Search

The Darcy–Bénard problem in a bidisperse porous medium with an exothermic reaction at the lower boundary is investigated. The layer is saturated with a non-isothermal liquid containing a concentration of the reactive chemical, and the porous medium is of the Darcy type. The linear instability problem is given a thorough study. The nonlinear stability problem is studied in a case that is believed to be physically relevant, and the stability threshold is compared directly to that found by linear instability theory. The Chebyshev collocation method provides the foundation for the numerical techniques we use, and the QZ algorithm is used to solve the associated finite-dimensional generalized matrix eigenvalue problem. It is demonstrated that there is a region where sub-critical instability can arise. [ABSTRACT FROM AUTHOR]

Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor β which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter β ^ proportional to the compressibility factor β , proving that β ^ enhances the onset of convective motions. Article Highlights: The onset of convection in fluid-saturated porous media is analyzed, taking into account fluid compressibility effect. The critical Rayleigh-Darcy number is determined in a closed algebraic form via linear instability analysis. The critical Rayleigh-Darcy number is shown to be a decreasing function of the dimensionless compressibility factor. [ABSTRACT FROM AUTHOR]

This work deals with a Darcy–Bénard convection problem in the presence of combustion and with local thermal non-equilibrium between the fluid and the solid phases. The effects of combustion and local thermal non-equilibrium on the onset of convection is studied in the linear and nonlinear regimes. Unlike all reported local thermal non-equilibrium problems reported so far, the present problem has a unique situation of having thermal non-equilibrium not only in the perturbed state but also in the basic state. Further, we observe that local thermal non-equilibrium does not, under any circumstance, lead to local thermal equilibrium except in an approximate sense when the combustion is quite weak. The effect of combustion is to advance the onset of convection compared to that in its absence. The effect of local thermal non-equilibrium is to reinforce the effect of combustion. In the presence of both these effects, sub-critical instability exists. The results are obtained numerically and have implication in practical porous medium convection problems. [ABSTRACT FROM AUTHOR]

This work focuses on the impacts of varying penetrability and porosity through the natural convective heat transmission flow of copper–water in a glass bead permeable matrix within a right trapezoidal cavity in consideration of thermal non-equilibrium conditions among the permeable medium, nanoparticles, and the base fluid using the Darcy–Brinkman–Forchheimer model. The model equations are simulated using the Galerkin weighted residual finite element strategy. We analyze the influences of the various model factors particularly, the critical Rayleigh number, the porosity factor, the nanoparticles volume fraction, the interface heat transmission parameters, and the bead diameter in the realms of flow and heat. Furthermore, we investigate the effects of the aspect ratios of the trapezoidal cavity and various thermal boundary situations on the rate of heat transmission for base fluid, nanoparticles, and porous matrix in detail. The results show that the critical Rayleigh number for the commencement of local thermal nonequilibrium states reduced with the enhancement of the bead diameter and the porosity parameter. The average Nusselt number in the base fluid, nanoparticles, and solid matrix increased with the increase of the bead diameter for about 11.7%, 11.6%, and 1.4%, respectively, when it rises from 0.4 to 0.6. The trapezoidal cavity exhibits the greatest heat transmission rate for the base fluid, nanoparticles, and solid matrix in comparison with the cube and the rectangular cavity. Article Highlights: Glass bead diameter and porosity parameter control the state of thermal nonequilibrium. Heat transmission in porous medium enhanced significantly with the glass bead diameter. Heat transmission in the trapezoidal cavity is highest compared to the heat transmission in the cube and rectangular cuboid. [ABSTRACT FROM AUTHOR]

