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.     

NON-DARCIAN FORCED CONVECTION ANALYSIS IN AN ANNULUS PARTIALLY FILLED WITH A POROUS MATERIAL

Numerical solutions are presented for fully developed forced convection in concentric annuli partially filled with a porous medium. The porous medium is attached at the inner cylinder, which is maintained at uniform heat flux or at uniform wall temperature while the outer cylinder is adiabatic. The Brinkman-Forchheimer-extended Darcy model was used to model the flow inside the porous medium. The dependence of the fluid flow and heat transfer on several parameters of the problem is thoroughly documented. The inertia coefficient at which the inertial effects reduce the flow rate by 5% is determined as a function of the Darcy number for various thicknesses of the porous substrate. It is also shown that a critical thickness at which the value of the Nusselt number reaches a minimum does not exist if the effective thermal conductivity of the fluid-saturated porous medium is much higher than the fluid conductivity.     

Natural Convection Heat Transfer in an Open-Ended Inclined Channel-Partially Filled with Porous Media

A numerical simulation of the steady-state, laminar, two-dimensional, natural convection heat transfer in an open-ended channel partially filled with an isotropic porous medium is presented. The Darcy-Brinkman-Forchheimer model along with Boussinesq approximation is used to describe the fluid flow in the porous region. Meanwhile, the Navier-Stokes equation along with Boussinesq approximation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on Rayleigh number, inclination angle, Darcy number, inertia coefficient, Prandtl number, porous width to channel width ratio, the ratio of the porous effective conductivity to fluid conductivity, and channel width to length ratio is investigated. The numerical results obtained indicate that air gap presence may reduce the average flow in the porous substrate to zero. This leads to the presence of an optimum average Nusselt number at low and high values of the effective thermal conductivity ratios.     

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.     

Unsteady flow through a porous medium with the presence mass transfer

Unsteady flow through a very porous medium with the presence mass transfer is considered. The porous medium is bounded by a vertical plate and this plate absorbs the fluid with a constant velocity. Also the free stream velocity of the fluid vibrates about a mean constant value. The influences of the permeability parameter and the modified Grashof number on the velocity field are discussed.     

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.     

Stability of Natural Convection of Power—law Fluid and non—Darcy Flow in Forous Media

IutnductionThe convection in porous media has been stUdied fora half centUryl"']. In recent years the nonlinear Propanesof the convection are emphatically sindiedp-7]. They areimPOrtant parts of nonlinear conhnuous media meChhocs,and this stUdy is of oportant theoretical sense as well aswide-ranging aPPlication Prospect such as thedevelopment of geothermal technique and heaVy Oilindustry. But up tO date the effect of the non-Newtonianfluid and the non-Darcy flow on the nonlinear behavior…     

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.     

Heat transfer in flow through a porous medium bounded by an infinite vertical plate under the action of a magnetic field

An analysis of steady two-dimensional flow, of an electrically conducting fluid through a porous medium, occupying a semi-infinite region of the space bounded by an infinite, vertical and porous limiting surface under the action of a transverse magnetic field is considered. Approximate solutions have been derived for the velocity and temperature fields and the rate of heat transfer (Nusselt number). The variations of the velocity and Nusselt number are shown on graphs.     

Forced convection in a channel partly occupied by a bidisperse porous medium: Asymmetric case

This paper presents an analytic investigation of forced convection in parallel-plate channel partly occupied by a bidisperse porous medium and partly by a fluid clear of solid material, the distribution being asymmetrical. The walls of the channel are subject to an uniform heat flux; the flow is assumed to be hydrodynamically and thermally fully developed. The layer of a bidisperse porous medium is attached to one of the channel walls; it is modeled utilizing a two-velocity two-temperature formulation using Darcy’s law. The Beavers–Joseph boundary condition is employed at the bidisperse porous medium/clear fluid interface. The dependences of the Nusselt number on a conductivity ratio, a velocity ratio, a volume fraction, internal heat exchange parameter, and the position of the porous-fluid interface are investigated. Both cases of symmetric and asymmetric heating are investigated, which is specified by the asymmetry heating parameter introduced here. For the case of asymmetric heating, a singular behavior of the Nusselt number is found and explained.     

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.     

Entropy analysis in MHD Couette flow of chemically reacting viscoelastic fluid past a deformable porous channel

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region.     

Unsteady free convective flow and mass transfer through a porous medium bounded by an infinite vertical limiting surface with constant suction and time-dependent temperature

In this work an analysis of the two-dimensional unsteady free convective flow and mass transfer is given, for an incompressible viscous fluid through a porous medium bounded by an infinite vertical limiting surface. The suction velocity perpendicular to the limiting surface is constant and the temperature of the limiting surface fluctuates with time about a non-zero constant mean. Expressions for the velocity, temperature and concentration fields are obtained and the effects of the various parameters of the problem, e.g. modified Grashoff number, permeability of the porous medium and the frequency on the velocity field are discussed.     

