Layer Of Porous Medium Research Articles

Study of mixed convection in two layers of saturated porous medium and nanofluid with rotating circular cylinder

In this study, a numerical investigation of mixed convective heat transfer in a square enclosure partitioned in two layers with a rotating circular cylinder at the middle of the cavity has been carried out. The experiments are performed with Al2O3–water nanofluid (upper layer) and superposed porous medium (lower layer). The upper and lower horizontal walls are assumed to be insulated, while the left and right walls are kept at high and low temperature respectively. Galerkin finite element method has been used to solve the dimensionless governing equations. This study is focused to investigate the effect of Darcy number (10−2≤ Da ≤10−5), Rayleigh number (103≤ Ra≤106), dimensionless angular rotational velocity (−6000≤ W ≤ 6000), solid volume fraction (0≤ ɸ ≤0.06), and the radius of the inner circular cylinder (R = 0.1, 0.2 and 0.3) on the heat transfer, fluid flow, and the physical characteristics thermal of the thermal fields. The results show that the intensity of the flow, steep temperature gradient, and the average Nusselt number (Nu) increase with increasing the value of Darcy number, Rayleigh number, and solid volume fractions at any cylinder radius. Moreover, the recirculation and isotherm distribution lines of the fluid at low Darcy numbers are high when the cylinder rotates counter-clockwise compering with clockwise. The findings also revealed that when W = 0, the maximum Nu is at R = 0.1 and decreases as the cylinder radius increases. Moreover, at high Darcy number, the highest local Nusselt number is found at the porous layer region in case of clockwise rotation while at the nanofluid layer region in case of anti-clockwise rotation.

Motion of circular cylinders during natural convection flow in X-shaped cavity filled with a nanofluid using ISPH method

PurposeThis study aims to illustrate the impacts of the motion of circular cylinders on the natural convection flow from variable heated partitions inside the X-shaped cavity filled with Al2O3-water nanofluid. A partial layer of a homogeneous/heterogeneous porous medium is located in the top area of the X-shaped cavity.Design/methodology/approachThree different cases of the porous media including homogeneous, horizontal heterogeneous and vertical heterogeneous porous media were considered. Three different thermal conditions of the embedded circular cylinders including hot, cold and adiabatic conditions are investigated. An incompressible scheme of smoothed particle hydrodynamics (ISPH) method is modified to compute the non-linear partial differential equations of the current problem. Two variable lengths of the left and right sides of the X-shaped cavity have a high-temperature Th and a low-temperature Tc, respectively. The other wall parts are adiabatic. The numerical simulations are elucidating the dependence of the heat transfer and fluid flow characteristics on lengths of hot/cold source Lh, porous cases, Darcy parameter, thermal conditions of the embedded circular cylinders and solid volume fraction.FindingsOverall, an increment in length of hot/cold source leads to augmentation on the temperature distributions and flow intensity inside the X-shaped cavity. The hot thermal condition of the circular cylinder augments the temperature distributions. The homogeneous porous medium slows down the flow speed in the top porous layer of the X-shaped cavity. The average Nusselt number decreases as Lh increases.Originality/valueISPH method simulated the motion of circular cylinders in the X-shaped cavity. The X-shaped cavity is saturated with a partial layer porous medium. It is found that an increase in hot source length augments the temperature and fluid flow. ISPH method can easily handle the motion of cylinders in the X-shaped cavity. Different thermal conditions of cylinders can change the temperature distributions in X-cavity.

Lattice Boltzmann Method development of PEMFC in mesoscopic scale

Proton exchange membrane fuel cell (PEMFC) mainly relied on the modeling analysis of the traditional numerical method. However, the scale of the research is bigger than porous medium layer of the particle that can’t meet the actual mechanism of the simulation. Hence, as a new mesoscopic numerical method, Lattice Boltzmann method (LBM) builds a model based on the microstructure and analyzes the dynamics, while the transfer state of the porous media layer of PEMFC can be more realistically described during its actual operation.

