framework for handling the double-diffusive natural convection within annuli is available, based on the bipolar equations. In addition, the achievement of this work could help researchers design thermal systems supported by annulus passages. Applications of the results can be of value in various arrangements such as storage of liquefied gases, electronic cable cooling systems, nuclear reactors, underground disposal of nuclear wastes, manifolds of solar energy collectors, etc.

Given the geometry concerned, the bipolar coordinates have been used to set the inner and outer walls boundary conditions properly without interpolation. In addition, since studies on double-diffusive natural convection in annuli are lacking, the obtained results may be of interest to handle other configurations (e.g., elliptical-shaped speakers) with other boundary conditions.

The purpose of this paper is to study analytically and numerically the Soret effect on double diffusive natural convection induced in a horizontal Darcy porous layer subject to lateral heat and mass fluxes. The work focuses on the particular situation where the solutal to thermal buoyancy forces ratio, N, is related to the Soret parameter, S_P, by the relation. For this particular situation, the rest state is a solution of the problem. The analytical identification of the parallel flow bifurcations counts among the objectives of the study. The effect of the governing parameters on the fluid flow properties and heat and mass transfer characteristics is also examined.

Both the Darcy model and the Boussinesq approximation are used for the mathematical formulation of the problem. The geometry under study is a horizontal porous cavity filled with a binary fluid. The problem is solved analytically on the basis of the parallel flow approximation, valid in the case of a shallow cavity. The analytical results are validated numerically using a second‐order finite difference method.

The main finding is the absence of a supercritical bifurcation for this problem. More precisely, in the studied case, only the subcritical convection was found possible for the parallel flow structure and its threshold was determined analytically versus the governing parameters. It is also shown that the S_P‐Le plane can be divided into two parallel flow regions; in one region the flow is counterclockwise while it is clockwise in the other. At sufficiently large values of R_T, two solutions of ψ0, termed as “stable” and “unstable” and varying, respectively, as R_T^1/3 and R_T⁻¹ were obtained. The flows corresponding to these solutions are rotating in the same direction with different intensities. An analytical expression is established for the critical Rayleigh number which allows a control of the onset of motion in the system.

The thermodiffusion phenomenon in saturated porous geometries is of practical interest in several natural and technological processes such as the migration of moisture through air contained in fibrous insulations, food processing, contaminant transport in ground water, electrochemical processes, etc.

The study concerns the Soret effect within a system subject to outside mass flux. Only one type of bifurcation (subcritical bifurcation) was found possible for the parallel flow structure in the present configuration instead of two kinds of bifurcations (supercritical and subcritical).

This paper aims to numerically investigate the magnetohydrodynamic (MHD) convection heat transfer of nanofluid inside a differentially heated enclosure with various fin morphologies.

The fluid flow within the cavity was governed by N-S equations while it within porous medium was solved by the non-Darcy model, called the Darcy–Forchheimer model based on representative element-averaging method. Empirical correlations from experimental data are used to evaluate the effective thermal conductivity and dynamic viscosity. Relevant governing parameters, including thermal Rayleigh number (10⁵-10⁷), Hartmann number (0-50), Darcy number (10⁻⁶-10⁻¹), thermal conductivity ratio of porous matrix (1-10³), nanoparticles volume fraction (0-0.04) and topology designs of porous fins, are sensitively varied to identify their effects and roles on the fluid flow and heat transfer. Particularly, heatlines are used to investigate the mechanism of heat transport.

Numerical results demonstrate that the predictions of average Nusselt number are augmented by using more porous fins with high permeability, and this effect becomes opposite in tiny Darcy numbers. Particularly, for high Darcy and Rayleigh numbers, the shortest fins could achieve the best performance of heat transfer. In addition, the prediction of average Nusselt number reduces with an increase in Hartmann numbers. An optimal nanoparticles concentration also exists to maximize heat transfer enhancement. Finally, numerical correlations for the average Nusselt number were proposed as functions of these governing parameters.

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering. In addition, optimum thermal removals could enhance the lifetime of electronics, therefore reducing the cost of energy and materials.

To the best knowledge of authors, there are not any studies considering the synergetic effects of porous fins on MHD convection of nanofluids. Present work could benefit the thermal design of electronic cooling and thermal carriers in nanofluid engineering.

