Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Free convection heat and mass transfer to steady flow in a semi-infinite vertical porous medium

Analytical solutions are derived for flow in a semi-infinite vertical porous medium with heat and mass transfer. When the temperature and mass concentration are uniform a constant pressure is possible and sustains a fully developed flow. Thereafter there is a small perturbation of the wall temperature and concentration, and the subsequent two-dimensional problem is tackled for large Prandtl number and free convection parameters and small Reynolds number. The heat transfer rate at the wall is discussed quantitatively.     

Free convective visco-elastic flow with heat and mass transfer through a porous medium with periodic permeability

The problem of three dimensional free convective flow with heat and mass transfer of a visco-elastic fluid through a highly porous medium with periodic permeability has been investigated. The porous medium is bounded by an infinite vertical porous plate with constant suction. The free stream velocity is supposed to be uniform. The analytical expressions for dimensionless skin-friction, the rate of heat transfer, the rate of mass transfer have been obtained and these results have been presented graphically for different values of the flow parameters involved in the solution.     

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO₂ with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.     

Soret and Dufour effects on free convection along a vertical wavy surface in a fluid saturated Darcy porous medium

In this article, free convection of heat and mass transfer along a vertical wavy surface in a Newtonian fluid saturated Darcy porous medium is studied by considering cross diffusion (namely the Soret and the Dufour effects) in the medium. The vertical wavy wall and the flow governing equations are transformed to a plane geometry case by using a suitable transformation. Then a similarity solution to this problem is presented under the large Darcy–Rayleigh number assumption. The governing partial differential equations are reduced to a set of ordinary differential equations that are integrated using numerical methods to study the nature of the non-dimensional heat and mass transfer coefficients in the medium. The results are presented for a range of the flow governing parameters such as the diffusivity ratio parameter, the buoyancy ratio parameter, the Soret parameter, the Dufour parameter and the amplitude of the wavy surface.     

The thermal modeling of a matrix heat exchanger using a porous medium and the thermal non-equilibrium model

Heat transfer and fluid flow characteristics through a porous medium were investigated using numerical simulations and experiment. For the numerical simulations two models were created: a two-dimensional numerical model and a Fluent™ computational fluid dynamics (CFD) porous media model. The experimental investigation consisted of a flow channel with a porous medium section that was heated from below by a heat source. The results of the numerical models were compared to the experimental data in order to determine the accuracy of the models. The numerical model was then modified to better simulate a matrix heat exchanger. This numerical model then generated temperature profiles that were used to calculate the heat transfer coefficient of the matrix heat exchanger and develop a correlation between the Nusselt number and the Reynolds number.     

Heat and Moisture Transfer in a Rectangular Cavity Partially Filled with Hygroscopic Porous Media

Abstract

This work deals with turbulent natural convection heat and moisture transfer with thermal radiation in a rectangular cavity partially filled with hygroscopic porous medium. The governing equations for the momentum and heat transfer in both free fluid and hygroscopic porous media and moisture content transfer in hygroscopic porous medium were solved by the finite element method. Comparisons with experimental and numerical results in the literature have been carried out. Effects of thermal radiation, Rayleigh number on natural convection and heat transfer in both free fluid and porous medium and moisture content transfer in porous medium were analyzed. It was found that surface thermal radiation can significantly change the temperature and moisture content fields in the regions of free flow and hygroscopic porous medium. With the increase in Rayleigh number, the temperature of porous medium at the interface increased slightly, and the magnitude of moisture change becomes smaller.     

