Solutal Grashof Number Research Articles

Slip boundaries effects on double-diffusive convection of magneto-pseudoplastic nanofluid on peristaltic flux in an inclined asymmetric channel

The implications of double-diffusive convection and an inclined magnetic field on the peristaltic transport of a pseudoplastic nanofluid in an inclined asymmetric channel with slip boundaries were investigated in this research. The present problem is mathematically modeled using lubrication techniques, which results in highly nonlinear equations for the proposed problem that is solved using a numerical technique. The graphical findings show how temperature, pressure rise, concentration, pressure gradient, nanoparticle fraction, and stream functions affect key physical parameters of interest. It is revealed that the velocity value rises as the velocity slip parameter, temperature, and solutal Grashof number rise. Furthermore, increasing thermal slip, Dufour, Soret, Brownian motion, and thermophoresis factors increase the temperature profile. If [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] the viscous model of classical Newtonian fluid is a special case of the preceding model.

Flow characteristics in a parallel-plate porous channel under convective boundary conditions and triple diffusion for the non-Darcy porous matrix

This article inspects the effect of triple diffusion in a vertical conduit encapsulated with porous matrix and subjected to third kind boundary conditions. Third kind boundary condition is a combination of Dirichlet and Neumann boundary conditions which specifies a linear combination of function and its derivative values on the boundary. Homogeneous chemical reaction along with viscous and Darcy dissipation effects are included. Adapting the Boussinesq approximation, the soultal buoyancy effects due to concentration gradients of the dispersed components are taken into account. Applying suitable transformations, the conservation equations are reduced into dimensionless form and the dimensionless parameters evolved are thermal Grashof number (0≤Λ1≤20), solutal Grashof number (for species 1 and 2, 0≤Λ2,Λ3≤20), porous (2≤σ≤8) and inertial parameters (0≤I≤6), Biot numbers (at the left and right walls, 1≤Bi1,Bi2≤10), Brinkman number (0≤Br≤1), Schmidt numbers (0≤Sc1,Sc2≤6), Soret numbers (Sr1=Sr2=1) and temperature difference ratio (RT=1). Adopting perturbation technique, the analytical solutions which are applicable only when the Brinkman number is less than one is appraised. However for any values of the Brinkman number, Runge-Kutta shooting method is operated. The impact of selected parameters on the momentum, heat and dual species concentration fields are presented in the form of pictures. The solutions computed by numerical method are justified by comparing with the analytical method. The numerical and analytical solutions are equal in the absence of Darcy and viscous dissipations and the discrepancy advances as the Brinkman number expands. Further the solutions obtained are also justified by comparing the results with Zanchini [1] in the absence of chemical reaction for clear fluid. The thermal field is augmented with the Brinkman number for symmetric and asymmetric Biot numbers. However the profiles are highly distinct at the cold plate for unequal Biot numbers in comparison with equal Biot numbers. The conclusions are admissible to materials processing and chemical transport phenomena.

Characteristics of thermophoresis and Brownian motion on radiative reactive micropolar fluid flow towards continuously moving flat plate: HAM solution

The present objective of this study is to develop a mathematical model and rheological aspects by combining the micropolar fluid model to simulate the reactive flow from a continuously moving flat plate. The current flow model is formulated with employment Thermophoretic diffusion, Brownian motion and chemically reactive species. The focal micropolar based flow equations are transmitted into a non-dimensional form via similarity transformation for which Homotopy Analysis Method (HAM) is employed to obtain approximate analytical solutions. The role of numerous parameters on dimensionless flow phenomena are observed in very effective way utilizing graphical presentation. Various order of approximations for the convergence of HAM has been tabulated. Proper validation is conducted to show a strong relationship between our results with related published ones in literature with some limiting conditions. Furthermore, streamlines and isotherms are also plotted to know the pattern of the fluid flow. More so, the analysis shows that enhancement in Thermal Grashof number, solutal Grashof number and microrotation parameter rises the fluid spin rotation. Temperatures are suppressed with higher thermophoresis and Brownian parameters. Concentrations are elevated with higher thermophoresis parameter. Finally, the observations revealed that the presence of thermophoresis and Brownian motion is more effective to improve heat transportation phenomenon.