Examination of the nanofluid convective instability of vertical constant throughflow in a porous medium layer with variable gravity

In the current article, the impact of varying gravitational field and flow on the beginning of nanofluid convective instability in a permeable medium layer is studied numerically utilizing Galerkin technique. The permeable layer is directed to a regular vertical throughflow and irregular descendent gravitational force which changes with the length from the layer. The influences of three types of gravitational force inconsistency: (a) linear, (b) parabolic, and (c) exponential are examined on the formation of nanofluid convective instability with vanish nanoparticle flux condition at the plates. Results proved that the throughflow factor $$Q$$ and gravity inconsistency factor $$\delta$$ suspend the start of convective instability, while the nanoparticle Rayleigh-Darcy number $$R_{{{\text{np}}}}$$ and the altered diffusivity ratio $${\text{NA}}_{{{\text{nf}}}}$$ quick the start of nanofluid convection. The measurement of the convective cells diminishes with $$R_{{{\text{np}}}}$$ and $${\text{NA}}_{{{\text{nf}}}}$$ , while $$Q$$ , $$\delta$$ and the altered nanofluid Lewis number $${\text{Le}}_{{{\text{nf}}}}$$ have duel effects on the measurement of convective cells.

Double-Diffusive of a Nanofluid in a Rectangle-Shape Mounted on a Cavity Saturated by Heterogeneous Porous Media

This study presents numerical simulations on double-diffusive flow of a nanofluid in two cavities connected with four vertical gates. Novel shape of an outer square shape mounted on a square cavity by four gates was used. Heterogeneous porous media and Al 2 O 3 -water nanofluid are filled in an inner cavity. Outer rectangle shape is filled with a nanofluid only, and its left walls carry high temperature T h and high concentration C h . The right walls of a rectangle shape carry low temperature T c and low concentration C c and the other walls are adiabatic. An incompressible smoothed particle hydrodynamics (ISPH) method is applied for solving the governing equations of velocities, temperature, and concentration. Results are introduced for the effects of a buoyancy ratio − 2 ≤ N ≤ 2 , Darcy parameter 10 − 3 ≤ Da ≤ 10 − 5 , solid volume fraction 0 ≤ ϕ ≤ 0.05 , and porous levels. Main results are indicated in which the buoyancy ratio parameter adjusts the directions of double-diffusive convection flow in an outer shape and inner cavity. Adding more concentration of nanoparticles reduces the flow speed and maximum of the velocity field. Due to the presence of a porous medium layer in an inner cavity, the Darcy parameter has slight changes inside the rectangle shape.

Effects of variable heat source on convective motion in an anisotropic porous layer

The onset of convective motion in a fluid saturated anisotropic porous medium layer is examined analytically in the occurrence of the qualitative effect of the source of variable internal heat. Three different kinds of heat source functions: (i) N (z) = z (linear) (ii)N(z) = z2 (parabolic) and (iii) N (z) = z 3 (cubic) are considered. The resulting eigenvalue problem was analytically solved using regular perturbation technique. A parametric study is carried out by varying the following parameters: the heat source parameter (X), thermal anisotropy parameter(n), and mechanical anisotropy parameter(ξ). Results indicates that the effects of the increasing values of λ and ξ will enhance the convection of a anisotropic porous layer system while the increasing of n will help to stabilize the system. It is also noted that for case (iii) the system is more stable, while for case (i) the system is more unstable

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.

Rotating cylinder and magnetic field on solid particles diffusion inside a porous cavity filled with a nanofluid

This study deals with the roles of a magnetic field and circular rotation of a circular cylinder on the dissemination of solid phase within a nanofluid-filled square cavity. Two wavy layers of the non-Darcy porous media are situated on the vertical sides of a cavity. An incompressible smoothed particle hydrodynamics (ISPH) method was endorsed to carry out the blending process concerning solid phase into nanofluid and porous media layers. Initially, the solid phase is stationed in a circular cylinder containing two open gates. Implications of a buoyancy ratio ( N = −2: 2), Hartmann number ( Ha = 0: 100), rotational frequency [Formula: see text], Darcy parameter [Formula: see text], Rayleigh number [Formula: see text], nanoparticles parameter [Formula: see text], and amplitude of wavy porous layers [Formula: see text] on the lineaments of heat/mass transport have been carried out. The results revealed that the diffusion of the solid phase is permanently moving toward upward except at opposing flow mode [Formula: see text] toward downward. The lower Rayleigh number reduces the solid-phase diffusions. A reduction in a Darcy parameter lessens the nanofluid speed and solid-phase diffusions in the porous layers. A reduction in [Formula: see text] from [Formula: see text] to [Formula: see text] diminishes the maximum of streamlines [Formula: see text] by 13.19% at [Formula: see text], by 46.75% at [Formula: see text], and by 74.75% at [Formula: see text].

