Search results

Mixed convection heat transfer in ventilated cavities submitted to a constant heat flux has been numerically studied using the Navier‐Stokes equations with the Boussinesq approximation. Results in terms of streamlines and isotherms are produced for different values of the governing parameters, namely, the Rayleigh number (10³ ≤q Ra ≤q 10⁶) and the Reynolds number (5 ≤q Re ≤q 5, 000). The geometrical parameters are the aspect ratio of the cavity A = L^’/H^’ = 2 and the relative height of the openings B = h^’/H^’ = 1/4. Results of the simulations show that the maximum interaction between natural and forced convection occurs for couples (Ra, Re) which can be correlated as Re = a Ra^b.

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 Ra_E = 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.

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.

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.

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.

The investigation of heat transfer and fluid flow by mixed convection in a vertical rectangular cavity containing adiabatic partitions attached to the heated wall is numerically studied. The parameters governing this problem are the Rayleigh number (10³≤Ra≤4×10⁵), the Reynolds number (5≤Re≤100), the aspect ratio of the cavity (2.5≤A≤15), the partitions length (0.1≤B≤0.95), the aspect ratio of the micro cavities (0.33≤C≤0.66) and the Prandtl number (Pr=0.72). The results obtained indicate that the heat exchange between the system and the external medium, through the cold wall and the upper vent, are considerably affected by the presence of the partitions and for all the values of A and Ra considered. However, the quantity of heat released by the higher opening remains insensitive to the presence of the partitions; it depends only on the intensity of the forced flow. Moreover, it is shown that for critical values of Re and Ra, these rates of heat transfer pass by maxima of which the value is independent of A when this parameter is equal to or higher than 10. For high Reynolds numbers, the flow is dominated by forced convection for low values of Ra and high values of B. Finally, the competition between natural and forced convection occurs when Ra≥10⁴. The heat transfer is correlated with the main parameters and presented for an eventual utilization in design.

The interaction between mixed convection and thermal radiation in ventilated cavities with gray surfaces has been studied numerically using the Navier‐Stokes equations with the Boussinesq approximation. The effect of thermal radiation on streamlines and isotherms is shown for different values of the governing parameters namely, the Rayleigh number (10³ ≤ Ra ≤ 10⁶), the Reynolds number (50 ≤ Re ≤ 5000) and the surfaces emissivity (0 ≤ ε≤ 1). The geometrical parameters are the aspect ratio of the cavity A = L’/H’ = 2 and the relative height of the openings B = h’/H’ = 1/4. Results of the study show that thermal radiation alters significantly the temperature distribution, the flow fields and the heat transfer across the active walls of the cavities.

The aim of the present investigation was to study numerically the natural convection in partitioned enclosures with localized heating from below. Two‐dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using finite difference method. Various geometrical parameters were: aspect ratio A = 0.4−0.6, isothermal surface length B = 0.5, its position C = 0.3, partition position D = 0.5−1.0, its length E = 0.2−0.6, heat source length X = 0.05−1.00, and its position ε = variable. The Rayleigh number was varied from 103 to 106. The results are reduced in terms of the normalized Nusselt number as a function of the Rayleigh number, and other non‐dimensional geometrical parameters. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions.

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.

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).

The aim of this work consists of studying numerically the coupling between natural convection and radiation in a tall rectangular cavity by examining the effect of the emissivity of the walls, ε, the Rayleigh number, Ra, and the inclination of the cavity, θ, on the flow characteristics and the existence ranges of the multiple solutions obtained.

The Navier‐Stokes equations were discretized by using a finite difference technique. The vorticity and energy equations were solved by the alternating direction implicit method. Values of the stream function were obtained by using the point successive over‐relaxation method. The calculation of the radiative heat exchange between the walls of the cavity is based on the radiosity method.

For an inclined cavity (θ=45°), up to four different solutions are obtained and their range of existence is found to be strongly dependent on the Rayleigh number and the emissivity of the cavity walls. In the case of a vertical cavity (θ=90°), the weak reduction of the convection effect due to radiation is largely compensated for by the contribution of the radiation which enhances the overall heat transfer through the cold surface of the cavity and favours the appearance of secondary cells.

The existence of multiple steady‐state solutions in an inclined cavity (θ=45°) and the number of the obtained solutions are affected by the presence of radiation. In face, the increase of the emissivity reduces the number of solutions for weak values of the Rayleigh number. Also, the increase of this parameter favours the multiplicity of solutions for all the considered values of the emissivity. For a vertical cavity (θ=90°), the effect of radiation generates an oscillatory convection for large values of the Rayleigh number.

The purpose of this paper is to consider flow over heat generating bodies in an open‐ends cavity, which finds applications in electronics cooling and industrial processing. Heat transfer rates depend on the flow situation in the cavity, which is influenced by the cavity inlet and exit port locations, heat transferring body size and its orientation in the cavity, and the cavity size. Consequently, modeling of flow over heat transferring bodies in an open‐ends cavity and examination of the effect of the aspect ratio and orientation of the heat transferring bodies on the flow field and heat transfer rates becomes essential.

The flow over heat generating solid blocks situated in an open‐ends cavity is considered and the effects of blocks' orientations and aspect ratios on flow field as well as heat transfer rates are examined. A numerical scheme using a control volume approach is introduced to predict flow field in the cavity and heat transfer rates from the blocks.

It is found that complex flow structure is generated in the cavity due to the aspect ratios and orientations of the blocks. This, in turn, influences significantly heat transfer rates from the blocks in the cavity.

Surface areas of blocks are kept the same and aspect ratio is varied such that the surface area of each block remains the same in the simulations. In addition, Steady flow situation is considered for governing equations of flow and heat transfer in the cavity. However, for the future study transient heating and flow situations can be considered while varying the surface araes of the blocks. This will provide useful information on the circulations in the cavity and the enhancement of heat transfer due to the complex flow structure.

In practice, cooling effectiveness can be improved through changing the aspects ratio of the heat generating bodies in the cavity.

The findings are original and will be useful for the scientists and the design engineers working the specific area of heat transfer and fluid flow.

The aim of this work is to study numerically and analytically flow and heat transfer characteristics and multiplicity of steady states for natural convection in a horizontal rectangular cavity, filled with non‐Newtonian power‐law fluids and heated from all sides.

The governing equations are discretised by using the well known second‐order central finite difference method and integrated by combining the ADI and PSOR techniques. The analytical approach is based on the parallel flow assumption.

Natural and anti‐natural flows existence is proved when the Rayleigh number exceeds a critical value and the side lateral heating intensity values is chosen inside a specific range. The analytical results are found to agree well with those obtained numerically. The fluid flow and the heat transfer are found to be rather sensitive to the non‐Newtonian power‐law behaviour.

The obtained results are limited to non‐Newtonian power‐law fluids and cannot be extended to fluids having other behaviours.

The problem is implied in some industrial thermal processes.

Existence of multiple steady state‐solutions in the range of the side lateral heating intensity values ensuring, that is reduced by the shear‐thickening behaviour and extended by the shear‐thinning one for a given value of Rayleigh number.