Horizontal Porous Medium Research Articles

Computation of Internal Heat Source, Viscous Dissipation and Mass Flow Effects on Mono-Diffusive Thermo-Convective Stability in a Horizontal Porous Medium

Computation of Internal Heat Source, Viscous Dissipation and Mass Flow Effects on Mono-Diffusive Thermo-Convective Stability in a Horizontal Porous Medium

Effect of gravity settling on the onset of thermal convection in a nanofluid-saturated porous medium layer

The onset of convection in a horizontal porous medium layer saturated with a nanofluid and heated from below is investigated via linear stability analysis and numerical simulation. The Darcy–Buongiorno model is used to describe the convective transport behaviour of the nanofluid and the settling effect of nanoparticles due to gravity is considered in addition to thermophoresis and Brownian diffusion. The linear stability analysis shows that the gravity settling is a substantial stabilizing mechanism restraining the destabilizing factors such as thermal buoyancy and thermophoresis. The stability threshold is determined by the relative strength of thermophoresis to gravity settling. It is found that the system is destabilized when the thermophoretic mobility prevails. As the nanoparticle size increases, the gravity settling effect is promoted and makes the system more stable. In particular, the onset of instability is dominated by the oscillatory mode once the nanoparticle concentration is in a stably stratified profile across the porous layer. When the Rayleigh–Darcy number $Ra_D$ exceeds the critical value, the spectrum of the growth rates of the unstable modes rises with increasing $Ra_D$ and $Rn$ (i.e. the concentration Rayleigh number), and eventually the unstable modes in the high-wavenumber region exhibit the same instability. The evolution of the convection is further examined by numerical simulation. The results verify the stability characteristics predicted by linear stability analysis. Moreover, the pattern of fingering convection of the nanofluid concentration is observed once the nanofluid concentration is unstably stratified and the density difference across the porous layer is large enough.

Effect of Finite Thermal Conductivity Bounding Walls on Darcy–Bénard Convection

Abstract Natural convection in fluid-saturated, horizontal porous-media is quintessential to many applications like geothermal reservoirs and solar thermal storage systems. Researchers have dedicated substantial effort over the years in pursuit of altering natural convection within a horizontal porous-media (Darcy–Bénard) system. Although significant research efforts have been directed toward understanding the effects of bounding walls in horizontal (Rayleigh–Bénard) convection systems, similar investigations for Darcy–Bénard convection systems are still lacking. Therefore, this study examines the effect of thermal properties of horizontal bounding plates on porous-media Nusselt number at high Rayleigh–Darcy numbers (105−107). Numerical simulations are performed by employing Darcy–Forchheimer model within a three-dimensional cylindrical computational domain to emulate Darcy–Bénard systems for two aspect ratios (1 and 2) and six different plate materials having nondimensional plate thicknesses of 0.02, 0.08, and 0.16. Polypropylene and compressed CO2 gas are chosen as solid and fluid phases for the porous media, respectively, that encompass a range of Darcy numbers (10−6−10−3). Findings reveal that when the ratio of thermal resistances of porous layer and plates falls below 4.61, the corrected Nusselt number deviates by more than 10% from the corresponding ideal Nusselt number with infinitely conducting bounding plates. The study also proposes a correction factor to estimate this deviation, which shows a good agreement with numerical results.

A Revised Work on the Rayleigh-Bénard Instability of Nanofluid in a Porous Medium Layer

To reveal the mechanism of the enhanced heat transfer in nanofluids, Buongiorno (ASME J. Heat Transfer, vol. 128, 2006, pp. 240–250) developed a convective transport model by considering the slip mechanisms of nanoparticles migration. By now, many extended researches are based on his model. Among them, the study on porous medium flow pioneered by Nield & Kuznetsov (Int. J. Heat & Mass Transfer, vol. 52, 2009, pp.5796–5801) has received much attention. Their work employed the Darcy model and Buongiorno’s model to investigate the thermal instability in a horizontal porous medium layer saturated by a nanofluid. Through a sophisticated analysis, they obtained an approximate formula capable of predicting the stability threshold. However, a potential contradiction exists in their analysis owing to an improper assumption about the thermophoretic coefficient, which may lead to an unphysical result. To date, much of current works still adopted this improper assumption in various extended problems. To resolve this contradiction, the present study revises their work by considering the dependence of thermophoretic coefficient on the volume fraction of nanoparticles. A nonlinear basic-state solution of concentration is obtained and then used to implement the linear stability analysis. In comparison with Nield’s formula, the present result shows that the threshold of instability shifts to a lower concentration by more than one order of magnitude. The mechanism causing the shift is discussed and the novelty of the present study is stressed.

