Mixed convection inside a fluid‐porous composite cavity with centrally rotating cylinder

The mixed convection in a fluid‐porous composite medium lying inside a square cavity with a centrally rotating cylinder has been investigated in the present work. The bottom half of the cavity is filled with a porous material and the top half is filled with a clear fluid. The bottom wall of the cavity is at a higher temperature, and the top wall is at a lower temperature. The vertical walls are thermally insulated. The convection inside the cavity sets through the combined mechanisms of the thermal buoyancy force and the shearing action of the centrally rotating cylinder. The relative importance of each driving mechanism over the other is featured through the Richardson number. The Darcy–Brinkman–Forchheimer equation is used for the flow modeling in the porous medium, and a single‐domain approach is adopted for the numerical solution in the fluid‐porous composite medium. The simulation is carried out with ANSYS Fluent software, and a parametric analysis involving the Rayleigh number (), Richardson number (), and the Darcy number () is conducted showing their effects on the flow and heat transfer. The phenomena are quite interesting at higher Darcy number and Rayleigh number. The distributions of isotherms, streamlines, and vector plots are plotted, along with the local Nusselt numbers for different parameters, to explore the underlying physics of the phenomenon. The system is found stable at lower Darcy number, and the heat transfer is minimum around Ri = 10. From the numerical study, an empirical correlation for the average Nusselt number is developed as a function of the other dimensionless numbers.     

Appropriate position of porous insert in a heat exchanger by thermohydraulic analysis

This paper presents numerically an appropriate position of a porous insert to get a better thermohydraulic performance from a porous heat exchanger. The simulation is based on the Darcy‐Brinkman‐Forchheimer model in the porous field. Two‐dimensional continuity, momentum, and energy equations with incompressible, laminar, steady assumptions have been solved using a finite volume approach. The analysis is performed for different values of porous layer thickness, length, and porosity at a fixed value of Reynolds number (Re = 100) and thermal conductivity ratio (Rc = 5). The results showed that there is about a 48% and 13% reduction in pressure drop and Nusselt number, respectively, by decreasing horizontal porous substrate thickness from 1 to 1/2 for δ_v = 1/3 at ε = 0.7. As a result, the pressure drop reduces considerably with a reasonable reduction in heat transfer rate by decreasing horizontal porous substrate thickness from 1 to 1/2.     

Linear stability of convection in a vertical channel filled with nanofluid saturated porous medium

The convection in a vertical channel filled with a porous medium saturated by a nanofluid is studied numerically. The effects of Brownian motion and thermophoresis are incorporated in the model used for nanofluid. Also, the flow within the porous region is governed by Brinkman's equation. The generalized eigenvalue problem for the perturbed state is obtained from a normal mode analysis and solved using the Chebyshev spectral collocation method. The Rayleigh number is expressed as an implicit function of the wavenumber with other parameters. The critical wavenumber and the critical Rayleigh number are calculated for different parameters. The preferred modes under critical conditions are detected.     

Slip boundary condition effect on double‐diffusive convection in a porous medium: Brinkman Model

The model of double‐diffusive convection in a porous medium layer was analyzed using the Brinkman model and concentration based on an internal heat source. Linear instability analysis of the model was performed. Particularly, we analyzed the effect of slip boundary conditions on the instability of the system. We analyzed when the instability started and computed the critical Rayleigh number as a function of the slip coefficient.     

Double diffusive convection of a micropolar fluid saturated in a sparsely packed porous medium

This study examines the double diffusive convection of a sparsely packed micropolar fluid‐saturated porous medium by using a linear stability analysis. The Darcy–Brinkman–Forchheimer model is employed for the porous fluid layer. The stability criterion is sought analytically with the simple free‐free, iso‐thermal, and iso‐solutal boundary conditions. The dependence of stationary or oscillatory convection on the porous parameter, Lewis number, solutal Rayleigh number, and parameters involved in micropolar fluids is drawn and discussed. The results show that the critical wave number is found to be insensitive to the variation of governing parameters except for the porous parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21052     

The onset of Darcy‐Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects

In this study, the influence of constant throughflow and varying downward gravity field on the onset of Darcy‐Brinkman convection in a porous medium layer is examined numerically. We considered two cases of gravity field variations: (a) linear and (b) parabolic. A higher‐order Galerkin‐weighted residual technique and QZ procedure are used to get the numerical solution for the entire Darcy numbers amid $\text{Da}=0$ (Horton‐Rogers‐Lapwood convection) and $\text{Da}\to \infty$ (Rayleigh Bénard Convection). It is obtained that the throughflow, the downward gravity field and the Darcy number are to holdup the beginning of convection. It is also obtained that the system is more stable for linear variation of gravity field in comparison to the parabolic variation.     

