Unsteady Double-diffusive Natural Convection Research Articles

A space-time generalized finite difference method for solving unsteady double-diffusive natural convection in fluid-saturated porous media

In this paper, the space-time generalized finite difference scheme is proposed to effectively solve the unsteady double-diffusive natural convection problem in the fluid-saturated porous media. In such a case, it is mathematically described by nonlinear time-dependent partial differential equations based on Darcy's law. In this work, the space-time approach is applied using a combination of the generalized finite difference, Newton-Raphson, and time-marching methods. In the space-time generalized finite difference scheme, the spatial and temporal derivatives can be performed using the technique for spatial discretization. Thus, the stability of the proposed numerical scheme is determined by the generalized finite difference method. Due to the property of this numerical method, which is based on the Taylor series expansion and the moving-least square method, the resultant matrix system is a sparse matrix. Then, the Newton-Raphson method is used to solve the nonlinear system efficiently. Furthermore, the time-marching method is utilized to proceed along the time axis after a numerical process in one space-time domain. By using this method, the proposed numerical scheme can efficiently simulate the problems which have an unpredictable end time. In this study, three benchmark examples are tested to verify the capability of the proposed meshless scheme.

Some Insights on Unsteady Double Diffusive Natural Convection of Porous Medium in Vertical Open-Ended Cylinder

The work presented in this paper deals with combined heat and mass transfer by natural convection in porous media. The aim is to investigate numerically the effect of control parameters on the flow behavior as well as the enhancement of heat transfer in vertical porous enclosure. The side wall temperature is periodic function of time which is the case in several physical problems. The Darcy’s flow model coupled with the energy and mass equations is considered. The numerical results show that the flow’s behavior is strongly dependent on the buoyancy ratio values. Three types of flows take place: chimney, reversal and top aspiration flow. Further, the effect of buoyancy ratio (N) at which the different flow types occur is significantly influenced by the values of control parameters. The relative heat transfer enhancement between constant and periodical wall temperature is profoundly affected by thermal Rayleigh number (Ra), buoyancy ratio and dimensionless amplitude (XA). In the case of opposing double diffusive flow, the relative difference becomes to the favor of the stationary case for high Ra and XA.

Unsteady double-diffusive natural convection in a two-sided lid-driven inclined porous enclosure with sinusoidal boundary conditions with Soret and Dufour effects

ABSTRACTUnsteady double-diffusive natural convection in an inclined porous enclosure with sinusoidal boundary conditions and Soret and Dufour parameters is studied. The unique aspects of the set-up are that the left vertical and bottom walls are heated and concentrated non-uniformly and uniformly, respectively, while the right vertical wall is well insulated and the top wall is maintained at a constant concentration and cold temperature. A staggered grid finite-difference method is used to solve the system of partial differential equations that model heat and mass transfer inside the enclosure. We demonstrate the effects of the Soret and Dufour parameters and the inclination angle on the unsteady double-diffusive natural convection in the inclined porous enclosure. With all the numerical studies, the least square curve fitting (exponential non-linear curve fitting) of average Nusselt number and average Sherwood number with respect to different Soret and Dufour numbers at the left vertical wall which is non-uniformly heated and concentrated is examined here. Comparison with previously published results shows an excellent agreement.

Unsteady double-diffusive convection in a water-based Al2O3-nanofluid in a two-sided lid-driven porous cavity

ABSTRACTA numerical investigation of the flow and behaviour of properties of a water-based Al2O3-nanofluid inside a two-sided lid-driven inclined non-uniformly heated and concentrated porous cavity is made in this paper. The focus of the study is on determining how the buoyancy ratio and the inclination angles influence the unsteady double-diffusive natural convection in a cavity filled with a porous medium, and with non-uniform boundary conditions. We further consider different nanoparticle volume fractions of the nanofluid. It is assumed that the left and right vertical walls are insulated, while the bottom wall is heated and concentrated non-uniformly and the top wall maintained at a constant cold temperature. The top and bottom walls move from left to right and right to left with constant speed, respectively. The governing equations are solved numerically using a staggered grid finite-difference method for streamlines, isotherms, iso-concentrations, average Nusselt number and average Sherwood number for various values of nanoparticle volume fraction, inclination angle and buoyancy ratio. The change in the flow, temperature and concentration profile patterns with respect to time is depicted and described. The results are compared with previously published work and excellent agreement has been obtained.