In the present study, a multiple-relaxation-time lattice-Boltzmann method is considered to investigate double-diffusive natural convection in a cavity with heating and diffusing plate inside. The cavity is filled with a porous medium at representative elementary volume scale based on the generalized model. The heated plate is placed horizontally at the center of the cavity with higher temperature and concentration. The horizontal walls of the cavity are assumed to be insulated, no conducting, and impermeable to mass transfer. The vertical walls are kept at low temperature and concentration. The combined effects of buoyancy ratio N ( - 5 ≤ N ≤ 5 ), thermal Rayleigh number Ra T ( 10 4 ≤ Ra T ≤ 10 7 ), Darcy number Da ( 10 - 6 ≤ Da ≤ 10 - 2 ), Lewis number Le ( 1 ≤ Le ≤ 10 ), and porosity of the porous medium ε ( 0.4 ≤ ε ≤ 0.8 ) on double-diffusive natural convection are analyzed numerically. Results are presented in terms of streamlines, isotherms, iso-concentrations, and average Nusselt and Sherwood numbers. Results show that the flow structure, the shape of isotherms, and iso-concentrations are well affected by the control parameters. The heat and mass transfers are promoted by the increase of Darcy number. The effect of the Lewis number on heat transfer is negligible for low Darcy values, but this effect is promoted by increasing Darcy number. [ABSTRACT FROM AUTHOR]

The two-temperature model of local thermal nonequilibrium is employed to study the onset of convection in a triply diffusive fluid-saturated porous medium. The Darcy equation including the time-derivative term is used to describe the flow in the porous medium. The criteria for the stationary and oscillatory instabilities of the basic flow are obtained in the closed form by performing the linear instability analysis. The topology of neutral stability curves is discussed for finite and infinite values of the Prandtl–Darcy number. The disconnected closed oscillatory neutral curves similar to those witnessed in the non-porous and porous (LTE case) domains are found indicating the requirement of three values of thermal Darcy–Rayleigh number to specify the linear instability criteria. There is degeneracy in the closed oscillatory neutral curve between infinite and finite values of the Prandtl–Darcy number; heart-shaped (quasiperiodic bifurcation) in the former case and closed convex in the latter case. Besides, the sensitivity of governing parameters on the nature of instabilities is emphasized. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convection in an electrically conducting fluid-saturated porous layer is studied. The convective flow in the porous medium is induced by horizontal temperature and concentration gradients with net horizontal mass throughflow. The effect of magnetic field on the instability of convection is taken into consideration. The stability of the steady-state solution is investigated in two different approaches, namely the linear instability analysis and nonlinear stability analysis. The nonlinear stability analysis is performed by constructing the energy functional. The eigenvalue problems which are derived from the stability analyses are numerically integrated using the shooting and Runge–Kutta methods. The variation in the critical thermal Rayleigh number against each flow governing parameter is shown graphically. It is observed that Hartman number H a 2 delays the onset of convection to commence and helps to reduce the region of subcritical instabilities. When the solute is concentrated at lower boundary of the porous layer, the onset of convection is in the form of stationary modes, but it switches to oscillatory mode of convection when the solute is concentrated at upper boundary. Interestingly, Hartman number H a 2 plays an important role in delaying this transition from stationary mode to oscillatory mode of convection. [ABSTRACT FROM AUTHOR]

A linear stability analysis for the onset of mixed convection in a saturated porous medium through an absolute instability of both two- and three-dimensional disturbances is performed. Relevant control parameters associated with the inclined temperature gradient and the vertical throughflow are the vertical and horizontal Rayleigh numbers, R v and R h , and the vertical Péclet number, Q v , respectively. This work extends previous studies on the very same problem in two fronts. For two-dimensional disturbances, the present results do not agree with the literature for a few of the parametric conditions reported. This is caused by the collision of the convectively unstable downstream propagating branch with multiple upstream propagating branches, which generates several saddle points and, hence, makes the identification of the correct pinching point more difficult. In other words, literature results are all saddle points but not always pinching points. For three-dimensional disturbances, this issue is not present and the current results agree with the literature. On the other hand, due to the inherent difficulties associated with a three-dimensional absolute instability analysis, literature results have only been able to report the group velocities at the onset of convective instability. When their real parts are zero, transition occurs directly from stable to absolutely unstable. Otherwise, transition occurs from stable to convectively unstable first and nothing can be said about the onset of absolute instability. In this work, a novel technique recently developed by the authors allowed the identification of the onset of absolute instability under all parametric conditions investigated in the literature, extending earlier results. Doing so confirmed the dichotomy already observed in these earlier studies, i.e., the onset of absolute instability for two- and three-dimensional longitudinal modes indeed differs. [ABSTRACT FROM AUTHOR]

