non-Darcy Porous Medium Research Articles

A New Approach in Differential transformation method with application on MHD flow in non-Darcy medium between porous parallel plates considering hall current

The study of fluid flow in non-Darcy porous medium subjected to Hall current is very important in scientific and engineering applications such as water filters, groundwater discharge in aquifers, petroleum engineering, MHD generators and chemical engineering. Forchheimer model is needed at high flow rate, where, flow will exhibit non-linearity with respect to velocity which make Darcy law inapplicable at these conditions. In this case, the momentum equations become non-linear. The classical differential transformation method transforms the non-linear differential equations to a non-linear algebraic system which gives more than one solution and may be unstable that leads to divergence of the required solution. The novelty of present method that it is a power series solution avoiding solution multiplicity and divergence by a linearization technique that is applied on non-linear governing equations to obtain the unique and convergent solution. The uniqueness, convergence and stability of the new technique are tested by comparisons with previously available works and it is also verified by a fourth order accurate finite difference (FOFDM) solution. The effects flow parameters on the velocity and friction factor are illustrated. The values of parameters in the present work are chosen according to: the available previous results, the power of the persent method to compute over a lagre range of parameters and the distinctiveness between curves in figures.

Melting effect on non-Newtonian fluid flow in gyrotactic microorganism saturated non-darcy porous media with variable fluid properties

This paper deals with the melting effect on steady mixed convection flow of a non-Newtonian fluid containing gyrotatic microorganism along a vertical plate embedded in a saturated non-Darcy porous medium. Variable fluid properties are considered in this paper to describe the variation of permeability, porosity, thermal conductivity which is approximated by an exponential function. The changed non-dimensional governing ordinary differential equations via similarity transformation characterize the flow phenomena subjected to melting surface boundary condition are solved numerically by Matlab bvp4c solver. To analyze the consequences of flow influencing parameters to the flow variables are tabulated and visualized graphically. With increasing non-Darcy and mixed convection parameters velocity profiles decays. Temperature escalates for mixed convection parameter and plunges for melting parameter. Concentration slow down for high melting effect and rises for high Lewis number. Bioconvection Lewis number and Peclet number has an increasing impact on the microorganism profiles. Mixed convection parameters show pronouncing impact on Sherwood number, Nusselt number and motile microorganism density profiles but they decrease mostly for pseudo plastic fluid. Comparisons with prior works show splendid agreement between the results.

Natural convection flow in a fluid-saturated non-Darcy porous medium within a complex wavy wall reactor

This study elucidates a numerical simulation of natural convective flow inside a confined 2D reactor containing a fluid-saturated non-Darcy porous medium. The lower wall of the reactor is wavy, while all other walls are plane surfaces. All walls of the reactor are kept at surrounding temperature. A chemically reacting fluid produces flow within the reactor by a heat generating exothermic reaction. A coordinate transform is dispensed to turn the waviness of walls into the plane surface, and then, the flow governing equations in transformed coordinates are solved using the finite difference scheme. Streamlines and isotherms that describe, respectively, the flow patterns and temperature distributions within the reactor are displayed varying the dimensionless numbers, namely the Darcy number (10−4 ≤ Da ≤ 10−2), the Rayleigh number (103 ≤ Ra ≤ 105), the Frank-Kamenetskii number (0.5 ≤ Kf ≤ 3.0) and the Forchheimer drag parameter (0 ≤ F ≤ 1). Also local Nusselt numbers at the upper and lower walls are plotted to observe the heat transfer characteristics. The remarkable results reveal that the strength of vorticity and the highest temperature within the reactor increase with increasing the Frank-Kamenetskii number and the amplitude of waves. Because of increasing the Darcy number and Rayleigh number, the strength of vorticity enhances but the highest temperature diminishes. Opposite characteristics are observed due to an increase in the Forchheimer drag parameter. Heat transfer is relatively stronger in plane wall than in wavy wall in every case of dimensionless number. Moreover, maximum heat transfer is noticed at the points on the upper wall that are exactly above the peaks of the wave.