ANALYTIC HEAT AND SOLUTE TRANSPORT OF MHD REACTIVE MIXED CONVECTION FLOW OVER A HORIZONTAL POROUS STRETCHING SHEET WITH MULTIPLE SLIPS

The present paper interprets the unsteady magnetohydrodynamic (MHD) flow with heat and mass transfer over a stretching sheet embedded in a horizontal porous medium. The effects of viscous and Darcy dissipation, heat source, and chemical reaction is elaborately discussed in the presence of multiple slip effects for velocity, temperature, and concentration. Introducing a similarity transformation, the governing partial differential equations are transformed into a system of nonlinear, coupled partial differential equations. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation techniques and, compared with the numerical results and the verification of the computational code made with the earlier works, serves as the benchmark of reliability of the present study. The important findings reported herein are: porosity acts as an aiding force for the fluid velocity, more dissipative heat leads to higher velocity and temperature, chemical reaction parameter adversely affects the concentration. The main motivation behind this study is to perform the fluid flow, heat, and mass transfer analysis of a Newtonian fluid with mixed MHD flow, which has important applications in many industries, in particular, the process of extrusion/layer of fluid dispersed with solutal particles is extruded over other materials to increase the strength and durability of the final product.

EFFECT OF VISCOUS DISSIPATION AND INTERNAL HEAT SOURCE ON MONO-DIFFUSIVE THERMOCONVECTIVE STABILITY IN A HORIZONTAL POROUS MEDIUM LAYER

A mathematical model is developed for studying the onset of mono-diffusive convective fluid flow in a horizontal porous layer with temperature gradient, internal heat generation, and viscous dissipation effects. Darcy's model is used for the porous medium, which is considered to be isotropic and homogenous. A linear instability analysis is conducted, and transverse or longitudinal roll disturbances are examined. The dimensionless emerging eigenvalue problem is solved numerically with the Runge-Kutta and shooting methods for both cases of disturbances, i.e,. longitudinal and transverse rolls. Critical wave number and critical vertical thermal Rayleigh number <i>R<sub>z</sub></i> are identified. For higher values of Gebhart number, Ge, a significant destabilizing effect of Hadley-Prats flow is computed. Internal heat generation also strongly modifies the critical vertical Rayleigh number. Extensive interpretation of the solutions related to the onset of convection is provided. The study is relevant to geophysical flows and materials processing systems.

Time-evolving to space-evolving Rayleigh–Bénard instability of a horizontal porous medium flow

The Rayleigh–Bénard instability of the stationary throughflow in a horizontal porous layer, also known as Prats' problem, is analyzed here in a fresh new perspective. In fact, the classical analysis of linear instability, carried out by employing time-evolving and space-periodic Fourier modes, is reconsidered here by focusing on the effects of time-periodic and space-evolving modes. The basic stationary flow is assumed to be perturbed by a localized source of perturbation that is steady-periodic in time. Then, the spatial development of such perturbations is monitored in order to detect their possible amplification or decay in their direction of propagation. Accordingly, the spatial stability/instability threshold is determined. The study is carried out by employing a Fourier transform formalism, where the transformed variable is time.