Soret and Dufour effects on unsteady double diffusive natural convection in porous trapezoidal enclosures

This work examines the Soret and Dufour effects on the unsteady double-diffusive natural convection inside trapezoidal enclosures filled with isotropic porous medium with exponential variation of boundary conditions. The analysis uses a two-dimensional trapezoidal enclosure with the inclined walls being kept at constant cold temperature and concentration while the temperature and concentration vary exponentially on the bottom wall of the enclosure. The top wall of the trapezoidal is thermally insulated. The physical problems are represented by non-dimensional governing equations along with the corresponding boundary conditions are solved numerically by the finite difference method. The present results are validated by favorable comparisons with previously published results. Representative results depicting the effects the various parameters, namely, the buoyancy ratio parameter, and the Dufour and Soret numbers on the streamlines, isotherms, isoconcentration lines as well as the local Nusselt and Sherwood numbers are reported. In addition, numerical results for the average Nusselt and Sherwood numbers are presented in tabular forms for various parametric conditions and discussed.

多孔介质中非平稳双扩散自然对流的有限差分法

多孔介质中非平稳双扩散自然对流的有限差分法

Unsteady double-diffusive natural convection with Soret and Dufour effects inside a two-sided lid-driven skewed enclosure in the presence of applied magnetic field

This article describes the heat and mass transfer as well as the entropy generation in an unsteady double-diffusive natural convection in the presence of an external magnetic eld, Soret and Dufour e ects. The analysis uses a two- dimensional skewed enclosure, where the inclined walls make a skew angle  with x-axis. The governing equations in the physical domain are transformed into an orthogonal computational domain by co-ordinate transformations, and then are solved using a nite volume method based on SIMPLE algorithm. The computations are carried out in the six skewed enclosures with skew angles  = 15, 30, 45, 60, 75, and 90, for a wide range of the Hartman number, Lewis number, buoyancy ratio, and Dufour coecient, while Soret coecient is kept constant at 0.25 in most of the study. Results show that the fluid flow, heat and mass transfer, as well as the entropy generation are sensible to some extent to the skew angle variation. Meanwhile, the Lewis number and buoyancy ratio have an aiding and opposing action, respectively, on suppression eff ect of Lorentz force against convective heat and mass transfer. It is also shown that the average entropy generation is an increasing function of Lewis number, buoyancy ratio, and Dufour coecient, while its a decreasing function of Hartman number.

Three-dimensional numerical investigation on thermosolutal convection of power-law fluids in anisotropic porous media

The present study simulates the 3D unsteady double-diffusive natural convection subject to opposing thermal and solutal buoyancy forces (N<0) in a porous cubic by a generalized non-Darcy model, in which the effects of the crucial parameters such as the porous thermal Rayleigh numbers, buoyancy ratio and anisotropy ratio on the flow structure, heat and mass transfer of power-law fluids are investigated independently. The top and bottom walls are given different temperatures and concentrations, while the other walls are adiabatic and impermeable. A compact high order finite volume method is adopted to describe the flow structure and the resulting heat and mass transfer characteristic of non-Newtonian fluids in the anisotropy porous cubic. Our simulations show that the flow structure develops from conduction-dominated to convection-dominated as buoyancy ratio or anisotropy ratio or porous thermal Rayleigh number increases. The average Nusselt and Sherwood numbers keep constants during the conduction-dominated stage, then increase along the transition route. On the other hand, the impacts of different power-law indexes on the convection are mainly manifested in rheological properties, which elucidate that the shear-thinning fluids is more effective in heat and mass transfer enhancement than shear-thickening fluids. The studies may help us establish a physically reasonable methodology to systemically assess double-diffusive convection of non-Newtonian power-law fluids in anisotropy porous media in the real world.

An Unsteady Double-Diffusive Natural Convection in an Inclined Rectangular Enclosure with Different Angles of Magnetic Field

An unsteady double-diffusive natural convection flow in an inclined rectangular enclosure subject to an applied magnetic field and heat generation parameter is studied. The enclosure is heated and concentrated from one side and cooled from the adjacent side. The other two sides are adiabatic. The governing equations are solved numerically using a staggered grid finite-difference method to determine the streamline, isotherm and iso-concentration contours. We have further obtained the average Nusselt numbers and average Sherwood numbers for various values of buoyancy ratio and different angles of the magnetic field by considering three different inclination angles of the enclosure while keeping the aspect ratio fixed. The results indicate that the flow pattern, temperature and concentration fields are significantly dependent on the buoyancy ratio and the magnetic field angles. It is found that different angles of the magnetic field suppress the convection flow and its direction influences the flow patterns. This leads to the appearance of inner loop and multiple eddies.

