Search results

Studies a two‐dimensional natural convection in a porous, square cavity using a regular asymptotic development in powers of the Rayleigh number. Carries the approximation through to the 34th order. Analyses convergence of the resulting series for the Nusselt number in both monocellular and multicellular cases, providing insight in the validity regions of the power series.

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.

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.

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.

The present work is the first to consider thermosolutal convection with Soret effect in a square enclosure.

Studies numerically natural convection in a saturated porous medium bounded by two horizontal, isothermal eccentric cylinders by solving the governing two‐dimensional Darcy‐Boussinesq equations on a very fine grid for different values of the eccentricity ε. For a radius ratio of 2 and ε < 0.5, both a bicellular and a tetracellular flow patterns remain stable for moderate Rayleigh numbers. For ε ≥ 0.5, the transition from one flow regime to the other occurs with one of the solutions losing stability. Suggests that in a real situation, insulation is more efficient if the eccentricity is set to the maximum value for which the four‐cell flow pattern is physically realizable than to the value that minimizes the heat transfer when the flow pattern is bicellular. The net gain with respect to a concentric insulation can be of the order of 10 per cent.

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 purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.

The discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.

It is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.

To the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.

Natural convection in a porous layer between two horizontal, concentric cylinders is investigated numerically by solving the 2‐D Darcy‐Boussinesq equations on a very fine grid. The parabolic‐elliptic system was solved by a second order finite difference scheme based on the implicit alternating direction method coupled with successive under relaxation. The calculations show that for radius ratios above 1.7, the functional relationship between the mean Nusselt number and the Rayleigh number exhibits a closed hysteresis loop associated with the transition from a two to a four cell flow pattern. For very small radius ratios, steady state regimes containing 2, 4, 6, and 8 cells are progressively obtained as the Rayleigh number is increased, but no hysteresis behaviour is observed. For a radius ratio of 2, the numerical results are in good agreement with the experimental data. Multi‐cellular regimes and hysteresis loops have also been reported in the literature for fluid annuli but some differences between the two cases exist and are fully explained below.

The effect of the tube wall heat conduction on the natural convection in a tilted long cylindrical envelope with constant, but different temperature of the two ends and an adiabatic outer surface was numerically investigated. The envelope is supposed to be a simplified model for the pulse tube in a pulse tube refrigerator when the pulse tube is positioned at different orientations. It is found that the cylindrical envelope lateral wall heat conduction can enhance the heat transfer from the hot end to the cold end, not only because of the increase in pure heat conduction in the wall, but more importantly, also the intensification of the natural convection within the enclosure. This enhancement is resulted from the big temperature difference between the tube wall and the adjacent fluid near the hot and cold ends. Adoption of low thermal conductivity tube can effectively reduce such additional heat transfers from hot to cold end, thus reducing the loss of cooling capacity for the pulse tube refrigerator.

In general, the bifurcation phenomenon of the natural convection has largely been studied. But the bifurcation of natural convection under magnetic conditions has not been studied as per the authors’ knowledge. This paper aims to investigate the changes in bifurcation phenomenon by the self-induced circular magnetic field.

The authors numerically solved the natural convection in an annulus. The SIMPLE algorithm was adopted for pressure-momenturm coupling. The Boussinesq approximation was used for numerical modeling of natural convection. Finally, the Lorentz force effect by the magnetic field was considered through the source terms in the momentum conservation equation.

It was determined that the heat-transfer rate changes by 17% owing to the applied magnetic effect, and the range of the Rayleigh number for flow bifurcation is changed by the magnetic effect. Moreover, under the strong magnetic condition, the flow bifurcation continues even at very high Ra. Previously, flow bifurcation has been understood as a flow instability phenomena, and the Lorentz force was regarded as a flow-damping effect; however, in this study, it was found that the magnetic field can boost the flow instability and induce flow bifurcation even in the Rayleigh number region where the bifurcation does not appear.

This paper is dealing with the bifurcation phenomenon in MHD natural convection problems. In the past, the electromagnetic forces were regarded as always acting to damp out the existing flows; herewith, the authors first investigated that the magnetic effect can boost the bifurcation of a kind of flow instability phenomenon.

This numerical study of natural convection flow in a horizontal cylindrical annulus is aimed at establishing the utility of the Galerkin‐spline formulation for natural convection problems. The annulus has isothermal walls and the fluid is of constant material properties except for its density; density variation is incorporated via the Boussinesq approximation. Two formulations are employed, the velocity formulation and the streamfunction formulation. We are able to demonstrate the usefulness of the Galerkin‐spline formulation for the problem and in comparison with published data, show that it leads to greater accuracy than the finite difference method. We also show the streamfunction formulation to be superior computationally to the velocity formulation. We find no bifurcation from the basic state up to 60,000 in Grashof number, even without a priori assumption of symmetry about the vertical plane. This last finding is in sharp contrast to results obtained when porous material fills the annulus.

This paper aims to present a study on stability analysis of Jeffrey fluids in the presence of emergent chemical gradients within microbial systems of anisotropic porous media.

This study uses an effective method that combines non-dimensionalization, normal mode analysis and linear stability analysis to examine the stability of Jeffrey fluids in the presence of emergent chemical gradients inside microbial systems in anisotropic porous media. The study focuses on determining critical values and understanding how temperature gradients, concentration gradients and chemical reactions influence the onset of bioconvection patterns. Mathematical transformations and analytical approaches are used to investigate the system’s complicated dynamics and the interaction of numerous characteristics that influence stability.

The analysis is performed using the Jeffrey-Darcy type and Boussinesq estimation. The process involves using non-dimensionalization, using the normal mode approach and conducting linear stability analysis to convert the field equations into ordinary differential equations. The conventional thermal Rayleigh Darcy number RDa,c is derived as a comprehensive function of various parameters, and it remains unaffected by the bio convection Lewis number Łe. Indeed, elevating the values of ζ and γ′ in the interval of 0 to 1 has been noted to expedite the formation of bioconvection patterns while concurrently expanding the dimensions of convective cells. The purpose of this investigation is to learn how the temperature gradient affects the concentration gradient and, in turn, the stability and initiation of bioconvection by taking the Soret effect into the equation. The results provide insightful understandings of the intricate dynamics of fluid systems affected by chemical and biological elements, providing possibilities for possible industrial and biological process applications. The findings illustrate that augmenting both microbe concentration and the bioconvection Péclet number results in an unstable system. In this study, the experimental Rayleigh number RDa,c was determined to be 4π2at the critical wave number (δcˇ) of π.

The study’s novelty originated from its investigation of a novel and complicated system incorporating Jeffrey fluids, emergent chemical gradients and anisotropic porous media, as well as the use of mathematical and analytical approaches to explore the system’s stability and dynamics.