Nonlinear thermal radiation and chemical reaction effects on Maxwell fluid flow with convectively heated plate in a porous medium

This paper investigated the chemically reactive radiating flow by using a two‐dimensional Darcy‐Forchheimer model with the convectively heated plate. The nonlinear thermal radiation is described by Joule heating and heat generation. Also, Darcy‐Forchheimer equation is related to porous medium flows. For the solution of equations, we used the numerical method. Further, more physical interpretation of the parameters was demonstrated with figures. It is found that an increase in the Prandtl number had a direct effect on the Nusselt number and temperature, whereas the opposite scenario was observed in the Eckert number.     

Free convection of composite porous medium in a vertical channel

A fully developed free convection flow of immiscible fluids in a vertical channel filled with a porous medium is analyzed in the presence of source/sink. The flow is modeled using the Darcy–Brinkman–Forchheimer equation model. The viscous and Darcy dissipation terms are included in the energy equation. The channel walls are maintained at two different constant temperatures. The transport properties of both fluids are assumed to be constant. Continuous conditions for velocity, temperature, shear stress, and heat flux of both fluids at the interface are employed. The resulting coupled nonlinear equations are solved analytically using regular perturbation method and numerically using finite difference method. The velocity and temperature profiles are obtained in terms of porous parameter, Grashof number, viscosity ratio, width ratio, conductivity ratio, and heat generation or heat absorption coefficient. It is found that the presence of porous matrix and heat absorption reduces the flow field. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20340     

Mixed convection heat and mass transfer over a vertical plate in a power‐law fluid‐saturated porous medium with radiation and chemical reaction effects

Mixed convection heat and mass transfer from a vertical plate embedded in a power‐law fluid‐saturated Darcy porous medium with chemical reaction and radiation effects is studied. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using the shooting method. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21058     

Unconditional nonlinear stability for double‐diffusive convection in a porous medium with temperature‐dependent viscosity and density

In this study, fluid flow in a porous medium is analyzed using a Forchheimer model. The problem of double‐diffusive convection is addressed in such a porous medium. We utilize a higher‐order approximation for viscosity‐temperature and density‐temperature, such that the perturbation equations contain more nonlinear terms. For unconditional stability, nonlinear stability has been achieved for all initial data by utilizing the or norms. It also shows that the theory of is not sufficient for such unconditional stability. Both linear instability and nonlinear energy stability thresholds are tested using three‐dimensional (3D) simlations. If the layer is salted above and salted below then stationary convection is dominant. Thus the critical value of the linear instability thresholds occurs at a real eigenvalue , and our results show that the linear theory produces the actual threshold. Moreover, it is known that with the increase of the salt Rayleigh number, R_c, the onset of convection is more likely to be via oscillatory convection as opposed to steady convection. The 3D simulation results show that as the value of R_c increases, the actual threshold moves towards the nonlinear stability threshold, and the behavior of the perturbation of the solutions becomes more oscillatory.     

Cross‐diffusion and viscoelastic effects on multidiffusive porous convection

The onset of triply cross‐diffusive convection in a viscoelastic fluid‐saturated porous layer is investigated as the study is found very relevant for describing natural phenomena (contaminant transport, underground water flow, improved oil recovery, polymer processing). A modified Darcy‐Oldroyd‐B model is used to describe the viscoelastic fluid flow in a porous medium with full cross‐diffusion terms in the diffusivity matrix. A normal mode analysis yields an exact dispersion equation of fifth degree and accordingly the criterion for the onset of stationary and oscillatory convection is obtained. The numerical computations are carried out for diffusivity elements experimentally determined for lysozyme‐sodium chloride‐bovine serum albumin (BSA)‐water system. Instability is found to occur via oscillatory mode for a certain choice of governing parameters. The relaxation and retardation viscoelastic parameters portray opposing contributions on the oscillatory onset and an increase in the relaxation parameter is to increase the range of retardation parameter up to which the oscillatory convection is preferred. The cross‐diffusion is to either delay/hasten the onset of instability based on the magnitude of the stratifying agents. Even minute variations in the cross‐diffusion elements indict complete change in the linear instability criteria. The topology of neutral curves disclosed the occurrence of disconnected closed convex oscillatory neutral curve revealing the requirement of three critical solute Darcy‐Rayleigh numbers to state fully the instability criteria instead of the usual single value; a novel result ensured from the study. Moreover, the nature of instability for Oldroyd‐B, Maxwell and Newtonian fluids turns out to be dissimilar for the same governing parameters.     

Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid‐saturated porous medium

This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non‐linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20300     

Effect of anisotropic permeability on double‐diffusive bidisperse porous medium

The model of thermosolutal convection in a fluid‐saturated bidisperse porous medium of Darcy type is studied in this paper. The permeability is allowed to be horizontally isotropic for both the macro‐ and microphases. The linear instability and nonlinear stability are analyzed by taking the Soret effect into account. Furthermore, the effect of anisotropy parameter, Soret coefficient, and other physical parameters on the stability of the system are investigated. It is shown that the linear instability boundaries and the energy stability boundaries do not coincide when the layer is heated and salted from below, where a region of potential subcritical instability occurs. The results reveal that the horizontal to vertical permeability ratio plays a crucial role in the stability of the system. It is also observed that for large values of the salt Rayleigh number, the onset of thermal convection is more likely to be via oscillatory convection rather than stationary convection. Furthermore, the onset of stationary convection is significantly influenced by the presence of the Soret coefficient.     