Laminar natural convection of nanofluids in a square cooled cavity enclosing a heated horizontal cylinder is studied numerically. This paper aims to investigate in what measure the nanoparticle size and average volume fraction, the cavity width, the cylinder diameter and position, the average temperature of the nanofluid and the temperature difference imposed between the cylinder and the cavity walls, affects the basic heat and fluid flow features, as well as the thermal performance of the nanofluid relative to that of the base liquid.

The four-equation system of the mass, momentum and energy transfer governing equations has been solved using a computational code incorporating three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity and the coefficient of thermophoretic diffusion, all based on a high number of experimental data available in the literature. The SIMPLE-C algorithm has been used to handle the pressure-velocity coupling. Simulations have been performed using Al₂O₃ + H₂O, for different values of the average volume fraction of the suspended solid phase in the range 0-0.04, the diameter of the nanoparticles in the range 25-75 nm, the temperature difference imposed between the cylinder and the cavity walls in the range 5-20 K, the average nanofluid temperature in the range 300-330 K, the ratio between the cylinder diameter and the cavity width in the range 0.1-0.5 m, the ratio between the distance of the cylinder axis from the bottom wall and the cavity width in the range 0.2-0.8 and the ratio between the distance of the cylinder axis from the left sidewall and the cavity width in the range 0.2-0.5.

The main results obtained may be summarized as follows: the overall solid phase migration from hot to cold results in a cooperating solutal buoyancy force which tends to compensate the friction increase consequent to the viscosity growth due to the dispersion of the nanoparticles into the base fluid; the effect of the increased thermal conductivity consequent to the nanoparticle dispersion into the base fluid plays the major role in determining the heat transfer enhancement of the nanofluid, at least in the upper range of the investigated average temperatures; at high temperatures, the nanofluid heat transfer performance relative to that of the pure base liquid increases with increasing the average volume fraction of the suspended solid phase, whereas at low temperatures, it has a peak at an optimal particle loading; the relative heat transfer performance of the nanofluid increases notably with increasing the average temperature, and just moderately as the imposed temperature difference, the width of the cavity and the distance of the cylinder from the bottom of the cavity, are increased; the relative heat transfer performance of the nanofluid increases as the nanoparticle size, the cylinder diameter and the distance of the cylinder from the sidewall, are decreased; as a consequence of the local competition between the thermal and the solutal buoyancy forces, a periodic flow arises when the cylinder is located in the vicinity of one of the cooled walls of the enclosure.

Framed in this general background, a comprehensive numerical study on buoyancy-driven convection of alumina-water nanofluids inside a cooled square cavity containing a heated circular cylinder is executed by the way of a two-phase model based on the double-diffusive approach accounting for the effects of the Brownian diffusion and thermophoresis.

The purpose of this paper is to model the convective flows in a room equipped by a glass door and a heated floor of length l = 0.8 × H and submitted to a sinusoidal temperature profile and mono alternative temperature profile.

The paper opts for a numerical study of convective flows in a large scale cavity using the Lattice Boltzmann Method (LBM) by considering a two dimensions (2D) square cavity of side H and filled by air (Pr = 0.71). All the vertical walls, the ceiling and the rest of the floor are thermally insulated, the hot portion of length l = 0.8×H is heated with two imposed temperature profiles of amplitude values 0.2 ≤  a  ≤ 0.6 and for two different periods ζ = ζ0 and ζ = 0.4×ζ0. One of the vertical walls has a cold portion θ_c = 0 that represents the glass door.

A systematic study of the flow structure and heat transfer is carried out considering principal control parameters: amplitude “a” and period ζ for Rayleigh number Ra = 10⁸. Effects of these parameters on results are presented in terms of isotherms, streamlines, profiles of velocities, temperature in the cavity, global and local Nusselt number. It has been found that an increase in amplitude or period increases the amplitude of the temperature in the core of cavity. The Nusselt number increases when the amplitude “a” of the imposed temperature increases, but this later is not affected by variation of the period.

The authors used LBM to simulate the convective flows in a cavity at high Ra, heated from below by tow imposed temperature profiles. Indeed, they simulate a local equipped by a solar water heater (SWH). The floor is subjected to a periodic heating: Sinusoidal heating (Case 1) for which the temperature varies sinusoidally (SWH without a supplement), and mono alternation heating (Case 2), the temperature evolves like a redressed signal (SWH with a supplement). The considered method has been successfully validated and compared with the previous work. The study has been conducted using several control parameters such as the signal amplitude and period in the case of turbulent convection. This allowed us to obtain a considerable set of results that can be used for engineering.