We address the problem of initiation of convective motion in the case of a fluid saturated porous layer, containing a salt in solution, which is heated and salted below. We amplify the very interesting recent results of Nield and Kuznetsov and examine in detail a whole range of temperature and salt boundary conditions allowing for a combination of prescribed heat flux and temperature. The behaviour of the transition from stationary to oscillatory convection is examined in detail as the boundary conditions vary from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convective instability of a horizontal throughflow induced by viscous dissipation in a fluid-saturated porous layer of high permeability is investigated. The porous layer is infinitely long along the horizontal direction and is bounded by two rigid surfaces maintained at constant, but different solute concentrations. The lower surface is thermally insulated, whereas the upper surface is considered to be isothermal. The Darcy-Brinkman model is adopted for deriving the equations governing flow in the medium, and the Soret effect is considered to persist in the flow. The instability in the base flow is considered to be induced by the non-negligible viscous heating. Disturbances in the base flow are assumed in the form of oblique rolls, where the longitudinal and the transverse rolls are at two extreme inclinations. The disturbance functions are assumed to be of O(1). It is considered that Ge≪1 and |Pe|≫1, where Ge is the Gebhart number and Pe is the Péclet number. The eigenvalue problem with coupled ordinary differential equations governing the disturbances in the flow is solved numerically using bvp4c in MATLAB. Results obtained depict that the flow is most stable in the Brinkman regime and the longitudinal rolls are the preferred mode of instability. The solute concentration gradient and the Soret parameter have both stabilizing and destabilizing effect on the flow in the medium, when the values of both are either positive or negative. However, they have either monotonically stabilizing or monotonically destabilizing effect on the flow, when the values of both have opposite signs. [ABSTRACT FROM AUTHOR]

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid mixture and subjected to vertical high-frequency and small-amplitude vibrations. Two configurations have been considered and compared: an infinite horizontal layer and a bounded domain with a large aspect ratio. In both cases, the initial temperature gradient is produced by a constant uniform heat flux applied on the horizontal boundaries. A formulation using time-averaged equations is used. The linear stability of the equilibrium solution is carried out for various Soret separation ratios φ, vibrational Rayleigh numbers Rv, Lewis numbers Le and normalized porosity. For an infinite horizontal layer, the critical Rayleigh number Rac is determined analytically. For a steady bifurcation to a one-cell solution (the critical wavenumber is zero), we obtain Rac=12/(φ(Le+1)+1) for all Rv. When the bifurcation is a Hopf bifurcation or when the critical wavenumber is not zero, we use a Galerkin method to compute the critical values. Our study is completed by a nonlinear analysis of the bifurcation to one-cell solutions in an infinite horizontal layer that is compared to numerical simulations in bounded horizontal domains with large aspect ratio. [ABSTRACT FROM AUTHOR]