Coupled effect of multislips and activation energy in a micropolar nanoliquid on a convectively heated elongated surface

AbstractThis research communication explores the impact of wall slips along with the suspension of nanomaterials in a chemically reactive micropolar liquid stream on a stretched surface with convective heating. Activation of energy is analyzed through the modified Arrhenius function. Radiative heat flux with nonlinearity and temperature‐dependent thermal source (sink) are considered in the heat transmission process. The Cattaneo–Christov approach featuring the time of thermal relaxation is employed. Successive application of scaling analysis followed by the Runge–Kutta–Fehlberg numerical approach delivered computational solutions for the partial differential equations delineating the problem under study. The response of flow variables for different values of various emerged physical variables is elaborated in detail via graphical and numerical presentations. Comparison of the outcome of the current analysis for certain cases is in accordance with the outcomes available in the literature. The findings reveal that pairs of velocity, microrotation, temperature, and species concentration oppositely reacted to both parameters of slip. The temperature of the nanofluid is improved by 18.5%, for specified values of radiation and temperature ratio parameters over that of the pure base liquid. Activation energy augments concentration. The drag coefficient declines with growing thermal and solutal Grashof numbers. Sherwood number is enhanced for higher values of the temperature difference and chemical reaction parameters.

INFLUENCE OF THERMAL RADIATION AND VISCOUS DISSIPATION ON MHD FLOW OF UCM FLUID OVER A POROUS STRETCHING SHEET WITH HIGHER ORDER CHEMICAL REACTION

This article presents the impact of heat and mass transfer on an unsteady conducting upper convected Maxwell fluid (UCM) flow over a stretching surface with porous medium and higher-order chemical reaction. The similarity transformation is used to transform the basic nonlinear partial differential equations and corresponding boundary conditions into a boundary value problem. The results of the study are illustrated with the help of the shooting technique. The variations of velocity, temperature, and concentration profiles are explained through graphs for different values of flow parameters. The tabular values are presented for the study of the physical quantities such as skin friction, Nusselt number, and Sherwood number. We identified the high velocity for large values of thermal and solutal Grashof numbers. There is a significant difference in temperature due to the radiation parameter. Also, it is noticed that the growth in the chemical reaction parameter reduces the concentration field. Further, the present results are validated with the existing results in the literature.

Numerical simulation of double diffusive convection and electroosmosis during peristaltic transport of a micropolar nanofluid on an asymmetric microchannel

A numerical computation is performed to analyze the double diffusive convection in micropolar nanofluids flow governed by peristaltic pumping in an asymmetric microchannel, in the presence of thermal radiation and an external magnetic field. The highly nonlinear governing equations are diluted by using desirable physical assumptions such as lubrication approximation and low zeta potential. Convective boundary conditions are employed. This enables us to determine numerical estimates of various physical flow variables such as velocity, pressure gradient, spin velocity, temperature of the nanofluid, concentration of solute, and volume fraction of nanoparticles for sundry parameters like micropolar parameter, coupling parameter, solutal Grashof number, thermophoretic diffusion coefficient, Grashof number, thermal radiation parameter and Helmholtz–Smoluchowski velocity with the aid of bvp4c function built-in command of MATLAB 2012b. Influence of each relevant parameter on flow, thermal and species characteristics are computed in this study. Influence of Soret and Dufour parameters are also simulated. This model is applicable to the study of chemical fraternization/separation procedures and various thermal management systems like of heat sinks, thermoelectric coolers, forced air systems and fans, heat pipes, and many more.

Soret, Dufour, and activation energy effects on double diffusive convective couple stress micropolar nanofluid flow in a Hall MHD generator system

In this paper, the effect of activation energy, Soret, and Dufour on non-isothermal heat transfer via the non-linear wall of the steady convective flow of micropolar nanofluid magnetohydrodynamics is investigated. Variations in thermophoresis, Brownian motion, couple stress, and Hall current are also considered. Transformations are used to simplify and then solve the governing equations using the optimal homotopy analysis method and are numerically visualized for results. The behavior was examined and explained in all profile graphs. Tables are presented to illustrate the effect of dimensionless parameters on skin friction coefficients, Nusselt and Sherwood numbers. The concentration reduces via the chemical reaction rate, a temperature relative parameter, and increases with an increase in the activation energy and Soret number. It was found that the local skin-friction coefficient at the generator increases with an increase in the Hall current parameter, solutal Grashof number, and couple stress parameter on the x-axis, the local heat rate decreases through the Dufour number and Brownian motion parameter, and the mass transfer rate increases with an increase in the activation energy parameter and Schmitz and Reynolds numbers.