Onset of instability in Hadley–Prats flow in a weakly heterogeneous porous layer with viscous dissipation

The stability of a flow subjected to an inclined temperature gradient (Hadley-type flow) in a horizontal porous media is studied in the presence of a basic horizontal mass flow (Prats flow). Therefore, the basic flow is called the Hadley–Prats flow. A weak vertical heterogeneity in permeability and conductivity is considered. The effect of viscous dissipation is taken to be non-negligible. The Rayleigh number corresponding to the vertical thermal gradient RaC is considered as an eigenvalue. Other parameters are the Péclet number (Pe) associated with the horizontal through flow, horizontal Rayleigh number (RaH) associated with the horizontal temperature gradient, Gebhart number (Ge) associated with viscous dissipation; parameters γ1 and γ2 represent the changes in permeability and conductivity, respectively. A linear stability analysis is done and the governing equations are solved numerically to obtain the critical Rayleigh number and wave number. Longitudinal and transverse rolls are discussed. Longitudinal rolls are the preferred modes for instability in most scenarios. It is found that when throughflow is present, the heterogeneity in permeability can show a stabilizing effect for longitudinal rolls but destabilizing effect for transverse rolls and vice versa depending on the direction of the throughflow. Increase in conductivity also may stabilize or destabilize the flow depending on the mass flow and viscous heating. The horizontal thermal gradient shows interesting effects in the presence of weak heterogeneity and horizontal throughflow. Significant change in the critical Rayleigh number is observed even for small values of the horizontal Rayleigh number.

Magnetic field and Rotation effect on thermal stability in an Anisotropic couple-stress fluid saturated Porous Layer under presence of Cross-Diffusion

The present paper is based on the investigation of thermal stability problem under the influence of rotation, solute, heat and magnetic field on electrically conducting fluid saturated rotating horizontal porous media under local thermal non-equilibrium effect. We have considered a rotating horizontal anisotropic porous medium saturated with binary fluid. Process of Heating and salting is made from above to the fluid layer.Governing equations is followed by Darcy Brinkman model for characterizing the convection through porous media under the above said physical configuration. Normal mode technique and Application of Linear stability analysis has been made under the consideration of free-free boundary conditions. Thereafter the characteristic graphs between critical Darcy-Rayleigh number and corresponding wave number for beginning of convection in stationary case has been drawn and the effect of rotation, magnetic and couple stress parameters has been illustrated.At last it has been observed the non-dimensonalise parametres regarding singnificant components like rotation magnetic field and anisotropic properties of the physical configuration in present study has stabilizing effect.

Natural convection flow of a nanofluid-filled V-shaped cavity saturated with a heterogeneous porous medium: Incompressible smoothed particle hydrodynamics analysis

The flow and heat transfer fields of a nanofluid within V-shaped cavity are analyzed using the incompressible smoothed particle hydrodynamic (ISPH) scheme. Novel studies on a nanofluid-occupied V-shaped cavity with a partial layer heterogeneous porous medium were conducted. The bottom and top corners of the V-shaped enclosure have isothermal conditions while the remaining boundaries are considered adiabatic. Lengths of the heated and cold parts are assumed to be variables. The flow domain is filled with a partial layer porous medium. Three levels of the porous medium are taken into account, namely, horizontal heterogeneous, vertical heterogeneous and homogeneous porous media. Impacts of the wide ranges of the hot–cold partitions lengths L p ( 0.2 ≤ L p ≤ 1.5 ) , the nanoparticles volume fraction ( 0 % ≤ ϕ ≤ 5 % ) , the Darcy number ( 10 - 2 ≤ D a ≤ 10 - 5 ) and the Rayleigh number ( 10 3 ≤ R a ≤ 10 5 ) on the features of the temperature and nanofluid flow are examined. The main outcomes disclosed that the average Nusselt number takes its maximum in case of the horizontal heterogeneous porous medium while the homogeneous porous medium case gives the lowest rate of the heat transfer. Therefore, for V-shaped cavity, the horizontal heterogeneous porous medium considers the best case of porous media. An augmentation on Rayleigh number rises the buoyancy force and accordingly the convective transport is enhanced. Further, the convective flow is enhanced as the hot–cold partitions lengths increase, regardless the porous case.