The linear stability of the double-diffusive convection in a horizontal porous layer is studied considering the upper boundary to be open. A horizontal temperature gradient is applied along the upper boundary. It is assumed that the viscous dissipation and Soret effect are significant in the medium. The governing parameters are horizontal Rayleigh number (RaH), solutal Rayleigh number (RaS), Lewis number (Le), Gebhart number (Ge) and Soret parameter (Sr). The Rayleigh number (Ra) corresponding to the applied heat flux at the bottom boundary is considered as the eigenvalue. The influence of the solutal gradient caused due to the thermal diffusion on the double-diffusive instability is investigated by varying the Soret parameter. A horizontal basic flow is induced by the applied horizontal temperature gradient. The stability of this basic flow is analyzed by calculating the critical Rayleigh number (Racr) using the Runge-Kutta scheme accompanied by the Shooting method. The longitudinal rolls are more unstable except for some special cases. The Soret parameter has a significant effect on the stability of the flow when the upper boundary is at constant pressure. The critical Rayleigh number is decreasing in the presence of viscous dissipation except for some positive values of the Soret parameter. How a change in Soret parameter is attributing to the convective rolls is presented. [ABSTRACT FROM AUTHOR]

The linear stability analysis of vertical throughflow of power law fluid for double-diffusive convection with Soret effect in a porous channel is investigated in this study. The upper and lower boundaries are assumed to be permeable, isothermal and isosolutal. The linear stability of vertical through flow is influenced by the interactions among the non-Newtonian Rayleigh number (Ra), Buoyancy ratio (N), Lewis number (Le), Péclet number (Pe), Soret parameter (Sr) and power law index (n). The results indicate that the Soret parameter has a significant influence on convective instability of power law fluid. It has also been noticed that buoyancy ratio has a dual effect on the instability of fluid flow. Further, it is noticed that the basic temperature and concentration profiles have singularities at Pe=0 and Le=1, the convective instability is looked into for the limiting case of Pe→0 and Le→1. For the case of pure thermal convection with no vertical throughflow, the present numerical results coincide with the solution of standard Horton-Rogers-Lapwood problem. The present results for critical Rayleigh number obtained using bvp4c and two-term Galerkin approximation are compared with those available in the literature and are tabulated. [ABSTRACT FROM AUTHOR]

The onset of double-diffusive convection in a horizontal fluid-saturated porous layer is examined by taking the Soret effect into consideration. The linear and nonlinear stability analyses are derived, and the corresponding eigenvalue problems are solved. The nonlinear stability analysis is achieved by using the energy method. In both the cases of linear and nonlinear stability theories, the onset criterion for all possible modes is derived analytically. For numerical computations of the eigenvalue problem, the Chebyshev tau method is employed. It is observed that the effect of stabilization or destabilization caused by the Soret parameter is significant for the Soret parameters which are less than Sr=2. In the absence of the Soret effect, the linear and nonlinear stability thresholds coincide. [ABSTRACT FROM AUTHOR]

Differentially heated enclosure with heat-generating porous layer on inner walls is studied computationally for non-Darcy flow and thermal non-equilibrium models. In this study, this problem is investigated for different internal and external Rayleigh numbers, Darcy numbers, porosity-scaled thermal conductivity ratio, solid-/fluid-scaled heat transfer coefficient and dimensionless thickness of the porous layer. The results indicate that the dimensionless thickness of the porous layer has an important effect on the heat transfer in the enclosure. It was found that the thermal non-equilibrium model is needed for small values of the porosity-scaled thermal conductivity ratio and the solid-/fluid-scaled heat transfer coefficient. It is shown that the convection of heat due to internal heat generation is increased in the enclosure when the ratio of internal Rayleigh number to external Rayleigh number is larger. [ABSTRACT FROM AUTHOR]

The effect of internal heat source on convection in a layer of fluid in a porous medium was analyzed using linear and nonlinear analysis, and boundaries are assumed to be stress-free and isothermal. Normal mode technique is used for linear analysis, and energy method is used for nonlinear stability analysis. The presence of heat generation leads to the possibility of the existence of a subcritical instability. Effects of increase of Darcy-Brinkman number and internal heat parameter on critical Rayleigh numbers were analyzed numerically using Chebyshev pseudospectral method. [ABSTRACT FROM AUTHOR]