Triple diffusive mixed convection flow in a duct using convective boundary conditions

The motivation of the current article is to explore a numerical investigation on steady triply diffusive convection in a vertical channel. Heat is exchanged from the external fluid with the plates. The reference temperature is taken as equal and also as different for the external fluid. Solutions in the absence of viscous dissipation and buoyancy forces are also obtained as special cases. General solutions including the effects of viscous dissipation and buoyancy forces are obtained analytically using the method of perturbation. The analytical solutions can be used only if the Brinkman number is small. Hence to know the flow properties for all values of Brinkman number, we resort to numerical solutions. The effects of thermal Grashof number, solutal Grashof number, and the chemical reaction parameter on the flow field are evaluated numerically. The obtained results are validated against previously published results for special case of the problems.

Nonlinear Convection Flow of Micropolar Nanofluid due to a Rotating Disk with Multiple Slip Flow

In this analysis, steady, laminar, and two-dimensional boundary layer flow of nonlinear convection micropolar nanofluid due to a rotating disk is considered. The mathematical formulation for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variables, the governing nonlinear boundary value problems were reduced into coupled high-order nonlinear ordinary differential equations with numerically solved. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of different parameters on skin friction coefficients f″0 and G′0, wall duo stress coefficients H1′0, -H2′0, and -H3′0, the Nusselt number -θ′0, and Sherwood number Ω′0, as well as the velocities, temperature, and concentration are analysed and discussed through tables and plotted graphs. The findings indicate that an increase in the values of thermal and solutal nonlinear convection parameters allow to increase the value of velocities f′η and Gη near surface of the disk and reduce at far away from the disk as well as thermal and solutal Grashof numbers tolerate to increase in the value of radial velocity f′η near surface of the disk.

Optimization of heat transfer properties on ferrofluid flow over a stretching sheet in the presence of static magnetic field

The main emphasis of the present research is to investigate the composite effects of magnetization force and rotational viscosity on two-dimensional ferrohydrodynamic non-conducting nanofluid flow over a stretching sheet under the influence of the stationary magnetic field. Microrotation of magnetic fluid and rotation of nanoparticles are also considered. Shliomis model is used in the problem formulation, and then the similarity transformation is applied to transform partial differential equations into a set of nonlinear-coupled ordinary differential equations in dimensionless form. Transformed nonlinear-coupled differential equations are solved through the finite element method using COMSOL Multiphysics under the mathematical modeling. Results for velocity distribution, temperature distribution, concentration distribution and angular velocity distribution are obtained after considering the effects of Maxwell parameter, ferromagnetic interaction number, thermal Grashof number, solutal Grashof number, Brownian motion parameter, thermophoresis number, chemical reaction parameter, radiation absorption coefficient, heat generation/absorption parameter, Prandtl number and Schmidt number in the flow. It has been observed that magnetic energy transforms into kinetic energy, thermal boundary layer and concentration boundary layer in the presence of considered physical parameters.

Mathematical Modelling of Triple Diffusion in Natural Convection Flow in a Vertical Duct with Robin Boundary Conditions, Viscous Heating, and Chemical Reaction Effects