Heat transfer from a porous composite sphere immersed in a moving stream

Convection heat transfer in the low Reynolds number regions from an isothermal sphere surrounded by a porous shell is numerically evaluated. In the limit of large porous medium Peclet numbers, the average Nusselt number based on the porous medium thermal conductivity becomes independent of the fluid Peclet number and becomes proportional to the porous medium Peclet number raised to the power one-third. In the limit of small fluid and porous medium Peclet numbers, the average Nusselt number approaches that given by the limiting case of pure conduction.     

Effects of chemical reaction,Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

The aim of the current study is to explore the effects of heat and mass transfer on unsteady chemically reacted Casson liquid flow over an exponentially accelerated vertical plate in a porous medium. It is assumed that the bounding plate has varying temperatures as well as concentrations in a porous medium under a uniform magnetic field. This phenomenon is modeled in the form of a system of partial differential equations (PDEs) with boundary conditions. The governing dimensionless PDEs are solved using Laplace transform method for velocity, temperature, and concentration. The impact of nondimensional parameters, which are controlling the flow like Casson parameter, Soret number, magnetic parameter, heat generation parameter, Prandtl number, radiation parameter, and Schmidt number is analyzed through graphs. The incremental values of the Casson fluid parameter lead to a reduction in velocity and discovered that for large values of the Casson parameter, the fluid is near to the Newtonian fluid. Also, the Sherwood number increases with enhancing dissimilar estimators of the Schmidt and Soret numbers. A comparison has been made with the published work (Kataria et al.) for a particular case, which was in good agreement.     

Experimental Investigation of the Effect of Tube-to-Tube Porous Medium Interconnectors on the Thermohydraulics of Confined Tube Banks

This experimental study investigates the effect of tube-to-tube copper porous interconnectors on the thermohydraulic performance of an in-line and staggered confined tube bank. The porous medium, having a transverse thickness equal to that of the diameter of the tube (9 mm), connects longitudinally six successive tubes kept as in-line and staggered arrangements with a square pitch of 2.0. The tubes are subjected to a constant and uniform heat flux and are cooled by forced convection under laminar-transition flow range (200 < Reynolds number < 1500) using air with a Prandtl number of 0.71 as cooling fluid. Experimental data presented here establish that by introducing tube-to-tube porous medium interconnectors for the maximum Reynolds number tested here, a reduction in the pressure drop by 18% is observed in the in-line configuration while the heat transfer is enhanced by 100% in the staggered configuration, when compared to their respective configurations without the porous medium. Defining an overall energy gain as the ratio of the heat transfer enhancement due to the presence of the porous inserts to the pressure drop incurred, it is seen that fixing the porous inserts in the in-line configuration is advantageous.     

Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

The present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.     

Transient natural convection and heat transfer during the storage of granular media

Transient heat transfer in an originally isothermal cylinder filled with a porous medium after sudden change of wall temperature is studied experimentally and computationally. Lab-scale experiments with water as the interstitial fluid are used in order to imitate the conditions prevailing in large, air-filled industrial silos. The proposed model assumes isotropy of the porous medium, local thermal equilibrium between the phases, Darcy flow and applicability of the Boussinesq approximation. Its predictions are in satisfactory agreement with the experimental results. Simulations reveal the role of dimensionless parameters like the modified porous media Rayleigh number and the cylinder aspect ratio. A criterion for neglecting the influence of natural convection on heat transfer is established.     

Electromagnetic field effects on transport through porous media

The effect of an imposed electromagnetic field on forced convection in porous media is analyzed in this work. The transient Maxwell’s equations are solved to simulate the electromagnetic field inside the waveguide and within a porous medium. The Brinkman–Forchheimer extended Darcy (generalized model) equations are used to represent the flow fluid inside a porous medium. The local thermal non-equilibrium (LTNE) is taken into account by solving the two-energy equation model for fluid and solid phases. Computational domain is represented for a range of Darcy number from 10^?5 to 10^?7 and dimensionless electromagnetic wave power P¹ from 0 to 1600, and dimensionless electromagnetic wave frequency f¹ from 0 to 8. The effect of variations of the pertinent electromagnetic field parameters in affecting the flow and thermal fields and the Nusselt number are analyzed. This investigation provides the essential aspects for a fundamental understanding of forced convection in porous media while experiencing an applied electromagnetic field such as applications in the material-processing field.     

The stability of flow in a channel or duct occupied by a porous medium

The hydrodynamic stability of flow of an incompressible fluid through a plane-parallel channel or circular duct filled with a saturated porous medium, modeled by the Brinkman equation, is discussed on the basis of an analogy with a magneto-hydrodynamic problem (Hartmann flow). Flow in a circular duct is found to be stable to small disturbances for all values of the Reynolds number, but for a plane-parallel channel the flow is unstable if the Reynolds number exceeds a critical value, dependent on a Darcy number.