FEM-CBS algorithm for convective transport of nanofluids in inclined enclosures filled with anisotropic non-Darcy porous media using LTNEM

PurposeThe Galerkin finite element method (FEM) based on the characteristic-based split (CBS) scheme is applied to simulate the nanofluid flow and thermal fields inside an inclined geometry filled by a heat-generating hydrodynamically and thermally anisotropic non-Darcy porous medium using the local thermal non-equilibrium model (LTNEM). Property of the hydrodynamic anisotropy is taken in both the Forchheimer coefficient and permeability and these tools are considered as functions of inclination of the principal axes. Also, the thermal conductivity for the porous phase is assumed to be anisotropic.Design/methodology/approachThe Galerkin FEM based on the CBS scheme is applied to solve the partial differential equations governing the flow and thermal fields.FindingsIt is noted that the net rate of the heat transfer between the nanofluid and solid phases are influenced by variations of the anisotropic properties. Also, the system is reached to the thermal equilibrium state at H > 100. Further, the maximum nanofluid temperature is reduced by 12.27% when the nanoparticles volume fraction is varied from 0% to 4%.Originality/valueThis paper aims to study the nanofluid flow and heat transfer characteristics inside an inclined enclosure filled with a heat-generating, hydrodynamically and thermally anisotropic porous medium using the CBS scheme. The LTNEM is considered between the nanofluid and porous phases while the local thermal equilibrium model (LTEM) between the base fluid (water) and the nanoparticles (alumina) is taken into account. The Galerkin FEM is introduced to discretize the governing system of equations. Also, examine influences of the anisotropic properties (permeability, Forchheimer terms and thermal conductivity of the porous medium), inclination angle and nanoparticles volume fraction on the net rate of the heat transfer between the nanofluid and porous phases and on the local thermal non-equilibrium state is one of the concerns of this paper.

Numerical simulation for bioconvection effects on MHD flow of Oldroyd-B nanofluids in a rotating frame stretching horizontally

A rotating MHD flow of electrically conducting Oldroyd-B fluid through non-Darcy porous medium across a stretching/shrinking surface is investigated in purview of bioconvection effects. The fluid velocity field, temperature field, concentration of nano materials and that of bio microorganisms have been simultaneously formulated in the form of coupled nonlinear partial differential equations. The quest for improved thermal performance in practicable situations has motivated to utilize some real fluids like Oldroyd-B nanofluids with support from bioconvection effect to stabilize nanoparticle fraction. The zero normal flux of the nanoparticles and convective boundary condition are imposed. The substitution of appropriate similarity functions has resulted a set of ordinary differential equations (ODE). The sparse system of transformed ODEs was simulated numerically with bvp4c solver facilitated by MATLAB commercial software. Computations were executed for specific parameters to perceive the response of velocity, temperature, concentration of nanoparticles and concentration of microorganisms, skin friction coefficient and local heat transfer rate with variation of influential parameters. It is detected that fluid temperature profile rises when Deborah number, Biot number, parameters for buoyancy ratio, porosity, rotation, magnetic field strength, thermophoresis diffusion are enhanced.

MHD Free Convection-Radiation Interaction in a Porous Medium - Part II: Soret/Dufour Effects

This paper is focused on the study of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium by taking into account of the Soret/Dufour effects. The boundary layer equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters, namely the buoyancy ratio parameter, Prandtl number, Forchheimer number, magnetohydrodynamic body force parameter, Soret and Dufour numbers. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. Increasing the Forchheimer inertial drag parameter reduces velocity but elevates temperature and concentration. Increasing the Soret number and simultaneously reducing the Dufour number greatly boosts the local heat transfer rate at the cylinder surface. A comparative study of the previously published and present results in a limiting sense is made and an excellent agreement is found between the results.

RADIATION EFFECT ON MAGNETOHYDRODYNAMIC CARREAU NANOFLUID FLOW PAST NON-LINEAR PERMEABLE HEATED STRETCHING SHEET WITH PARTIAL SLIP

The motion of a Carreau nanofluid past an infinite vertical non-linear permeable stretching sheet embedded in a non-Darcy porous medium is investigated. It is stressed by a uniform external magnetic field. The thermal radiation and heat generation are taken in consideration as well as Brownian motion with thermophoresis, chemical reaction and partial slip velocity at the boundary layer. The nonlinear partial differential equations describing the motion with heat and mass transfer are transformed to non-linear ordinary differential equations and solved by using Runge-Kutta method with approbriate boundary conditions. The effects of the physical parameters of the problem on the obtained solutions are discussed numerically and graphically. Through the section of discussion the skin friction and the rate of heat and mass transfer are computed. It is found that these physical parameters play an important rules to control the obtained velocity, temperature and concentration of the fluid.