The triple-diffusive convective flow (thermal diffusion and dual species diffusion) in a viscous fluid flowing within a vertical duct is investigated subject to Robin boundary conditions at the duct walls. Viscous heating and homogenous chemical reaction effects are included. The mass transfer (solutal) buoyancy effects due to concentration gradients of the dispersed components are taken into account using the Boussinesq approximation. Symmetric and asymmetric wall conditions for the temperature are taken into account. The conservation equations are rendered into dimensionless form via suitable transformations and the emerging ordinary differential equations feature a number of dimensionless parameters including thermal Grashof number, two solutal Grashof numbers (one for each of the diffusing components i.e. species 1 and species 2), left and right duct wall thermal Biot numbers, species 1 and species 2 chemical reaction parameters, Brinkman number and temperature difference ratio.These coupled and nonlinear dimensionless conservation equations are solved numerically using theRunge-Kutta shooting method. The solutions obtained numerically are validated with approximate analytical solutions obtained via a regular perturbation method which are valid for small values of Brinkman number.The impact of selected parameters on velocity, temperature and dual species concentration distributions is visualized graphically. Furthermore, the variation of skin friction and Nusselt number with these parameters is also tabulated. The solutions obtained numerically and analytically are found to be equal in the absence of viscous dissipation. However, the deviation is magnified with large values of Brinkman number. In the absence of chemical reaction, the results concur with the earlier computations of Zanchini (1998). Increasing second species solutal Grashof number is observed to decelerate the flow in the left duct half space, to accelerate the flow in the right duct half space and consistently reduce temperatures across the entire duct width. With increasing species 1 chemical reaction parameter the concentration magnitudes are elevated in the left duct half space whereas they are depressed in the right duct half space. A similar response is computed for the influence of species 2 reaction parameter on the concentration profile. Temperatures are strongly enhanced across the duct width with increasing Brinkman number and are symmetric in nature about the channel centerline for the symmetric Biot number case (equal thermal Biot numbers at the left and right walls). These profiles are morphed for the asymmetric Biot number case (equal thermal Biot numbers at the left and right walls). Temperatures descend from the left wall to the right wall, although they are still enhanced with increasing Brinkman number. The simulations are relevant to geochemical transport phenomena, industrial materials processing and thermal duct design.

Convection in a vertical duct under the chemical reaction influence using Robin boundary conditions

Convective flow with chemical reaction in a vertical duct using third kind boundary conditions is investigated. The heat is exchanged from the walls of the duct and the external fluid. The equations of balance are written in dimensionless form taking into account the effect of viscous dissipation. The inclusion of viscous dissipation reflects the transformation of original balance equations into nonlinear equations. Hence the closed form solutions are not possible. Therefore, the balance equations are resolved by the classical explicit Runge–Kutta method combined with shooting method which can be employed for various magnitudes of Brinkman number. The solutions obtained numerically are justified by solving the balance equations analytically using the perturbation technique which is applicable only for Brinkman numbers to be less than one. The flow profiles are shown graphically for different values of the thermal and solutal Grashof numbers, Biot numbers, Brinkman number, and chemical reaction parameter. The impacts of physical characteristics on the friction factor and Nusselt number are also evaluated and the results are tabulated. The solutions received by perturbation technique and Runge-Kutta method are equal when Br = 0 and as the Brinkman number increases, the error also increases.

Non-linear convection flow of micro polar nanofluid past an isothermal sphere

In this study, steady laminar two dimensional boundary layer flow of non-linear convection micropolar nanofluid over an isothermal sphere is examined. The mathematical developing for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variable, the governing non-linear boundary value problems were reduced into combined high order non-linear ordinary differential equations. Then, solution for velocity, microrotation, temperature and concentration has been obtained numerically. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of diffident parameters on skin friction coefficient, wall duo stress coefficient the Nusselt number, Sherwood number as well as the velocities, temperature, and concentration are analyzed and discussed through the tables and plotted graphs. A comparison with previous paper obtainable in the literature has been performed and an excellent agreement is obtained. The finding results indicate the raise in either the values of thermal Grashof number Gr or Brownian motion parameter Nb or Schmidt number Sc allows to bringing down the kinematic viscosity of the fluid causes improve the temperature profile distribution within the boundary layer. On the other hand, it can be diminished by the growth in either the value of solutal Grashof number Gm or solutal non linear convection parameter s which agrees to enlarge fluid density.

Soret effects on the mixed convection flow using Robin boundary conditions

AbstractAn investigation has been undertaken as Soret and Schmidt outcomes on the mixed convection flow using Robin boundary conditions. The results use a vertical channel being kept at constant cold temperature and concentration at the left wall and hot temperature and concentration at the right wall. The exchange of heat is done by help of plates with a fluid. We consider the external fluid with equal and different temperatures. This physical problem is solved by using nondimensional parameters with the corresponding boundary conditions. To find analytical solution, the regular perturbation series method is used, and for finding the numerical solution, the well‐known Runge–Kutta method with shooting technique is employed. Comparison of the current study is favorable with the previous published results. The obtained results depend on the governing parameters such as thermal Grashof number, solutal Grashof number, Biot numbers, symmetric and asymmetric wall temperatures, Schmidt number, Soret number, and Brinkman number. An influence of these parameters on the fields of velocity, temperature, and concentration is reported. Further, the numerical results for the Nusselt number, mean value of the velocity, dimensionless bulk temperature, skin friction, and molecular diffusion coefficient are tabulated for different parametric conditions and explained. For small value of Brinkman number, the obtained values agree with other published results for all considered cases.

