M. Naïmi, M. Hasnaoui and J.K. Platten
Analytical and numerical studies are conducted for two‐dimensional steady‐state coupled Marangoni and buoyancy convection of a non‐Newtonian power law fluid confined in a…
Abstract
Analytical and numerical studies are conducted for two‐dimensional steady‐state coupled Marangoni and buoyancy convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The results obtained by combining the two basic mechanisms (thermocapillarity and buoyancy) depend on whether their effects are aiding or opposite. The effect of the non‐Newtonian behavior on the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.
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M. Naïmi, M. Hasnaoui and J.K. Platten
Analytical and numerical studies are conducted for two‐dimensional steady‐state Marangoni convection of a non‐Newtonian power law fluid confined in a rectangular horizontal…
Abstract
Analytical and numerical studies are conducted for two‐dimensional steady‐state Marangoni convection of a non‐Newtonian power law fluid confined in a rectangular horizontal shallow cavity subjected to a horizontal temperature gradient between the two short vertical rigid sides, while the upper free surface and the lower rigid one are insulated. The effect of the non‐Newtonian behavior on the hydrodynamic stability, the fluid flow, the temperature field, and the heat transfer is studied. The parallel flow is obtained in some particular situations for which a good agreement is observed between the analytical results based on the parallel flow assumption and those corresponding to the numerical simulations.
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L. Kaffel Rebaï, A. Mojtabi, M.J. Safi and A.A. Mohamad
The purpose of this paper is to present a numerical and an analytical study of the thermohaline convection with Soret effect in a square enclosure filled with a binary fluid…
Abstract
Purpose
The purpose of this paper is to present a numerical and an analytical study of the thermohaline convection with Soret effect in a square enclosure filled with a binary fluid mixture.
Design/methodology/approach
The horizontal boundaries of the enclosure are impermeable and heated from below while its vertical walls are assumed to be adiabatic and impermeable. The Navier‐Stokes equations under the Boussinesq‐Oberbeck approximation are solved numerically. The results are given for different values of the separation ratio. The critical Rayleigh number at the onset of convection is determined analytically and numerically. The Hopf frequency at the onset of convection is obtained.
Findings
The existence of two stable stationary bifurcation branches is illustrated. Furthermore, it is shown that the existence of stable traveling waves in the transition from one branch to the other depends on the value of the separation ratio. For some values of Rayleigh number, asymmetric flows are observed. A good agreement is found between the numerical solution and analytical analysis.
Originality/value
The present work is the first to consider thermosolutal convection with Soret effect in a square enclosure.
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Safae Hasnaoui, Abdelkhalek Amahmid, Abdelghani Raji, Hassen Beji, Mohammed Hasnaoui, Youssef Dahani and Haykel Benhamed
The purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat generation. The…
Abstract
Purpose
The purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat generation. The enclosure is heated and salted from its long sides with constant but different temperatures and concentrations. The study focuses on the effects of three main parameters which are, the Soret parameter (Sr = 0 and –0.5), the internal to external Rayleigh numbers ratio 0 ≤ R ≤ 80 and the cavity inclination γ, varied from 0° (vertical position) to 60°. The combined effects of these parameters on fluid flow and heat and mass transfer characteristics are examined for the external Rayleigh number RaE = 105, the Prandtl number Pr = 0.71, the buoyancy ratio N = 1, the Lewis number Le = 2 and the aspect ratio of the cavity A = 2.
Design/methodology/approach
A hybrid lattice Boltzmann-finite difference method (LBM-FD) was used to tackle the problem under consideration. The LBM with the simple relaxation time was used for the fluid flow in the presence of the gravity force, while the temperature and concentration equations were solved separately using an explicit finite-difference technique at the Boltzmann scale.
Findings
The monocellular nature of the flow, obtained for R = 0 is not destroyed by varying the cavity inclination and the Soret parameter but rather by the increase of the parameter R. The Soret parameter and the cavity inclination become perceptible at high values of R. The inclination γ = 60° leads to high mean temperatures compared to the other inclinations. The effect of R on mean concentration is amplified in the presence of Soret effect but limited in the absence of the latter. The negative Soret parameter combined with high internal heat generation and a relatively high inclination is important when the objective is to maintain the fluid at a high concentration of species. The presence of bicellular flow combined with the important elevation undergone by the fluid temperature, makes both the cold and hot walls playing a cooling role with the most important exchanges taking place at the upper part of these walls. The analysis of the mean mass transfer shows that the increase of the inclination may lead to an increase or a decrease of the mass transfer depending on the range of R, in the case of Sr = 0. However, for Sr = −0.5, it is observed that the increase of γ is generally accompanied by a reduction of the mass transfer.