Heat and Mass Transfer in an Inclined Bi-L-Shaped Layered Porous Media: Effect of Buoyancy Ration

The effect of buoyancy ratio on the two dimensional natural convection heat and mass transfer generated in an inclined square bi-L-shaped layered porous cavity filled with Newtonian fluid has been investigated numerically. Each porous layer is considered isotropic, homogeneous and saturated with the same fluid. The cavity is heated and salted from below where as the vertical walls are assumed to be adiabatic and impermeable. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman-Forcheimer model, and the set of coupled equations is solved using a finite volume approach. The power-law scheme is used to evaluate the flow, heat and mass fluxes across each of the control volume boundaries. Tri diagonal matrix algorithm with under-relaxation is used in conjunction with iterations to solve the nonlinear discretized equations. An in-house code developed for this study is validated using previous studies. The results are presented graphically in terms of streamlines, isotherms and iso-concentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers.

Heat transfer enhancement in the complex geometries filled with porous media

The present numerical investigation aims to analysis the enhancement heat transfer in the nanofluid filled-complex geometries saturated with a partially layered porous medium. The vertical walls of the cavity are taken as complex wavy geometries. The horizontal walls of the cavity are flat with insulated temperature. The complex wavy cavity is filled with a nanofluid and the upper half of the wavy cavity is saturated with the porous medium. In the analysis, the governing equations are formulated for natural convection under the Boussinesq approximation in various environments including pure-fluid, nanofluid, and porous medium. In this investigation, the effects of the Rayleigh number (103 ? Ra ? 105), Darcy parameter (10?6 ? Da ? 10?3), thermophoresis parameter (0.1 ? Nt ? 0.5), nanofluid buoyancy ratio (0.1 ? Nr ? 0.5), Brownian motion parameter (0.1 ? Nb ? 0.5), inclination angle (0? ? ? ? 90?), and geometry parameters ?1 and R have been studied on the streamlines, temperature, nanoparticles volume fraction, local Nusselt number, and the local Sherwood number. It is found that, the performance of the heat transfer can be improved by adjusting the geometry parameters of the wavy surface. Overall, the results showed that the nanofluid parameters enhance the convection heat transfer and the obtained results provide a useful insight for enhancing heat transfer in two separate layers of nanofluid and porous medium inside complex-wavy cavity.

Графоаналитическое определение влагосодержания подвижной жидкости в капиллярной кайме пористой среды

Графоаналитическое определение влагосодержания подвижной жидкости в капиллярной кайме пористой среды

Solutal convection in horizontal porous layer with immobilization and clogging

The paper is devoted to the investigation of the solutal convection in a horizontal layer of porous media with horizontal seepage of the mixture and solute immobilization. The flow through porous media is modelled within the standard Darcy–Bousinesq model and immobilization is described by the mobile/immobile media (MIM) approach. The high concentrations of solute are considered which lead to taking into account the dependence of media permeability on porosity. The variation of porosity is modelled as a linear function of solute concentration in the immobile phase. It is shown that immobilisation leads to the stabilization of homogeneous filtration regime and to slow down of the perturbation dynamics. The increasing of critical parameters with the intensification of sorption is not monotonous due to saturation of porous matrix with the adsorbed solute.

Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media.

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.

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.

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.

Effects of rotation and varying gravity on the onset of convection in a porous medium layer: a numerical study

Purpose The purpose of this study is to examine the influence of rotation and varying gravitational strength on the onset of thermal convection in a porous medium layer numerically. The porous layer is acted to uniform rotation and inconsistent downward gravitational field which changing with depth from the layer. The authors presented three categories of gravitational strength deviancy, namely, linear, parabolic and exponential. Design/methodology/approach The higher-terms Galerkin weighted residual procedure is applied to get the eigenvalue of the problem. Findings The results illustrate that both rotation parameter and gravity variation parameter suspend the arrival of convection. The measurement of the convection cells decreases on enhancing the rotation parameter and gravity variation parameter. Originality/value It is also found that the scheme is more stable for category exponential, whereas it is more unstable for category parabolic.