Numerical Analysis of the Flow of a Casson Fluid in Magnetic Field over an Inclined Nonlinearly Stretching Surface with Velocity Slip in a Forchheimer Porous Medium

In this work, we have studied a magnetohydrodynamic, Casson fluid flow with velocity slip over an inclined nonlinearly stretching surface in Non-Darcy porous medium, numerically. In the mathematical model, we have transformed the momentum equation, energy equation and mass concentration equations to non-dimensional ordinary differential equations using similarity variables. We have solved the equations numerically by bvp4c using MATLAB for the numerical computation, and took and axes so that figures are clearly visible. We have discussed and analysed the magnitude of the velocity, temperature, concentration, Local Skin friction, Local Nusselt number and Local Sherwood number using their representative parameters and the effects of these parameters on the respective boundary layer regions using graphs, figures and tables.

Darcy–Forchheimer flow under rotating disk and entropy generation with thermal radiation and heat source/sink

This article investigates the second law of thermodynamics for chemically reactive Sisko nanofluid by a rotating disk saturated with non-Darcy porous medium. Thermophoresis and Brownian motion on irreversibility has been examined through Buongiorno model. The novel features of nonlinear thermal radiation, Joule heating, MHD and non-uniform heat source/sink are accounted. Modified Arrhenius model is executed to characterize the impact of activation energy. The governing flow equations are solved and validated numerically by adopting Runge–Kutta–Fehlberg method. It is noticed from the present analysis that irreversibility rate and Bejan number have reverse behavior for Brinkman number. Growing behavior of concentration is witnessed for greater estimations of activation energy variable. Total entropy generation has significant impact on reaction rate constant.

Magnetohydrodynamic micropolar fluid flow in a porous medium with multiple slip conditions

Theoretically, micropolar fluids are used in the biomedical investigations. This study analyzes the flow, heat and mass transfer in a magneto-micropolar reactive fluid over a nonlinear stretching sheet in a saturated non-Darcy porous medium. The impact of velocity, thermal and concentration slips with prescribed surface temperature and concentration boundary conditions are examined. Mathematical models are formulated and solved using an iterative technique spectral quasi-linearization method. The results of numerical simulations are depicted graphically. The present results when cross-checked with earlier reported data in the literature for limiting conditions exhibit good agreement. The results show that the momentum and thermal boundary layer thicknesses fall as the nonlinear stretching parameter increases while the opposite occur with a rise in the thermal conductivity parameter.

MHD Free Convection-Radiation Interaction in a Porous Medium - Part I: Numerical Investigation

A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement.

Non-Linear Radiation, Chemical Reaction, and Soret/Dufour Effects on Magnetohydrodynamic Natural Convection About a Permeable Horizontal Circular Cylinder in Non-Darcy Porous Media With Heat Source/Sink

Abstract In this paper, the nonlinear radiation, chemical reaction, and Soret/Dufour effects on magnetohydrodynamic (MHD) natural convection about a permeable horizontal circular cylinder in non-Darcy porous media with heat source/sink are numerically analyzed. The surface of the horizontal circular cylinder is subjected to uniform wall temperature and uniform wall concentration (UWT/UWC). The governing equations are transformed into dimensionless, non-similar forms using suitable non-dimensional variables and then solved using Keller box method (KBM). Comparisons with previously published work are performed, and the results are found to be in an excellent agreement. Numerical data of the dimensionless temperature profile, the dimensionless concentration profile, the Nusselt number, and the Sherwood number are presented in graphic and tabular forms for the main parameters. The physical aspects of the problem are discussed in detail. The Nusselt number increases with increasing the Soret parameter, radiation parameter, and surface temperature ratio. Increasing the Dufour parameter, radiation parameter, surface temperature ratio, coefficient of space-dependent internal heat generation/absorption, and dimensionless chemical reaction parameter enhances the Sherwood number.