Entropy Analysis in Double-Diffusive Convection in Nanofluids through Electro-Osmotically Induced Peristaltic Microchannel

A theoretical study is presented to examine entropy generation in double-diffusive convection in an Electro-osmotic flow (EOF) of nanofluids via a peristaltic microchannel. Buoyancy effects due to change in temperature, solute concentration and nanoparticle volume fraction are also considered. This study was performed under lubrication and Debye-Hückel linearization approximation. The governing equations are solved exactly. The effect of dominant hydrodynamic parameters (thermophoresis, Brownian motion, Soret and Dufour), Grashof numbers (thermal, concentration and nanoparticle) and electro-osmotic parameters on double-diffusive convective flow are discussed. Moreover, trapping, pumping, entropy generation number, Bejan number and heat transfer rate were also examined under the influence of pertinent parameters such as the thermophoresis parameter, the Brownian motion parameter, the Soret parameter, the Dufour parameter, the thermal Grashof number, the solutal Grashof number, the nanoparticle Grashof number, the electro-osmotic parameter and Helmholtz–Smoluchowski velocity. The electro-osmotic parameter powerfully affected the velocity profile. The magnitude of total entropy generation increased as the thermophoresis parameter and Brownian motion parameter increased. Soret and the Dufour parameter had a strong tendency to control the temperature profile and Bejan number. The findings of the present analysis can be used in clinical purposes such as cell therapy, drug delivery systems, pharmaco-dynamic pumps and particles filtration.

Unsteady Hydromagnetic Flow of Eyring-Powell Nanofluid over an Inclined Permeable Stretching Sheet with Joule Heating and Thermal Radiation

The present analysis deals with an unsteady magnetohydrodynamic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet. Effects of thermal radiation, Joule heating, and chemical reaction are considered. The effects of Brownian motion and thermophoresis on the flow over the permeable stretching sheet are discussed. Using Runge-Kutta fourth-order along with shooting technique, numerical and graphical results were obtained for the governing flow equations. The influence of various parameters on flow variables have been examined in detail. The results reveal that the temperature of the fluid enhanced with increasing Brownian and thermophoresis parameters. The increase of fluid velocity with the local Grashof number, the solutal Grashof number has been noticed. Further, the nanoparticles concentration decreased for a given increase in Brownian motion and chemical reaction parameters, while it increased with an increase in the thermophoresis parameter.

Convective-radiative double-diffusion heat transfer in power-law fluid due to a stretching sheet embedded in non-Darcy porous media with Soret–Dufour effects

A numerical model is developed to study the combined effects of Soret and Dufour on mixed convection heat and mass transfer in a Power-law fluid saturated with Darcy–Forchheimer porous medium in the presence of nonlinear thermal radiation, chemical reaction and Ohmic dissipation. The governing boundary layer equations are solved numerically by using shooting method with Runge–Kutta Fehlberg integration scheme. The influence of Soret and Dufour numbers, chemical reaction, thermal Grashof number and solutal Grashof number on velocity, temperature and concentration fields are studied. The effects of some important physical parameters on skin-friction, Nusselt number and Sherwood number are studied in detail.

Unsteady MHD chemically reactive double‐diffusive Casson fluid past a flat plate in porous medium with heat and mass transfer

AbstractIn this paper, an attempt has been made to analyze the effects of various parameters, such as Soret and Dufour effects, chemical reaction, magnetic field, porosity on the fluid flow, and heat and mass transfer of an unsteady Casson fluid flow past a flat plate. Convective boundary conditions in heat and mass transfer and slip constant on velocity have been taken into account for analysis. The governing equations of the model have been solved numerically using the MATLAB program bvp4c. The impact of various parameters of the model on the velocity, temperature, and concentration profiles has been analyzed through different graphs. To get an insight into the physical quantities of engineering interest, viz, skin friction, Sherwood number, and Nusselt number, their numerical values have been computed for various parameters. The range of the parameters used in numerical computations are , , , , , , and . It has been noticed from the tabulated values that the skin friction gets enhanced with the increase in the thermal and solutal Grashof number, whereas its reverse effects have been observed with an increase in the Biot number. In limiting case, the present study is also compared with the available results in the literature.