In this study, nonlinear stability analysis of double-diffusive convection in a horizontal fluid saturated porous layer has been investigated. Concentration based internal heat source and vertical throughflow effects are considered during investigation. Energy method has been implemented to develop the nonlinear stability analysis. Runge-Kutta and shooting methods have been used to solve the eigenvalue problem. Critical thermal Rayleigh number is obtained for assigned values of governing parameters. Results of linear and nonlinear theories have been compared. It is observed that for downward throughflow, when Peclet number Pe is high, the effect of concentration based internal heat source $$\gamma $$ is insignificant. [ABSTRACT FROM AUTHOR]

The present work investigates the thermal aspects of a differentially heated porous square enclosure in the presence of an adiabatic block of different block sizes utilizing Darcy-Rayleigh number in the range of 1-10,000 with Darcy number $$10^{-2}$$ - $$10^{-6}$$ . Heatlines and Nusselt number, streamlines, and entropy generation are used for the analysis of heat transfer, flow circulation, and irreversibility production in the enclosure. The study reveals that the presence of an adiabatic block affects the heat transfer process severely, and three different zones of heat transfer are identified. These are namely the zone of heat transfer augmentation, the zone of heat transfer augmentation along with entropy generation reduction, and the zone of both heat transfer and entropy generation reduction. It is also found that the presence of an adiabatic block can enhance heat transfer up to a certain critical block size; thereafter, further increasing in block size reduces the heat transfer rate. An optimal block size where the heat transfer enhancement is maximum is observed to be smaller than the critical block size. The study demonstrates the analyses of heat transfer and entropy generation for a better thermal design of a system. This study is also extended for higher Prandtl number fluids. [ABSTRACT FROM AUTHOR]

The stability of convection in a horizontal porous layer which is saturated with fluid and induced by horizontal temperature gradients subjected to horizontal mass flow is investigated by means of linear and nonlinear stability analysis. The effects of variable gravity field and vertical throughflow are also considered in this analysis. The nonlinear stability analysis part has been developed via energy functional. Shooting and Runge-Kutta methods have been used to solve eigenvalue problem in both cases. Critical vertical thermal Rayleigh numbers for both linear and nonlinear analyses $$R_\mathrm{L}$$ and $$R_\mathrm{E}$$ are evaluated for different values of horizontal Rayleigh number $$R_x$$ , horizontal Peclet number Pe, vertical Peclet number $$Q_\mathrm{v}$$ and variable gravity parameter $$\eta $$ . Comparison is made between linear and nonlinear stability results. It has been observed that linear stability results are overpredicting the onset of convection compared with nonlinear theory, and hence subcritical instabilities would arise before one gets the onset of linear stability threshold. [ABSTRACT FROM AUTHOR]

The possible relevance of the Soret effect in geoscientific studies is discussed. In particular, the question is addressed of whether the observation that salinity generally increases with depth in geologic basins can be explained by this effect. We proceed from the fact that salinity increases with depth, in many cases almost precisely linearly at larger depths. This suggests that salinity may be interdependent with the geothermal gradient that behaves in precisely the same way. Our work on a transient analysis suggests that the timescales involved in establishing corresponding steady state salinity distributions in the presence of a temperature gradient could be on the order of 100 million years. [ABSTRACT FROM AUTHOR]

In this investigation, we intend to present the influence of the prominent Soret effect on double-diffusive free convection heat and mass transfer in the boundary layer region of a semi-infinite inclined flat plate in a nanofluid saturated non-Darcy porous medium. The transformed boundary layer ordinary differential equations are solved numerically using the shooting and matching technique. Consideration of the nanofluid and the coupled convective process enhanced the number of non-dimensional parameters considerably thereby increasing the complexity of the present problem. A wide range of parameter values are chosen to bring out the effect of Soret parameter on the free convection process with varying angle of inclinations making the wall geometry from vertical to horizontal plate. The effects of angle of inclination and Soret parameter on the flow, heat and mass transfer coefficients are analyzed. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles, local wall temperature, local nanoparticle concentration, and local wall concentration reveal interesting phenomenon, and some of these qualitative results are presented through the plots. [ABSTRACT FROM AUTHOR]