Significance of inclined magnetic field in Darcy–Forchheimer flow with variable porosity and thermal conductivity

This article examines viscous fluid flow saturated in a non-Darcy porous medium having inclined magnetic field effects. Variable porosity and permeability are also taken into account. Furthermore heat transfer process is examined through variable thermal conductivity and heat absorption/generation. Brinkman–Forchheimer extended model is also studied for the boundary layer flow in a porous space. Governing equations of momentum and energy are transformed into nonlinear ordinary differential equations via suitable transformations. Shooting algorithm is used to generate solutions for the resulting equations. Contributions of various effective parameters that are involved in the current investigation are analyzed graphically for both the velocity and temperature distributions. Behaviors of Nusselt number as well as skin friction coefficient are explored numerically. Higher values of Reynolds number Re,local permeability parameter σ and variable permeability d result in an increment of velocity whereas temperature is reduced for higher values of unsteady parameter A, local permeability parameter σ, Reynolds number Re and Prandtl number Pr.

Effect of nonhomogeneous nanofluid model on transient natural convection in a non-Darcy porous cavity containing an inner solid body

Transient natural convection of an alumina-water nanofluid saturated in non-Darcy porous media is investigated in this paper. The domain of the nanofluid is an annulus composed from a square cavity confining a solid conductive body. The nanoparticles are assumed to be slipping in the base fluid according to Buongiorno model. The Brinkman-Forchheimer-extended Darcy formulation has been adopted for the porous medium. The dimensionless governing equations are solved by implementing the finite difference method. In this study, a special focus is given on the following model parameters; porosity of the porous medium, Darcy number and the nanoparticles average volume fraction. The results show that the nanoparticles possess high uniformity in the base fluid and the Nusselt number augments with increasing values of the Darcy number. The porosity increases the average Nusselt number at a higher Darcy number while its influence remains negligible at a low Darcy number. For the given porosity, there is a critical value of the nanoparticles volume fraction when the average Nusselt number is maximal.

Double-Diffusive Natural Convective Flow of a Nanofluid past an Inclined Wavy Plate in a Non-Darcy Porous Medium

In this paper, the double-diffusive convective flow along an inclined semi-infinite wavy plate in a nanofluid saturated non-Darcy porous medium is investigated numerically. Following Prandtl’s transposition theorem, a coordinate transformation is used to transform the irregular wavy surface into a smooth surface. The convective type thermal boundary condition is taken into account and also the Brownian motion and thermophoresis effects are considered into the present nanofluid model. The governing transport equations are initially reshaped into a system of coupled ordinary differential equations by choosing suitable similarity transformations and then solved numerically by using the Spectral Local Linearization Method (SLLM). The effects of various flow influenced parameters on the fluid flow, heat and mass transfer characteristics are explored and exhibited graphically.

Numerical study of double-diffusive dissipative reactive convective flow in an open vertical duct containing a non-Darcy porous medium with Robin boundary conditions

A mathematical model for thermosolutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is developed and studied. Robin boundary conditions are prescribed, and a first-order homogenous chemical reaction is considered. The Darcy–Forchheimer model is used to simulate both the first- and second-order porous mediums’ drag effects. For the general non-Darcy-case, a numerical solution is presented using the Runge–Kutta quadrature and a shooting method. The influences of thermal $$( {0 \le \lambda _1 \le 15} )$$ and solute Grashof numbers $$( {0 \le \lambda _2 \le 20} )$$, Biot numbers $$( {1 \le \textit{Bi}_1 \le 10, \textit{Bi}_2 =10 } )$$, Brinkman number $$( {0 \le \textit{Br} \le 0.5} )$$, first-order chemical reaction parameter $$( {2 \le \alpha \le 8} )$$, porous medium parameter $$( {2 \le \sigma \le 8} )$$ and Forchheimer (inertial drag) parameter $$( {0 \le I \le 12} )$$ on the evolutions of velocity, temperature and concentration (species) distributions are visualized graphically. Nusselt number and skin friction at the walls are also computed for specific values of selected parameters. The study is relevant to the analysis of geothermal energy systems with chemical reaction.