Originality/value
To the best of the authors’ knowledge, the hybrid LBM-FD was not used before to study such a problem. Combined effect of R and inclination may be useful in charging the fluid with species when the objective is to maintain high concentrations in the medium.
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H. Schweiger, A. Oliva, M. Costa, C.D. Pérez Segarra and A. Ivancić
Two‐dimensional finite difference calculations are carried out tostudy laminar flow in longitudinal and transverse convection rolls for threedifferent geometries: a single…
Abstract
Two‐dimensional finite difference calculations are carried out to study laminar flow in longitudinal and transverse convection rolls for three different geometries: a single rectangular cavity with high aspect ratio; a double cavity with a thin separation sheet; and a double cavity with a separation sheet and a honeycomb structure. The equations for the convection‐diffusion in the fluid and conduction in the solid region are solved simultaneously. Good agreement with experimental data is achieved for Rayleigh numbers not too high above the critical value for the onset of secondary convection rolls (Ra < 8500 for vertical and Ra < 2700 for horizontal cavities filled with air). Simulation fails for inclined cavities, where the flow structure is essentially three‐dimensional.
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M. Er‐Raki, M. Hasnaoui, A. Amahmid and M. Bourich
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…
Abstract
Purpose
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, SP, 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.
Design/methodology/approach
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.
Findings
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 SP‐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 RT, two solutions of ψ0, termed as “stable” and “unstable” and varying, respectively, as RT1/3 and RT−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.
Practical implications
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.
Originality/value
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).
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By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an…
Abstract
Purpose
By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an evaporating thin liquid film of pseudoplastic fluid.
Design/methodology/approach
The flow reversal attributed to the thermocapillary action is manifestly discernible through the streamline plots.
Findings
The thermocapillary strength is closely related to the viscosity of the fluid, besides its surface tension. The thermocapillary flow prevails in both Newtonian and pseudoplastic fluids at a large Marangoni number and the thermocapillary effect is more significant in the former. The overestimate in the Newtonian fluid is larger than that in the pseudoplastic fluid, owing to the shear-thinning characteristics of the latter.
Originality/value
This study provides insights into the essential attributes of the underlying flow characteristics in affecting the thermal behavior of thermocapillary convection in an evaporating thin liquid film of the shear-thinning fluids.
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Kuo‐Tong Ma and Chin Pan
The present work is to investigate nucleate boiling heat transfer at high heat fluxes, which is characterized by the existence of macrolayer. Two‐region equations are proposed to…
Abstract
The present work is to investigate nucleate boiling heat transfer at high heat fluxes, which is characterized by the existence of macrolayer. Two‐region equations are proposed to simulate both thermo‐capillary driven flow in the liquid layer and heat conduction in the solid wall. The numerical simulation results can clearly describe the activities of several multi vorticies in the macrolayer. These vorticies and evaporation at the vapor‐liquid interface constitute a very efficient heat transfer mechanism to explain the high heat transfer coefficient of nucleate boiling heat transfer near CHF. This study also explores the flow pattern of macrolayer with a high conducting solid wall, e.g. copper, and hence the temperature is uniform at the liquid‐solid interface, and the heat fluxes and the evaporation coefficient are found to have significant effect on flow pattern in the liquid layer. Furthermore, a parameter “evaporation fraction” as well as “aspect ratio” is proposed as an index to investigate the thermo‐capillary driven flow system. The model prediction agrees reasonably well with the experimental data in the literature.
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A. Raji, M. Hasnaoui and Z. Zrikem
Heat transfer by natural convection in a system formed by two and three cavities heated from below and covered by a cold plate is numerically studied using the Navier‐Stokes…
Abstract
Heat transfer by natural convection in a system formed by two and three cavities heated from below and covered by a cold plate is numerically studied using the Navier‐Stokes equations with the Boussinesq approximation. Presents results in terms of streamlines, isotherms and heat transfer for Rayleigh numbers ranging from 103 to 106 and the Prandtl number 0.72 (air). Geometric parameters are the aspect ratio A = L′/H′ = 1.5 and 2.5 respectively for two and three cavities, the relative height of the cavities B (1/8 ≤ B = h′/H′ ≤ 1/2) and the parameter C = l′1/l′2 = 1. The inclination angle Φ from the horizontal was varied from 0 to 180°. The calculations reveal that the flow regime depends strongly on the Rayleigh number, the parameter B and the inclination angle Φ of the system; it may be stationary, oscillatory periodic or chaotic. The geometrical parameter B has a significant effect on the transition from one regime to another.
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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…
Abstract
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.