COMPUTATION OF TRANSIENT RADIATIVE REACTIVE THERMOSOLUTAL MAGNETOHYDRODYNAMIC CONVECTION IN INCLINED MHD HALL GENERATOR FLOW WITH DISSIPATION AND CROSS DIFFUSION

The present article investigates the collective influence of chemical reaction, viscous dissipation and Hall current magnetic effects on timedependent radiative magnetohydrodynamic flow, heat and mass transfer from an inclined wall embedded in a homogenous, isotropic highpermeability porous medium. The model developed is relevant to near wall magnetohydrodynamic energy generator transport phenomena in which chemical corrosion effects may arise during operations. The governing non-linear partial differential equations for mass, momentum, energy and species conservation are transformed into a system of coupled non-linear dimensionless partial differential equations with appropriate similarity variables. The normalized conservation equations are then solved with a robust finite element method (MATLABFEM) subject to corresponding initial and boundary conditions. Important dimensionless parameters emerging are Eckert number, thermal Grashof number, solutal Grashof number, magnetic body force parameter, Hall parameter, permeability parameter, Dufour number, Soret number, time, radiation-conduction parameter, chemical reaction parameter, heat absorption parameter, Prandtl number, Schmidt number and wall angle. Primary velocity is enhanced with Eckert number, thermal Grashof number, solutal Grashof number, Hall parameter, permeability parameter, Dufour number, Soret number, radiation-conduction parameter and time whereas it is reduced with first order chemical reaction parameter, heat absorption, magnetic body force parameter, Prandtl number, Schmidt number and wall inclination. Secondary velocity is elevated with Eckert number, solutal Grashof number, thermal Grashof number, magnetic body force parameter, Hall parameter, radiation-conduction parameter, Dufour number, Soret number and time whereas it is suppressed with reaction parameter, heat absorption, Prandtl number, Schmidt number and wall inclination. Temperature is enhanced with Eckert number, Dufour number, heat absorption, radiation-conduction parameter and time whereas it is depressed with Prandtl number. Species concentration is reduced with increasing chemical reaction parameter (destructive homogenous reaction) and Schmidt number whereas it is elevated with Soret number and time. Extensive discussion of the finite element formulation, convergence and validation is provided Skin friction, Nusselt number and Sherwood number distributions are also provided for selected parameter variation. Validation of solutions with published literature is also included for several special cases, namely non-reactive, non-dissipative flow in the absence of heat generation or absorption. Further validation is included using a multi-step differential transform method (MS-DTM). The present simulations provide an interesting insight into complex fluid/thermal/species diffusion characteristics in the boundary layer region of relevance to working MHD generator systems.

Forced flow structure and mixed convection in a ventilated porous enclosure with a local contaminant source

In this paper forced flow structure and mixed convection in a ventilated porous enclosure with a local contaminant source centrally positioned on the floor have been investigated numerically. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. The set of coupled equations is solved via the SIMPLE algorithm. Comparisons with previously published work are performed and found to be in excellent agreement. An extensive series of numerical simulations is conducted in the range of, 200 ≤ Re ≤ 10,000, 0.02 ≤ Re · Da ≤ 20 and, 0.01⩽f=(Grs·Da2)/(Re·Da)⩽1000 where Re is the Reynolds number, Da is the Darcy number, Grs is the solutal Grashof number and f is derived from the discretized V equation and represents the relative magnitude between the effective solutal buoyancy and the effective external force. Streamlines are produced to illustrate the forced flow structure transition from eddy-free motion to multi-eddy pattern and Re · Da ≥ 0.2 is the critical condition of eddy emergence. The analysis of overall Sherwood number and iso-concentrations indicate that the parameter f is appropriate to be regarded as the criterion of mixed convection in porous medium.