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…     

The effect of rotation on the onset of convection in a horizontal anisotropic porous layer

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

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.     

Effects of thermal spot configurations on the flow through porous media driven by natural and forced convection

A study concerning the flow of a Newtonian fluid through a porous medium for the particular case natural convection is produced by hot and cold spots placed in the solid phase is presented. Results involving the interaction of forced convection with thermal spots are reported to visualize the mechanisms associated with the generation of complex flow patterns in the porous medium. For this purpose the computation of a two-field model is carried out. Two systems are studied: one is a rectangular porous cavity (RPC) of square cross section and the other is an annular porous cavity (APC) comprised by two concentric vertical cylindrical walls. It is shown, in general, that the flow patterns associated with each configuration and intensities of the thermal spots may be qualitatively inferred by following rules that are established through a basic study of mixed convection in the RPC.     

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.     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium

In the present study a general criterion for local thermal equilibrium is presented in terms of parameters of engineering importance which include the Darcy number, the Prandtl number, and the Reynolds number. For this, an order of magnitude analysis is performed for the case when the effect of convection heat transfer is dominant in a porous structure. The criterion proposed in this study is more general than the previous criterion suggested by Carbonell and Whitaker, because the latter is applicable only when conduction is the dominant heat transfer mode in a porous medium while the former can be applied even when convection heat transfer prevails. In order to check the validity of the proposed criterion for local thermal equilibrium, the forced convection phenomena in a porous medium with a microchanneled structure subject to an impinging jet are studied using a similarity transformation. The effects of the Darcy number, the Prandtl number, and the Reynolds number on local thermal non-equilibrium are systematically studied by comparing the temperature of the solid phase with that of the fluid phase as each of these parameters is varied. The proposed criterion is also validated with the existing experimental and numerical results for convection heat transfer in various porous materials that include some of the parameters used in the criterion such as a microchannel heat sink with a parallel flow, a packed bed, a cellular ceramic, and a sintered metal. It is shown that the criterion presented in this work well-predicts the validity of the assumption of local thermal equilibrium in a porous medium.     

Convection in modulated thermal gradients and gravity: experimental measurements and numerical simulations

This paper presents an investigation on natural convection in a cavity with imposed modulated thermal gradients or modulated gravity forces. Numerical computations are presented, which are based on the finite element solution of the transient Navier-Stokes and energy balance equations, along with appropriate thermal boundary conditions or time-varying gravity forces. In parallel with numerical development, an experimental system is setup where oscillating wall temperatures are prescribed to produce modulated temperature gradients and the velocity fields are measured by a laser-based particle image velocimetry (PIV) system. Computed results compare well with experimental measurements for various conditions. With the mathematical model, so verified by experimental measurements, numerical simulations are carried out to study the effects of modulation frequency and Prandtl number on the fluid flow. Results show strong non-linear interaction in a fluid with a relative high Prandtl number within the intermediate range of modulated frequency. It is also found that for a fluid with a small Prandtl number typical of molten metals and semiconductor melts, modulated gravity and thermal gradients produce almost the same flow field both in structure and in magnitude.     

Stability analysis of MHD radiative mixed convective flow in vertical cylindrical annulus: Thermal nonequilibrium approach

In the present study, the influence of the induced magnetic field on the MHD mixed convective electrically conducting fluid flow inside the vertical cylindrical annulus is analyzed numerically. The heat transfer is presumed to be due to a combination of mixed convection and radiation. The stability of the flow is examined when the solid and fluid phases are not in local thermal equilibrium. The governing equations are solved numerically by both finite difference and finite element methods. To control the flow formation rate more accurately the induced magnetic field is also considered in this study. As the magnetic Prandtl number (Pm) and Hartmann number (M) get enhanced, the velocity and induced magnetic fields get retarded in the annulus due to the presence of drag-like force, namely, the Lorentz force. When there is an increase in the mixed convection parameter the induced magnetic field gets enhanced. An increase in radiation parameter tends to decline the fluid temperature and reverse the behavior of the solid temperature. Increment in Pm decreases the wall shear stress near the conducting cylinder. Increasing values of porous, magnetic, and radiation parameters lead to an unstable system with smaller heat transfer coefficient values but the system gets stabilized for larger values of heat transfer coefficient. The results could be used as first-hand information for comprehending and developing the thermal flow phenomenon in porous media. The obtained numerical results are in good accordance with the existing results. Using an artificial neural network, heat transfer characteristics are analyzed through mean square error and regression analysis.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.     

Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration

This work examines the natural convection heat and mass transfer near a sphere with constant wall temperature and concentration in a micropolar fluid. A coordinate transformation is used to transform the governing equations into nondimensional nonsimilar boundary layer equations and the obtained boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt number and the local Sherwood number are presented as functions of the vortex viscosity parameter, Schmidt number, buoyancy ratio, and Prandtl number. For micropolar fluids, higher viscosity tends to retard the flow and thus decreases the natural convection heat and mass transfer rates from the sphere with constant wall temperature and concentration. Moreover, the natural convection heat and mass transfer rates from a sphere in Newtonian fluids are higher than those in micropolar fluids.     

Impact of the electromagnetic flow of an MHD Casson fluid over an oscillating porous plate

This study deals with the effect of electric force and magnetohydrodynamics (MHD) of the transient state on natural convection flow past an oscillating vertical plate. In addition to this, thermal radiation and porous media are also examined in the Casson fluid flow. The Poisson-Boltzmann equation is employed to show the electric potential character within the fluid region, which is put into a linear form by the implementation of Debye–Hückel linearization. It is possible to compute the precise solution to the governing equations using the Laplace transform approach. The expression of fluid velocity, fluid concentration, and temperature are exposed graphically, and numerical results for Nusselt and Sherwood numbers are also derived for vital pertinent flow constraints. Increasing electroosmosis parameters strongly boosts fluid velocity. The nonnegative values of the Helmholtz–Smoluchowski velocity highly induce the axial velocity and the negative value decelerates. With increasing radiation strength and Prandtl number, the fluid's temperature distribution diminishes. These more intricate electrokinetic rheological flows associated with electroosmotic separators, such as biomedical absorbers, are illuminated by these models.     

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.     

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

The onset of Darcy‐Brinkman convection in a binary viscoelastic fluid‐saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd‐B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy‐Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy‐Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676–703, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21056     

The lattice Boltzmann modeling on the nanofluid natural convective transport in a cavity filled with a porous foam

In this work, the natural convective transport was numerically investigated for nanofluids in a metal-foam cavity. A lattice Boltzmann (LB) model for the nanofluid natural convection in a porous medium was established by using the volume-averaging method. The velocity and temperature fields were obtained, and flow and thermal characteristics of the nanofluid convection in a porous medium were presented. The effects of the Rayleigh Number, the Darcy Number, the porosity, the solid thermal conductivity of porous medium, the nanoparticle thermal conductivity and the nanoparticle concentration on natural convection were examined. The average velocity was put forward to evaluate the convection effect and the natural convection onset was also discussed. It is shown that the Nusselt number of the natural convection increases with an increase in the Darcy number, the Rayleigh number, the porosity and the effective thermal conductivity. The change from the heat conduction regime to the convection regime is clearly shown from the numerical result, which verifies the onset point of the nanofluid natural convection in a porous medium. The highly conductive porous foam and the nanofluid can promote the thermal performance of the natural convection, which own great potential in practical thermal applications.     

Heat transfer and phase change of liquid in an inclined enclosure packed with unsaturated porous media

In this paper, we present a mathematical model to describe the simultaneous heat and mass transfer with liquid phase change in unsaturated porous media. Two-dimensional natural convective flow in an inclined rectangular enclosure with porous material unsaturated with fluid is analyzed numerically. The parameter variations are considered for the tilted angle, the aspect ratio and the Darcy–Rayleigh number. Local and global Nusselt numbers are presented as functions of those parameters. Compared with the saturated porous material, the heat transfer characters in the unsaturated case are discussed for the identical aspect ratio and Darcy–Rayleigh number, The discussion is also made for the field synergy of fluid velocity and heat flow in natural convection.     

Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition

This article investigates the effect of double dispersion on the natural convective flow of a micropolar fluid along an inclined plate in the presence of the convective thermal condition. In addition, the nonlinear convection is considered to analyze the heat and mass transfer phenomena of thermal systems, which are performed at moderate‐ and high‐level temperatures. A combination of local nonsimilarity and successive linearization techniques is used to evaluate the associated complicated nondimensional governing equations. This study discusses the impact of relevant factors on the fluid characteristics through graphs. The influence of nonlinear convection parameters on the heat and mass transfer rates seems to be more in Darcy porous media compared with that in non‐Darcy porous media.     

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.     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. The transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity.     

Natural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium

Presented here are the results of a numerical study of natural convection heat transfer in a stably stratified, fluid saturated low porosity medium, in which Darcy flow prevails. In this investigation, the boundary layer approximations are discarded and a wide range of ambient thermal stratification levels is considered. The results indicate that the ambient thermal stratification has a significant effect on the flow and temperature fields, and that this effect differs considerably at higher levels of stratification. The flow reversal and temperature defects are significantly smaller in the porous media than in a viscous fluid, due to the stabilization of the flow by the solid matrix. To generalize the result, the Nusselt number data are correlated with the thermal stratification parameter to yield a functional relationship.