Powell–Eyring fluid flow towards an isothermal sphere in a non-Darcy porous medium

Non-Newtonian viscoelastic fluid flow past an isothermal sphere embedded in non-Darcy porous medium is examined numerically in this work. To be specific, the non-Newtonian Powell–Eyring fluid in the presence of both the heat and mass characteristics is mathematically modelled in terms of differential system. A non-Darcy drag force model is employed to simulate the effects of linear porous media drag and second-order Forchheimer drag. The surface of the sphere is maintained at a constant temperature and concentration. The numerical solution of the resultant system is reported via the Keller box method. Both tabular and graphical forms are adopted to identify the variations in Powell–Eyring fluid velocity, Powell–Eyring fluid temperature, and Powell–Eyring fluid concentration. In addition, the surface physical quantities, namely, skin friction and heat and mass transfer rates, are explored. The obtained observations are validated with earlier Newtonian studies. We found an excellent match in this regard. It is found that the velocity is reduced with increasing fluid parameter (ε), Forchheimer parameter (Λ), and tangential coordinate (ξ). In contrast, the temperature and concentration are increasing with increasing value of ε. A very slight increase in velocity is seen with an increase in the local non-Newtonian parameter, δ. But the temperature and concentration decrease slightly with an increase in δ. An increase in Darcy parameter enhances velocity but reduces both temperature and concentration. The present study finds an extensive array of applications in modern nuclear engineering, mineral and chemical process engineering, nuclear waste in geomaterial repositories, petroleum product filtration, and insulation systems.

Correction to: Entropy generation analysis on electroosmotic flow in non-Darcy porous medium via peristaltic pumping

Correction to: Entropy generation analysis on electroosmotic flow in non-Darcy porous medium via peristaltic pumping

Incompressible smoothed particle hydrodynamics simulation of natural convection in a nanofluid-filled complex wavy porous cavity with inner solid particles

This study focus on the simulation of the natural convection of a nanofluid in a wavy cavity saturated with a partially layered non-Darcy porous medium. The motion of the embedded solid particles, which carry two different isothermal conditions inside a wavy cavity, was considered. The meshfree nature of incompressible smoothed particle hydrodynamics (ISPH) method helped us to simulate the motion of solid particles inside a wavy cavity. The dummy wall boundary particles with enough layers were used to prevent the particle penetrations during simulation of natural convection. The wavy cavity is filled with a nanofluid and a non-Darcy porous medium is embedded in the upper half of the wavy cavity. The results from the current investigation showed that, the motion of the inserted solid particles affects strongly on the strength of the fluid flows and heat transfer inside a wavy cavity. The position and isothermal condition of the inner solid particles try to change the distributions of temperature and fluid flow inside a wavy cavity. Average Nusselt number has higher values in the case of cool solid particles compare to hot solid particles. At the current model, an addition of nanoparticles has slight effects on enhancement heat transfer inside a wavy cavity.

Numerical study of non-linear thermal radiative heat transfer in a non-Darcy chemically reactive Casson fluid flow

Study of thermal radiative heat transport is relevant in several industrial applications. Analysis of radiative heat transfer in Newtonian fluids under different conditions has been studied extensively. However, not much attention has been paid to analyze the non-linear thermal radiative heat transfer in non-Darcy Casson fluid flows over stretching surfaces. Hence, in this paper an attempt is made to study the combined effect of non-linear thermal radiation and Navier slip in a magnetohydrodynamically and chemically reactive Casson fluid flow on a stretching surface immersed in a non-Darcy porous medium in the presence of thermo-diffusion. The physics of the problem is delineated by a set of partial differential equations. To solve these equations numerically scaling analysis and Runge–Kutta–Fehlberg method are sequentially applied. Computational results of the investigation are analyzed through graphs and tables. It is noted that the non-Newtonian rheology parameter, inertial and Lorentz forces are seen to suppress the flow while thermal and solutal buoyancy forces have an opposite effect. Parameters of temperature ratio and thermal radiation enhanced the temperature.