NUMERICAL SIMULATION OF NATURALLY FRACTURED SHALE GAS RESERVOIRS APPLYING THE LAYER MODEL

Typically, hydrocarbon reservoirs have heterogeneities that influence pressure variation in producing wells. In the case of natural fractures, the layer model has been widely applied to obtain analytical and numerical solutions. In this model, we superimpose the porous media layers representing the porous matrix and fractures. In this work, the layer model is used in the numerical simulation, using cylindrical geometry and finite differences, to determine the pressure in natural gas producing wells. We consider shale gas reservoirs, and obtain the numerical results investigating the effects resulting from the presence of fractures and non-Darcy flow due to slip and adsorption phenomena. This work studies grid refinement and performs numerical verification, as well as a sensitivity analysis varying the main physical parameters that directly influence the reservoir and well pressures, such as permeability, porosity, and thickness of the fracture, reservoir temperature, and the Langmuir pressure and volume. As expected, from specialized and diagnostic plots, we can visualize how fractures favor the flow while capturing typical flow regimes of fractured reservoirs described in the literature.

The effect of viscosity and Darcy number on the start of convective motion in a rotating porous medium layer saturated by a couple-stress fluid

In chemical process industry, food process industry, centrifugal filtration processes, and rotating machinery, convective flows are characterized by rotation, where couple-stress fluid (a type of non-Newtonian fluid) with variable viscosity in a porous medium can act as a working fluid. In the present work, the combined effect of the temperature-dependent viscosity, the Darcy number and the uniform rotation on the arrival of convective motion in a couple-stress fluid saturated porous layer is examined applying linear stability concept. The outcome of the viscosity variation parameter Q, the rotation parameter [Formula: see text], the couple-stress parameter [Formula: see text], and the Darcy number [Formula: see text] on both stationary and oscillatory convections is investigated analytically and presented graphically in terms of the critical thermal Darcy–Rayleigh number [Formula: see text]. Below the critical value [Formula: see text], no convective motion arises in the considered system. It is recognized that the arrival of convective motion is oscillatory only if the rotation parameter [Formula: see text] surpasses a threshold value which in turn depends on other physical parameters. The impact of the viscosity variation parameter Q has a destabilizing influence, while the couple-stress parameter [Formula: see text], rotation parameter [Formula: see text], the Darcy number [Formula: see text], the Prandtl number ⪻, and the heat capacity ratio γ show stabilizing influences on the stability of arrangement.

The Density-Driven Nanofluid Convection in an Anisotropic Porous Medium Layer with Rotation and Variable Gravity Field: A Numerical Investigation

In this study, a numerical examination of the significance of rotation and changeable gravitational field on the start of nanofluid convective movement in an anisotropic porous medium layer is shown. A model that accounts for the impact of Brownian diffusion and thermophoresis is used for nanofluid, while Darcy’s law is taken for the porous medium. The porous layer is subjected to uniform rotation and changeable downward gravitational field which fluctuates with the height from the layer by linearly or parabolic. The higher-order Galerkin technique is applied to obtain the numerical solutions. The outcomes demonstrate that the rotation parameter TD, the thermal anisotropy parameterh and the gravity variation parameter λ slow the beginning of convective motion, whereas the mechanical anisotropy parameter ξ, the nanoparticle Rayleigh-Darcy number Rnp, the modified diffusivity ratio NAnf and the modified nanofluid Lewis number Lenf quick the start of convective motion. For instance, by rising the gravity variation parameterfrom zero to 1.4, the critical nanofluid thermal Rayleigh-Darcy number Rnf,c and the critical wave numberboost maximum around 133% and 7%, respectively for linear variation of the gravity field, while it were 47% and 2.8% for parabolic variation of the gravity field. It is also observed that the system is more unstable for the parabolic variation of the gravity field.

Impact of Thermal Non-equilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid-Saturated Vertical Porous Layer with Internal Heat Sources

The stability of natural convection in a vertical layer of heat-generating Darcy porous medium saturated with an Oldroyd-B fluid using a local thermal non-equilibrium (LTNE) model has been investigated numerically. The impermeable vertical walls of the porous layer are maintained at different uniform temperatures. As a consequence of LTNE model, two temperature equations representing the fluid and solid phases separately are used for the heat transport equation. A uniform volumetric heating in both fluid and solid phases is considered and the transfer of heat between the phases is considered in the basic state. The internal heating introduced asymmetry in the basic flow which led to the existence of competing modes. The intricacies of internal heat source strength in the fluid and the solid phases are clearly discerned on the stability of the system. The stress relaxation parameter $$\Lambda_{1}$$ , fluid-heat generation parameter $$Q_{f}$$ , solid-heat generation parameter $$Q_{s}$$ and the porosity-modified conductivities ratio $$\gamma$$ were found to exhibit destabilizing effect on the system, while the strain retardation parameter $$\Lambda_{2}$$ shows an opposite trend even in the presence of internal heating.