Simulations of a Sloshing Circular Cylinder Inside an Enclosure Filled with Nanofluids

This study applied an incompressible version of the smoothed particle hydrodynamics (SPH) method for simulating a sloshing circular cylinder during natural convection flow over a T-shaped fin in an enclosure occupied by nanofluid. The center area of the enclosure is saturated with a heterogeneous porous medium. Variations in the thermal conditions of the embedded circular cylinder and T-shaped fin were considered. Vertical sloshing of the circular cylinder under a resonance sway excitation was carried out for different values of amplitudes and frequencies. The embedded circular cylinder and T-shaped fin inside the enclosure are maintained at a high temperature . The side walls of the enclosure are maintained at a low temperature , and the horizontal walls are adiabatic. The ranges of key physical parameters are T-shaped fin length (), circular cylinder radius (), Rayleigh number (), Darcy parameter (), solid volume fraction (), wave amplitude (), and resonance frequency (). The simulations revealed that an increment on T-shaped fin length augments the temperature distributions and flow velocity in the enclosure. The circular cylinder radius rises the temperature distributions in the enclosure. At a lower Darcy parameter, the horizontal heterogeneous porous medium in the center area of the enclosure is impeding the nanofluid flow. The hot circular cylinder gives the highest values of the fluid velocity and temperature distributions inside the enclosure.

Convective fluid flow and heat transfer in a vertical rectangular duct containing a horizontal porous medium and fluid layer

PurposeThe purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer.Design/methodology/approachThe Darcy–Brinkman–Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions.FindingsIt is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained.Originality/valueTo the author’s best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.

ISPH simulations of natural convection flow in E-enclosure filled with a nanofluid including homogeneous/heterogeneous porous media and solid particles

In this paper, the unsteady convective nanofluid flow in a novel geometry (E-enclosure) partially filled by a homogeneous/heterogeneous porous medium is numerically investigated using incompressible smoothed particle hydrodynamics (ISPH) method. The major contribution of the work is the introduction of multi-phase flows including solid-fluid particles through different porous media in natural convection of a nanofluid using stable scheme of ISPH method. The E-enclosure is partially saturated by a homogeneous/heterogeneous porous medium in the right area. The solid particles are settled in the left area of the E-enclosure. The inner solid particles are carrying three different thermal conditions including conducting solid particles, hot solid particles and cold solid particles. The current geometry of E-enclosure can be applied in analysis the thermophysical behaviors of the isothermal building. ISPH method is used to solve the dimensionless governing equations. Six cases based on the homogeneous/ heterogeneous properties were investigated and the other controlling parameters are the nanoparticles volume fraction ϕ (1% ≤ ϕ ≤ 5%), the Rayliegh number Ra (103 ≤ Ra ≤ 105) and the Darcy number Da(10−2≤Da≤10−5). The obtained results revealed that the case of the hot solid particles gives a high intensity of the fluid flow and temperature distributions inside E-enclosure. Moreover, the average Nusselt number reaches the maximum value at the case of a horizontal heterogeneous porous medium. Regardless the different cases of the porous media, an increase on the Rayleigh number enhances the rate of heat transfer. Further, case 6 (horizontal heterogeneous porous media for all of the right-area) increases the thermal boundary layers near to the isothermal walls and consequently, the average Nusselt number is supported.

A generalized model for spontaneous imbibition in a horizontal, multi-layered porous medium

Spontaneous imbibition of a wetting fluid in a homogeneous porous medium follows Washburn’s diffusive law. For heterogeneous porous media, the imbibition phenomenon deviates from the diffusive dynamics. A Washburn-like model, developed in the past predicts the imbibition in a three-layered porous medium. In this work, we use experiments to establish the applicability of the model for a horizontal three-layered porous medium. The model is dependent on a scaling law to determine the relative positions of the fronts in the layers. In a multi-layered porous medium, the scaling law cannot predict the relative front advancements. We use a five layered porous medium to develop a strategy and generalize the model for multi-layered porous medium. We show that, the layering pattern, capillary pressure and permeability contrasts among the layers impacts the imbibition behavior significantly and leads to different travel times of the fronts of the invading fluid in the layers.