Thermo‐solutal convection in an inclined porous cavity with various aspect ratios under mixed thermal and species boundary conditions

The problem of laminar thermo‐solutal convective flow of a binary fluid mixture in an inclined rectangular cavity filled with a uniform porous medium is considered. Mixed heat and mass fluxes and uniform temperature and concentration conditions are applied on two opposing walls of the cavity while the other two walls are kept adiabatic and impermeable to mass transfer. The problem is put in terms of the stream function‐vorticity formulation. A numerical solution based on the finite‐difference methodology is obtained. Representative results illustrating the effects of the inclination angle of the cavity, buoyancy ratio, Darcy number, and the cavity aspect ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at mid‐section of the cavity are reported. In addition, numerical results for the average Nusselt and Sherwood numbers as well as some useful correlations are presented for various parametric conditions and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20369     

Bioconvective Casson nanofluid flow toward stagnation point in non-Darcy porous medium with buoyancy effects,chemical reaction,and thermal radiation

The emphasis on non-Newtonian fluid encountered in biomedical, pharmaceuticals, mining, food, chemical, and plastics industries and in noticeably enormous diverse industrial applications influenced this article. This study is accomplished in a non-Darcy porous stretching surface to investigate the stagnation point of bioconvective Casson nanofluid. Chemical reaction, applied consistent magnetic field, radiative heat transfer, and buoyancy force consequences are studied for numerical examination. Composed of nonlinear partial differential equations for the above presumptions and reforming them into ordinary differential equations by means of compatible transformations are enforced. Adopting the fifth order Runge–Kutta Felhberg method with the shooting technique obtained a numerical solution. Obtained solutions are authenticated by comparing previous solutions. The major finding includes the reduction of the Casson parameter on the skin friction coefficient.     

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy‐Oldroyd‐B model, and the fluid and solid phase temperatures are represented using a two‐field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimension‐two points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study.     

Free convection in a square cavity filled with a bidisperse porous medium

The classical problem of steady Darcy free convection in a square cavity filled with a porous medium has been extended to the case of a bidisperse porous medium (BDPM) by following the recent model proposed by Nield and Kuznetsov [D.A. Nield, A.V. Kuznetsov, Natural convection about a vertical plate embedded in a bidisperse porous medium, Int. J. Heat Mass Transfer 51 (2008) 1658–1664] and Rees et al. [D.A.S. Rees, D.A. Nield, A.V. Kuznetsov, Vertical free convective boundary-layer flow in a bidisperse porous medium, ASME J. Heat Transfer 130 (2008) 1–9]. The transformed partial differential equations in terms of the dimensionless stream function and temperature are solved numerically using a finite-difference method for some values of the governing parameters when the Rayleigh number Ra is equal to 10² and 10³. Results are presented for the flow field with streamlines, temperature field by isotherms and heat transfer by local and mean Nusselt numbers are presented for both the f- and p-phases. It is found that the most important parameters that influence the fluid flow and heat transfer are the inter-phase heat transfer parameter H and the modified thermal conductivity ratio parameter γ.     

Simulation of thermally‐enhanced combustion in a porous medium burner

Premixed combustion in a porous medium burner is investigated numerically. A two‐dimensional steady, laminar flow model is used. A single‐step reaction of methane is used for the chemical kinetic model. The model also includes thermal radiation transport of the porous media that is placed inside the burner. The radiative transport equation is solved by using the discrete ordinate method. The results show that, for each equivalence ratio, the flame can be stabilized at various axial locations with different flame speeds. The flame temperature increases with the equivalence ratio and flame speed. Furthermore, the energy release rates are much higher than that of a free flame for the same equivalence ratio as a result of higher flame speed. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(1): 75–88, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20088     

Cross–diffusion effects on mixed convection from an exponentially stretching surface in non–Darcy porous medium

The Soret and Dufour effects on mixed convection flow and heat and mass transfers from an exponentially stretching surface in a quiescent fluid–saturated non–Darcy porous medium is studied. Stretching velocity, wall temperature, and wall concentration are assumed to have specific exponential function forms. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using an implicit finite difference scheme known as the Keller–box method. The present results are found to be in excellent agreement with previously published work on various special cases of the problem. The influence of buoyancy, Soret and Dufour numbers, and Darcy and non–Darcy parameters on the convective transport in the boundary layer region is analyzed. Also, the numerical values of the skin friction, heat, and mass transfer coefficients for different values of governing parameters are also tabulated. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21032     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114