Darcian Porous Medium Research Articles

Numerical study on natural convection in a saturated non Darcian porous medium under radiation and entropy generation effects

This work focuses on analyzing fluid flow, generation of entropy, and heat transfer during natural convection in a cavity enclosed with a non-Darcian saturated porous medium. The influence of viscous dissipation and thermal radiation are considered. The Lattice Boltzmann method is adopted to simulate the governing equations. The study discusses the general effect of dimensionless parameters on the fluid structure interaction properties, entropy generation and the thermal field. The parameters investigated include the Grashof number, Eckert number, Rayleigh number, Forchheimer Resistance, inverse Darcy, radiation parameter, and Prandtl number. The combination of studying dimensionless parameters on non-Darcian porous medium, along with the consideration of thermal radiation, viscous dissipation, and entropy analysis, has made this research valuable and worth pursuing. The findings reveal that the areas of high entropy generation are primarily located along the walls (vertical) of the cavity. Moreover, it is observed that as the inverse Darcy and Forchheimer resistance increase, their effect on the average Nusselt number diminishes for varying parameters of radiation. As the Prandtl number increases, the isotherms cluster along the walls (vertical) of the porous cavity. With high Grashof values, convection becomes turbulent, and the temperature distribution becomes non-uniform. Additionally, the entropy caused by heat and fluid friction decreases as the Forchheimer resistance increases.

Nano‐bioconvective anisotropic slip flow in anisotropic porous medium with Coriolis force effects

AbstractThe present paper examines the impact of the Coriolis force and anisotropic Darcian porous medium on the nonsteady convective flow of bio‐nanofluid along a three‐dimensional stretchable surface. The problem has applications in extrusion processes and the geographical movement of tectonic plates under a moveable ocean. Emphasis is placed on the combined effects of anisotropic porous medium, anisotropic momentum slip and temperature, and microorganism slips at the wall. The pertaining equations are condensed to a set of similarity equations before being simulated using the Keller‐box method, an efficient numerical technique. The study reveals that the friction factor along the y‐axis decreases as the rotation parameter increases. Moreover, the heat and nanoparticle volume fraction movement gradient decrease along the y‐axis when the Darcy number and stretching rate increase. However, these rates increase with a higher velocity slip. In addition, the density of microorganisms in the bio‐nanofluid decreases when there are higher levels of unsteadiness, rotation, and Darcy numbers, as well as with increased bioconvection parameters.

Magnetic carbon nanotubes (CNTs)-water-based nanofluid in the presence of thermal radiation and heat generation/absorption

The aim of this study is to examine the Marangoni boundary film problem of water-based CNTs nano-liquids in Darcian porous media. Two types of CNTs, namely Single Wall Carbon Nanotubes (SWCNTs-water) and Multi-Wall Carbon Nanotubes (MWCNTs-water), are considered in the presence of Bénard-Carlo Marangoni convection. The impact of an inclined magnetic field is considered. The heat transport mechanism is analyzed under the impression of nonlinear thermal radiation, heat generation, and absorption. Through Marangoni convection scattering, the system of partial differential equations is established. By utilizing generalized transformation, the model system is converted to an ordinary differential problem and then solved by using the Homotopy Asymptotic Method. It is demonstrated that the volume fraction of nanoparticles raises the velocity at the surface, whereas magnetic and porosity parameters lower the velocity at the surface. Furthermore, the controlling parameters help in increasing the heat transfer rate.

Arrhenius kinetics driven nonlinear mixed convection flow of Casson liquid over a stretching surface in a Darcian porous medium

The non-linear mixed convective heat and mass transfer features of a non-Newtonian Casson liquid flow over a stretching surface are investigated numerically. The stretching surface is embedded in a Darcian porous medium with heat generation/absorption impacts. The fluid flow is assumed to be driven by both buoyancy and Arrhenius kinetics. The governing equations are modelled with the help of Boussinesq and Rosseland approximations. The similarity solutions of the non-dimensional equations are obtained using two numerical approaches, namely fourth fifth Runge - Kutta Fehlberg method and the shooting approach. The velocity, temperature and concentration profiles are discussed for important physical parameters through various graphical illustrations. The skin friction, the non-dimensional wall temperature, and the concentration expressions were derived and analysed. The results indicate that the increasing values of linear and nonlinear convection due to temperature, nonlinear convection due to concentration, and heat of reaction increase the dimensionless wall temperature. The dimensionless wall concentration rises with the increasing values of heat of reaction, linear and nonlinear convection due to temperature, and nonlinear convection due to concentration parameters.