Unsteady Double Diffusive Natural Convection with Dufour and Soret Effects

Unsteady Double Diffusive Natural Convection with Dufour and Soret Effects

A model of coupled thermosolutal convection and thermoelasticity in soft rocks with consideration of water vapor absorption

The unsteady double-diffusive natural convection flow in a rectangular enclosure filled with soft rocks which are subjected to humid air, including water vapor absorption and thermoelasticity, is studied numerically. The high order compact finite difference schemes are adopted for better simulation of this problem, and a Darcy–Brinkman–Forchheimer extended model combined with the absorption and thermoelasticity effects is introduced. The effects of the thermal and solutal Rayleigh numbers, hygroscopicity, Darcy numbers and thermoelasticity on the flow are investigated in detail. Results are presented in the form of streamlines and isolines of temperature and mass fraction as well as the plots of average Nusselt and Sherwood numbers over the walls under different conditions. The flow structure develops from conduction-dominated to steady convection-dominated as increasing Rayleigh number or increasing buoyancy ratio as well as increasing Darcy numbers. The thermoelasticity effects of soft rocks play an important role in the analysis of thermal convection flow by the change of temperature and permeability, while the water vapor absorption effects may have a slight effect on the flow in the beginning and vanish with the absorption effects becoming weak. Nevertheless, the effect may significant reduce the mechanical strength properties of soft rocks.

An unsteady double-diffusive natural convection in an inclined enclosures filled with porous medium with non-uniform boundary conditions in presence of thermal radiation

An unsteady double-diffusive natural convection in an inclined enclosures filled with porous medium with non-uniform boundary conditions in presence of thermal radiation

Unsteady double diffusive convection in an inclined rectangular lid-driven enclosure with different magnetic field angles and non-uniform boundary conditions

The effect of buoyancy ratio on an unsteady double diffusive natural convection flow in an inclined lid-driven enclosure with different magnetic field angles is studied. The enclosure is non-uniformly heated and concentrated from the bottom side and uniformly heated and concentrated from the left vertical side. The right vertical wall is insulated and the top wall is cooled. The top wall moves in the positive direction with a constant speed from left to right. The governing equations have been solved numerically using the staggered grid finite-difference method to obtain streamlines, isotherms, iso-concentrations, average Nusselt and Sherwood numbers for various values of the buoyancy ratio and different magnetic field angles for three different cavity inclination angles. The results indicate that the flow pattern, temperature and concentration fields are significantly depend on the magnetic field and cavity inclination angles. It was found that different angles of the magnetic field may suppress the convection flow and that the direction of the magnetic field influences the flow pattern. Computations of the average Nusselt numbers at the left hot wall are made and these compare favorably with previously published results. The change in streamline, isotherm and iso-concentration patterns with time is described here.

Effects of buoyancy ratio on unsteady double-diffusive natural convection in a cavity filled with porous medium with non-uniform boundary conditions

The effects of buoyancy ratio on unsteady double-diffusive natural convection in a cavity filled with porous medium with uniform and non-uniform boundary conditions are analyzed in this paper. It is assumed that the left vertical wall and bottom wall are heated and concentrated (uniformly and non-uniformly), while the right vertical wall is maintained at a constant cold temperature, and the top wall is well insulated. The governing equations are solved numerically using a staggered grid finite-difference method to determine the streamlines, isotherms, isoconcentrations, local Nusselt number, local Sherwood number, average Nusselt number and average Sherwood number for various values of buoyancy ratio and Rayleigh number. The change of flow patterns with respect to time depicted and described here. The results are compared with previously published work and excellent agreement has been obtained.