The linear and non-linear stability of a rotating double-diffusive reaction-convection in a horizontal anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated considering a Darcy model that includes the Coriolis term. The effect of Taylor number, mechanical, and thermal anisotropy parameters, reaction rate, solute Rayleigh number, Lewis number, and normalized porosity on the stability of the system is investigated. We find that the Taylor number has a stabilizing effect, chemical reaction may be stabilizing or destabilizing and that the anisotropic parameters have significant influence on the stability criterion. The effect of various parameters on the stationary, oscillatory, and finite-amplitude convection is shown graphically. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer. [ABSTRACT FROM AUTHOR]

We consider the effects of rotation in a porous layer heated from below and subjected to a variable gravity field. The study is presented for large Vadasz numbers where no oscillatory convection is possible. It is demonstrated that the Coriolis acceleration stabilizes the convection in a variable gravity field, whilst the effect of gravity parameter stabilses the convection when reduced and destabilizes the convection when increased. [ABSTRACT FROM AUTHOR]

We consider the onset of thermo-solutal convection in a couple-stress fluid-saturated anisotropic porous medium, where the chemical equilibrium on the bounding surfaces and the solubility of the dissolved components depend on temperature. The entire study has been spilt into two parts: (i) linear stability analysis (ii) weakly non-linear stability analysis. Stationary case of linear stability analysis is discussed for two modes of bounding surfaces (a) realistic bounding surfaces i.e. Rigid-Rigid and Rigid-Free (R/R and R/F), (b) non-realistic bounding surfaces i.e. Free-Free (F/F). Howsoever, investigation of oscillatory state and weakly non-linear stability are restricted to F/F case. Galerkin method is used to solve the eigenvalue problem for R/R and R/F cases, whereas, exact solutions are obtained for F/F case.A comparative study among flow stability for above different cases is made as function of ratio of viscosities ( i.e., couple-stress viscosity to fluid viscosity which is defined as couple-stress parameter, $$(C)$$) and effective chemical reaction (i.e. chemical reaction parameter, $$(\chi )$$). It has been found that increasing viscosity of the couple-stress fluid, in terms of increasing $$C$$, increases flow stability in all three cases, but among all cases its stabilization effect for R/R is maximum. However, in the absence of couple-stress parameter the maximum stability of flow is observed for F/F. Apart from this, the chemical reaction stabilizes the flow for all the three cases. Furthermore, stability analysis for F/F case indicates that couple-stress parameter stabilizes the system in all modes (stationary, oscillatory and finite amplitude) of convection.Damköhler number $$(\chi )$$ is found to delay the stationary convection, however, it speeds up the onset of oscillatory convection. The non-linear theory based on truncated representation of Fourier series method predicts the occurrence of sub-critical instability in the form of finite amplitude motion. The effect of $$C$$ and $$\chi $$ on heat and mass transfer is also examined. [ABSTRACT FROM AUTHOR]

This article reports a numerical study of double-diffusive convection in a fluid-saturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio ( λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly. [ABSTRACT FROM AUTHOR]

This work studies the Soret and Dufour effects on the double-diffusive free convection over a downward-pointing vertical truncated cone with variable wall heat and mass fluxes in fluid-saturated porous media. A coordinate transformation is used to derive the nondimensional boundary-layer governing equations, and the obtained nonsimilar equations are then solved by the cubic spline collocation method. Results for local surface temperature and the local surface concentration are presented as functions of Soret parameters, Dufour parameters, power-law exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to increase the local surface temperature, while it tends to decrease the local surface concentration. An increase in the Soret number leads to a decrease in the local surface temperature for buoyancy assisting flows, while it leads to an increase in the local surface temperature for buoyancy opposing flows. Increasing the Soret number tends to increase the local surface concentration. Moreover, the local surface temperature and the local surface concentration of the truncated cones with higher power-law exponents are lower than those with lower exponents. [ABSTRACT FROM AUTHOR]