An Entropy Generation on Viscous Fluid in the Inclined Deformable Porous Medium

The present investigation deals with the flow of a viscous fluid in an inclined deformable porous layer bounded by rigid plates. The lower and upper moving plates are maintained at constant different temperatures. A heat source of strength $$Q_0 $$ is introduced in the porous layer. The coupled phenomenon of the fluid movement and solid deformation in the porous layer has been considered. An exact solution of governing equations has been obtained in closed form. The expressions for the fluid velocity, solid displacement and temperature distribution are obtained. The influence of pertinent parameters on flow quantities is discussed. In the inclined deformable porous medium, it is observed that the fluid velocity and temperature decreases with increasing viscous drag $$\delta $$ . But the solid displacement increases with increasing viscous drag $$\delta $$ . A table of comparison is made for flux in the present work and that of flux observed by Nield et al. (Transp Porous Media 56:351–367, 2004) for viscous flow in a horizontal undeformable porous medium. One of the important observations is that the volume flow rate is less for deformable porous media when compared with undeformable (rigid) porous media. The present result coincides with the findings of Nield et al. (2004). The results obtained for the present flow characteristics reveal many interesting behaviors that warrant further study of viscous fluid flow in an inclined deformable porous media.

Effect of near‐surface wind speed and gustiness on horizontal and vertical porous medium gas transport and gas exchange with the atmosphere

SummaryEffects of wind speed and wind gustiness on horizontal and vertical subsurface gas transport and subsurface–atmosphere gas exchange were investigated experimentally using a 40 cm × 40 cm, 35‐cm‐deep stainless steel container, filled with a dry granular porous medium (crushed basalt) of 2–4‐mm grain size. Experiments used CO2 and O2 as tracer gases and were conducted under both steady and gusty wind at speeds ranging from 0 to 5.6 m s−1. Tracer gas breakthrough curves were measured at 20 locations within the porous medium to assess both horizontal and vertical gas movement. Results indicated that horizontal gas movement in wind‐exposed porous materials is important, especially near the wind‐exposed surface, and suggested considerable effects of both wind speed and wind gustiness on both horizontal and vertical gas transport inside the porous medium as well as subsurface–atmospheric gas exchange. Although wind‐induced subsurface gas transport is likely to be multidimensional, one‐dimensional model simulations indicated that vertical transport is an adequate approximation of the resulting average gas transport and exchange with the atmosphere over a larger area.Highlights Experimental assessment of near‐surface gas movement in wind‐exposed porous medium Near‐surface gas movement in wind‐exposed porous media occurs both horizontally and vertically. Wind speed and wind gustiness affect gas movement near the soil–atmosphere interface. Wind‐induced bulk subsurface‐to‐atmosphere gas mass transport may be approximated as vertical.

Study on Reduction Effect of Natural Convection in a Horizontal Porous Media with High Density Layer at the Middle

Study on Reduction Effect of Natural Convection in a Horizontal Porous Media with High Density Layer at the Middle

Heat Transfer Characteristics of Horizontal Porous Media with a High Density Layer at the Middle

Heat Transfer Characteristics of Horizontal Porous Media with a High Density Layer at the Middle

Nonlinear study of heat transfer in nanofluid saturated horizontal porous medium

The present paper deals with weak nonlinear stability analysis of heat transfer in a nanofluid saturated porous layer. We consider a set of new boundary conditions for the nanoparticle fraction, which is physically more realistic. The new boundary condition is based on the assumption that the nanoparticle fraction adjusts itself so that the nanoparticle flux is zero on the boundaries. We use Darcy model that incorporates the effects of Brownian motion and thermophoresis. The governing equations has been reduced to Ginzburg-Landau equation and solved by homotopy analysis method (HAM). The obtained results have been compared with the numerical results obtained by Mathematica NDSolve. The results are valid for the feasible domain with high accuracy. Thermal Nusselt number and Nanoparticle Nusselt number are calculated for different values of parameters. The results have been depicted graphically.

Nonlinear thermal instability in a horizontal porous layer with an internal heat source and mass flow

Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in Rz as the mass flow moves from negative to positive for different internal heat sources.