Numerical simulation of unsteady double-diffusive natural convection within an inclined parallelepipedic enclosure

Unsteady three-dimensional (3D) double diffusive convection in tilted enclosure having a parallelepipedic shape has been analyzed numerically. The governing unsteady, 3D flow, energy and concentration transport equations, have been solved using an accelerated multigrid implicit volume method. Main attention was paid to the effects of the Rayleigh number Ra , buoyancy ratio N and the inclination angle γ of the cavity on the flow structure and heat and mass transfer rates. Typical distributions of velocity contours, temperature and concentration fields in wide range of defining parameters 103 ≤ Ra ≤ 2 × 104, -5 ≤ N ≤ 5 have been obtained. It is found, that the optimal heat and mass transfer rates for the aiding situation have been observed at two particular inclination angles namely 30° and 75° about the horizontal direction. It should be noted that the flow undergoes a periodic behavior for particular parameters Ra = 104 and γ = 75° according to the aiding flow case. The results also suggest that when N is in range -2 ≤ N ≤ -0.6, the flow continues to be three-dimensional keeping different heat and mass rates. Furthermore, it has been argued that the 2D assumption can be adopted for the 3D flows when the buoyancy ratio N is in range (-0.5–0).

Effects of chemical reaction and thermal radiation on unsteady double diffusive convection

Purpose – The purpose of this numerical paper is to investigate the simulation of an unsteady double diffusive natural convection in square enclosure filled with a porous medium with various boundary conditions in the presence of thermal radiation and chemical reaction effects. Design/methodology/approach – In this study, the governing dimensionless equations were written using the Brinkman Forchheimer extended Darcy model. They are numerically solved by using finite difference method by applying adiabatic boundary condition in top surface. The bottom surface is maintained at uniform temperature and concentration and left and right vertical walls are cooled. Findings – Results are presented by streamlines, isotherms, temperature and concentration contours profiles as well as the local Nusselt number and Sherwood numbers for different values of the governing parameters such as Darcy number, buoyancy ratio, Rayleigh number, thermal radiation parameter and chemical reaction parameter. It is found that that both of the local Nusselt and Sherwood numbers increase as the Rayleigh number, buoyancy ratio and Darcy number increase. Moreover, increasing the thermal radiation effects leads to a pronounced increase in the local Nusselt number, while the opposite behavior is displayed by the local Sherwood number. Furthermore, the local Sherwood number increases and the local Nusselt number decrease when the chemical reaction parameter increase. Originality/value – The originality of this study is the square cavity with various boundary conditions filled with a porous medium with thermal radiation and chemical reaction effects.

Unsteady Double Diffusive Natural Convection in Porous Media-Application to CO2 Storage in Deep Saline Aquifer Reservoirs

Storage capacity of carbon dioxide (CO2) in deep saline aquifers is a challenging task. However, an assessment must be performed to determine whether there is sufficient capacity in a storage site for any CO2 sequestration project. We evaluated the CO2 storage capacity for a simplified reservoir system, which the layered potential storage formations are overlaid by sealing cap rock.In this paper, we aim to investigate numerically the storage of CO2 at supercritical conditions in deep saline aquifer reservoirs. Numerical simulations were carried out on non-deformable saturated porous material inside a vertical enclosure, assumed to be impermeable and isolated on three sides. The porous medium is considered to be homogeneous and isotropic with constant thermo-physical properties with the exception of the density of the fluid varying according to Boussinesq approximations.A dynamic model assuming that flow is two-dimensional and obeying to Darcy's law for motion has been used. We assume also that the thermal equilibrium assumption is valid. The set of the conservation equations along with the appropriate initial and boundary conditions have been resolved numerically by the classical finite volume method [1]. Spatio-temporal variations of different state variables such as pressure, velocity, temperature and concentration were numerically simulated and plotted versus different controlling parameters particularly, thermal and solutal Rayleigh numbers and Lewis number. Great attention was paid to examine the sensitivity of heat and mass transfer rates according to the reservoir form and the operating conditions.

Effect of sinusoidal variations of boundary conditions on unsteady double diffusive convection in a square enclosure filled with a porous medium

PurposeThe purpose of this paper is to deal with unsteady double diffusive natural convection in a square enclosure filled with a porous medium with various boundary condition effects in the presence of heat source or sink.Design/methodology/approachFinite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, amplitude wave length ratio, dimensionless time parameter, Darcy number, buoyancy parameter and heat generation/absorption parameter on the streamlines, temperature and concentration contours, as well as Nusselt number and Sherwood number, were considered.FindingsThe sinusoidal variations of the temperature and concentration remove the singularities which appear in the case of fixed temperature and concentration.Originality/valueThe paper's results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.