Flow control with electrode bank arrangements by electrohydrodynamics force for heat transfer enhancement in a porous medium

Active flow control with electrohydrodynamics (EHD) force in the channel flow has been numerically investigated for enhancing heat transfer. This study focuses on the effect of electrode bank arrangements and the number of electrodes on corona wind and fluid flow for heat transfer onto a porous medium. Aligned and staggered configurations of electrode banks are compared. The numerical results show that electric field intensity depends on electrical voltage and the number of electrodes. Shear flow is increased with larger numbers of electrodes and in the aligned configuration, resulting in the enhancement of vortex strength. The swirling flow from staggered configurations spread wider than that of aligned configurations, but the aligned configuration produced more turbulence. In addition, the temperature distribution in the channel flow is increased with increasing numbers of electrodes. With the effect of swirling flow, airflow above the porous sample surface is faster leads the heat to more transfer to the porous sample surface. This causes the temperature of porous medium to increase rapidly so the convective heat transfer coefficient on porous medium surface is increased. Finally, the modified case of the numerical results is validated against the experimental results. The experimental flow visualization is based on the incense smoke technique, in order to verify the accuracy of the swirling flow pattern subjected to the electric field. It is shown that the comparison results in both techniques are in good agreement.     

Developing fluid flow and heat transfer in a channel partially filled with porous medium

A three-dimensional computational model is developed to analyze fluid flow in a channel partially filled with porous medium. In order to understand the developing fluid flow and heat transfer mechanisms inside the channel partially filled with porous medium, the conventional Navier–Stokes equations for gas channel, and volume-averaged Navier–Stokes equations for porous medium layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain along a channel using the vorticity–velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature field at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside the channel partially filled with porous medium are also analyzed in the present study.     

Performance of a Circular Fin in a Cylindrical Porous Enclosure

The problem of natural convection heat transfer from a vertical cylindrical fin to a saturated porous medium in a cylindrical enclosure is solved numerically. A conjugate conduction-convection analysis is accomplished by solving the equation of heat conduction in the fin together with the mass, momentum and energy balance equations in the porous medium. Numerical results are obtained by using ADI method. The effects of the conduction-convection ratio parameter, aspect ratio and Darcy number on local heat transfer coefficients and fin efficiency are discussed. Comparison of the local heat transfer coefficients and fin efficiency is shown with those for non-porous medium.     

Augmentation of heat transfer from a solid cylinder wrapped with a porous layer

In the present study, the heat transfer from a porous wrapped solid cylinder is considered. The heated cylinder is placed horizontally and is subjected to a uniform cross-flow. The aim is to investigate the heat transfer augmentation through the inclusion of a porous wrapper. The porous layer is of foam material with high porosity and thermal conductivity. The mixed convection is studied for different values of flow parameters such as Reynolds number (based on radius of solid cylinder and stream velocity), Grashof number, permeability and thermal conductivity of the porous material. The optimal value of porous layer thickness for heat transfer augmentation and its dependence on other properties of the porous foam is obtained. The flow field is analyzed through a single domain approach in which the porous layer is considered as a pseudo-fluid and the composite region as a continuum. A pressure correction based iterative algorithm is used for computation. Our results show that a thin porous wrapper of high thermal conductivity can enhance the rate of heat transfer substantially. Periodic vortex shedding is observed from the porous shrouded solid cylinder for high values of Reynolds number. The frequency of oscillation due to vortex shedding is dampened due to the presence of the porous coating. Beyond a critical value of the porous layer thickness, the average rate of heat transfer approaches asymptotically the value corresponding to the case where the heated cylinder is embedded in an unbounded porous medium.     

Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.     

Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a downward-pointing vertical cone in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local Nusselt number tends to decrease as the Dufour parameter is increased. The effect of the Dufour parameter on the local Nusselt number becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number.     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Experimental study of mixed convection heat transfer in a vertical duct filled with metallic porous structures

This paper reports the results of an experimental investigation to examine the potential of a simple and inexpensive porous insert developed specifically for augmenting heat transfer from the heated wall of a vertical duct under forced flow conditions. The porous insert used in the study consists of a stack of metallic perforated plates filled inside the duct. The characteristic features of the porous medium model on the hydrodynamic and heat transfer behavior have been investigated. The porous medium model developed in the present study shows thermo- hydrodynamic performance similar to those seen in metal foams. A correlation has been developed for predicting the Nusselt number from the geometry under consideration. The key novelty in the present work is the development of a new correlation for the Nusselt number that does not require any information from hydrodynamic studies. Over the range of parameters considered, the largest increase in the average Nusselt number of 4.52 times that for clear flow is observed with a porous material of porosity of 0.85.     