The double-diffusive convection in a horizontal fluid-saturated porous layer, which is heated and salted from below in the presence of Soret and Dufour effects, is studied analytically using both linear and nonlinear stability analyses. The linear analysis is based on the usual normal mode technique, while the nonlinear analysis is based on truncated representation of Fourier series. The generalized Darcy model that includes the time derivative is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of solute Rayleigh number, Lewis number, normalized porosity parameter, Vadasz number, Soret and Dufour parameters on the stationary, oscillatory convection, and heat and mass transfers are shown graphically. The Vadasz number has dual effect on the threshold of the oscillatory convection. Some known results are recovered as special cases of the present problem. [ABSTRACT FROM AUTHOR]

The free convective flow and heat transfer, within the framework of Boussinesq approximation, in an anisotropic fluid filled porous rectangular enclosure subjected to end-to-end temperature difference have been investigated using Brinkman extended non-Darcy flow model. The studies involve simultaneous consideration of hydrodynamic and thermal anisotropy. The flow and temperature fields in general are governed by, Ra, the Rayleigh number, AR, the aspect ratio of the slab, K*, the permeability ratio and k*, the thermal conductivity ratio, and Da, Darcy number. Numerical solutions employing the successive accelerated replacement (SAR) scheme have been obtained for 100 ≤ Ra ≤ 1000, 0.5 ≤ AR ≤ 5, 0.5 ≤ K* ≤ 5, 0.5 ≤ k* ≤ 5, and 0 ≤ Da ≤ 0.1. It has been found that $${\overline {Nu}}$$, average Nusselt number increases with increase in K* and decreases as k* increases. However, the magnitude of the change in $${\overline {Nu}}$$ depends on the parameter Da, characterizing the Brinkman extended non-Darcy flow. [ABSTRACT FROM AUTHOR]

The effect of rotation on the onset of double diffusive convection in a sparsely packed anisotropic porous layer, which is heated and salted from below, is investigated analytically using the linear and nonlinear theories. The Brinkman model that includes the Coriolis term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and a dispersion relation are obtained analytically using linear theory. The effect of anisotropy parameters, Taylor number, Darcy number, solute Rayleigh number, Lewis number, Darcy-Prandtl number, and normalized porosity on the stationary, oscillatory and finite amplitude convection is shown graphically. It is found that contrary to its usual influence on the onset of convection in the absence of rotation, the mechanical anisotropy parameter show contrasting effect on the onset criterion at moderate and high rotation rates. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfers. The effect of various parameters on heat and mass transfer is shown graphically. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study. [ABSTRACT FROM AUTHOR]

The Darcy Model with the Boussinesq approximation is used to study natural convection in a horizontal annular porous layer filled with a binary fluid, under the influence of a centrifugal force field. Neumann boundary conditions for temperature and concentration are applied on the inner and outer boundary of the enclosure. The governing parameters for the problem are the Rayleigh number, Ra, the Lewis number, Le, the buoyancy ratio, $${\varphi }$$ , the radius ratio of the cavity, R, the normalized porosity, $${\varepsilon }$$ , and parameter a defining double-diffusive convection ( a = 0) or Soret induced convection ( a = 1). For convection in a thin annular layer ( R → 1), analytical solutions for the stream function, temperature and concentration fields are obtained using a concentric flow approximation and an integral form of the energy equation. The critical Rayleigh number for the onset of supercritical convection is predicted explicitly by the present model. Also, results are obtained from the analytical model for finite amplitude convection for which the flow and heat and mass transfer are presented in terms of the governing parameters of the problem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations. [ABSTRACT FROM AUTHOR]