MHD viscoelastic fluid non-Darcy flow over a vertical cone and a flat plate

A study has been carried out to analyze the double dispersion effects on unsteady, free convective, chemically reacting, MHD viscoelastic fluid (Walters liquid-B model) flow over a vertical cone and a flat plate saturated with non-Darcy porous medium in the presence of Soret and Dufour effects. The constitutive equations for the boundary layer regime are solved by an efficient finite difference scheme of the Crank-Nicolson type. The features of the fluid heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail to interpret the effect of significant parameters of the problem. The overall heat and mass transfer profiles are enhanced for increasing the thermal and solutal dispersion effects, respectively. The results indicate that the Soret and Dufour effects have considerable effect on the viscoelastic fluid flow through non-Darcy porous medium.     

The onset of convection in a tridisperse porous medium

This paper develops a theory of mass, momentum, and heat transfer in a tridisperse porous medium. Coupling between three different scales present in this medium is accounted for by introducing momentum and interphase heat transfer coupling coefficients. The developed theory is then applied to solve the classical Rayleigh–Bénard problem, for the onset of convection in a horizontal layer uniformly heated from below, for this new type of a porous medium. The formulation uses the Darcy law, which now results in three different filtration velocities in three porosity scales present in this medium. The linear stability analysis leads to an expression for the critical Rayleigh number as a function of three volume fractions, two permeability ratios, two thermal capacity ratios, two thermal conductivity ratios, two inter-phase heat transfer parameters and two inter-phase momentum transfer parameters. The dependence of the critical Rayleigh number on these parameters is investigated.     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

A universal model of opposed flow combustion of solid fuel over an inert porous medium

In this study, a universal model is developed to examine the behavior of combustion wave observed in porous solid matters (e.g., smoldering, self-propagating high-temperature synthesis (SHS), diesel particulate filter (DPF) regeneration process). Analytical expressions of the combustion characters of solid combustible (e.g., diesel particulate matters trapped in a DPF) deposited over an inert porous medium are obtained employing large activation energy asymptotic taking into account the sensible transport processes; namely, heat transfer between the porous medium and gas phases, radiation heat transfer from the porous medium, heat loss from the porous medium to the environment, mass transfer of oxygen from the gas stream to the surface of solid fuel and the effective diffusion in modeling the species diffusion. Then it has been validated that the present model is applicable and adaptable for predicting the characteristics of smoldering combustion and thus SHS process. As a result, the features of combustion wave of the present phenomena would be useful to other processes. From practical point of view and for deep understanding of the behavior of combustion wave of these processes, we investigate the effects of various physical parameters over a wide range of conditions. We observe that the moving speed of the reaction front increases with the increase of porosity of the porous medium, mass transfer coefficient and initial fuel mass fraction; while it decreases owing to the increase of heat transfer rate from the porous medium to the gas, heat loss to the environment and radiative heat transfer. Furthermore, the results reveal that extinction tends to occur due to lower porosity of the porous medium, higher radiative heat transfer from the porous medium, higher heat transfer rate from the porous medium to the gas and higher heat losses from the porous medium to the environment. Even the observed near-extinction behavior in reaction front speed versus heat loss diagram is found to be similar what we got in gaseous premixed flame propagating through the porous medium. An extinction limit diagram has been presented as a function of radiation-conduction parameter and the gas flow velocity. In addition to, the impact of radiation and the combined effect of the inclusion of Knudsen diffusion and tortuosity are demonstrated in terms of the spatial temperature and species profiles to examine how these two parameters modify the reaction front structure. Furthermore, the governing equations have been solved numerically and it is observed that asymptotic analysis gives a good agreement with the numerical solution.