Double diffusive convection in a rotating anisotropic porous layer, saturated by a viscoelastic fluid, heated from below and cooled from above has been studied making linear and non-linear stability analyses. The fluid and solid phases are considered to be in equilibrium. In momentum equation, we have employed the Darcy equation which includes both time derivative and Coriolis terms. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary and oscillatory convection. A weak non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number and Sherwood number as functions of time. We have solved the finite amplitude equations using a numerical scheme. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady and unsteady streamlines, isotherms, and isohalines for various parameters. [ABSTRACT FROM AUTHOR]

The double diffusive convection in a horizontal couple stress fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameter, solute Rayleigh number, Lewis number, couple stress parameter, and Vadasz number on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the thermal anisotropy parameter, couple stress parameter, and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The mechanical anisotropy parameter has destabilizing effect on stationary, oscillatory, and finite amplitude convection. The Lewis number has stabilizing effect in the case of stationary and finite amplitude modes, with dual effect in the case of oscillatory convection. Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decrease with an increase in the values of couple stress parameter, while both increase with an increase in the value of solute Rayleigh number and mechanical anisotropy parameter. The thermal anisotropy parameter and Lewis number have contrasting effect on the heat mass transfer. [ABSTRACT FROM AUTHOR]

Combined heat and mass transfer process by natural convection from a wavy vertical surface immersed in a fluid-saturated semi-infinite porous medium due to Soret and Dufour effects for Forchheimer extended non-Darcy model has been analyzed. A similarity transformation followed by a wavy to flat surface transformation is applied to the governing coupled non-linear partial differential equations, and they are reduced to boundary layer equations. The obtained boundary layer equations are solved by finite difference scheme based on the Keller-Box approach in conjunction with block-tridiagonal solver. Detailed simulations are carried out for a wide range of parameters like Groshof number ( Gr*), Lewis number ( Le), Buoyancy ratio ( B), Wavy wall amplitude ( a), Soret number ( S), and Dufour number ( D). Comparison tables local and average Nusselt ( Nu) number, local and average Sherwood ( Sh) number plots are presented. [ABSTRACT FROM AUTHOR]

Abstract  The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq binary fluid, which is heated and salted from below in the presence of Soret and DuFour effects is studied analytically using both linear and non-linear stability analyses. The linear analysis is based on the usual normal mode technique, while the non-linear analysis is based on a minimal representation of double Fourier series. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumbers for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effects of anisotropy parameter, solute Rayleigh number, and Soret and DuFour parameters on the stationary, oscillatory convection, and heat and mass transfer are shown graphically. Some known results are recovered as special cases of the present problem. [ABSTRACT FROM AUTHOR]

Abstract  The effect of rotation and anisotropy on the onset of double diffusive convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. The effect of rotation, mechanical and thermal anisotropy parameters, and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The finite amplitude analysis is performed to find the thermal and solute Nusselt numbers. The effect of various parameters on heat and mass transfer is also investigated. [ABSTRACT FROM AUTHOR]

Abstract  This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 ⩽ N ⩽  10, 0 ⩽ R t ⩽ 200, 10−2 ⩽ Le ⩽ 200, and 0.125 ⩽ L ⩽ 0.875, where N, R t , Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment. [ABSTRACT FROM AUTHOR]

This paper addresses the derivation of the macroscopic momentum equation for flow through a nonhomogeneous porous matrix, with reference to dendritic structures characterized by evolving heterogeneities. A weighted averaging procedure, applied to the local Stokes' equations, shows that the heterogeneous form of the Darcy's law explicitly involves the porosity gradients. These extra terms have to be considered under particular conditions, depending on the rate of geometry variations. In these cases, the local closure problem becomes extremely complex and the full solution is still out of reach. Using a simplified two-phase system with continuous porosity variations, we numerically analyze the limits where the usual closure problem can be retained to estimate the permeability of the structure. [ABSTRACT FROM AUTHOR]