Aspects of Arrhenius kinetics and Hall currents on gyratory Couette flow of magnetized ethylene glycol containing bi‐hybridized nanomaterials

AbstractIncomparable thermal features of hybrid nanofluids (NFs) have been well recognized. Hybrid nanomaterials are prolifically used in chemistry processes, enzyme nanotechnology, pharmaceutical manufacturing, and so on. Motivated by numerous novel applications, in the present article, a theoretical study is conducted to demonstrate a time‐dependent hydro‐magnetic Couette flow and heat transport features inside a gyrating channel filled with a reactive second‐grade hybrid NF (copper–alumina–ethylene glycol) and Darcian porous medium under multiparty impacts of Hall currents, temperature‐dependent thermal conductivity, and Arrhenius chemical reaction. The modeled momentum equations are rendered nondimensional and solved analytically by means of the sophisticated Laplace transform technique. ND Solver in Mathematica is deployed to estimate the numerical solution of the energy equation. The computational outcomes are plotted and interpreted via physical constraints using line graphs and tables. The graphical outcomes assert that Hall currents significantly modify the gyratory flow dynamics and thermal features. The thermal profile and heat transfer rate manifest a diminishing pattern over widening Hall and rotation parameters. The change in thermal conductivity has a substantial impact on heat transmission. The novelty of the research study is a new insight into the hydro‐thermal manners of magnetized rotational non‐Newtonian hybrid NF.

Numerical simulation on Cu–H2O nanofluid of destructive and generative reactions in a Darcian medium: application of wall suction and blowing

Application of – nanoparticles in a base fluid of water means the growth of thermal conductivity of Nanofluid. This physical behavior recommends the prospect of applying nanofluids in electronic cooling and advanced nuclear systems. The formulated leading equations are transformed to non-dimensional form by appropriate similarity transformations and finally solved numerically through Runge–Kutta Shooting method of 4th order. The novelty of the current investigation is to examine the impact of wall suction/ injection over the dual solutions by numerical simulation for time-independent, two- dimensional nanofluid flow along a semi-infinite porous stretching horizontal wall placed in a Darcian medium under the application of magnetic drag force. The significant outputs are portrayed in dual solutions for suction/injection and deliberated their salient effects of various emerging physical variables on velocity, temperature, and molar concentration of Copper nanoparticles in water base fluid. It is obtained that the nanoparticle concentration grows via larger destructive chemical reaction and lessens when generative chemical reaction is enhanced. This investigation leads to opposite behavior due to endothermic reaction. The significance of such investigation in Darcian porous medium have frequent applications in the major area of industrial and engineering technologies that covers the bio-engineering, rubber technology and material processing.

Mass Transfer of a Thermally Radiative MHD Cattaneo-Christov Nanofluid between Two Stretchable Spinning Disks

The investigation on the impacts of magnetic field, thermal radiation, generation of heat and mass transfer in a porous-medium-embedded homogenous nanofluid flow between two stretchable spinning disks is crucial since spinning disks are prevalent in many engineering and technological applications. The objective of this research was to analyze the influences of these parameters using the Cattaneo-Christov heat flux model against the flow’s temperature, velocity and concentration profiles. Temperature profile is a decreasing function of thermal relaxation time parameter due to the particles require a longer period to transfer heat to the next particles. The rates of heat transfer at both spinning disks decrease as values of heat generation, Eckert number, Prandtl number, Brownian diffusion, thermophoresis diffusion and rotation ratio increase. The disks’ rates of mass transfer decrease with more thermophoresis diffusion, heat generation, heat transfer dissipation, and momentum diffusivity, but they increase with thermal radiation parameter. The current work attempts to include the transport profile of a Buongiorno’s nanofluid embedded in a Darcian porous medium between dual spinning disks with magnetic field, thermal radiation and generation of heat using the heat flux model of Cattaneo-Christov’s. Von Karman transformations are utilized to transform the nonlinear partial differential equations of fluid dynamics into coupled nonlinear ordinary differential equations (ODEs). These coupled ODEs are later solved by employing a shooting method with MATLAB bvp4c algorithm. All numerical evidences from this investigation are conferred through tables and figures after validation of present computations.

Chemically reactive transport of magnetized hybrid nanofluids through Darcian porous medium

Nowadays, nanofluid is the traditional procedure to increase the thermal conductivity of common fluids such as water, glycerin, and motor oil due to the deterioration of thermal aspects. The term “nanoliquid” refers to a liquid created by nanometer-sized particles with diameters less than 100 nm. Nanofluids are utilized in a variety of automotive purposes including fuel combustion, medication delivery, cooling of automobile engines, geothermal force extraction and heat transmission. This research aims to show the MHD transport of hybrid nanofluids with viscous dissipation through porous medium. By using an efficient similarity transformation process, PDEs are converted into system of nonlinear ODEs. The bvp4c (shooting method) is used to solve the complete nonlinear ODEs with suitable boundary conditions. To investigate the thermal transport aspects, hybrid nanoparticles and water as base fluid are used. To determine the flow behavior, several physical flow factors on velocity and thermal profiles are explored by using tables and graphs. The outcomes specify that porosity number and magnetic and slip parameters reduced the velocity profile. The higher estimations of slip parameter and Eckert number lead to stronger thermal profile. The concentration profile is decayed for growing estimations of chemical-reaction number.

Natural convection of nanofluids in a wavy porous cavity

In this piece of work, a numerical investigation of natural convection is carried out on the buoyancy-driven flow of nanofluids and heat transfer through porous media packed inside a wavy cavity. The cavity is placed horizontal, and its right vertical wall is of wavy nature, the bottom and top walls of the cavity are adiabatic, and there is a temperature difference between the left and right vertical wall. The dimensionless governing equations for the flow of nanofluids through the Darcian porous media are solved iteratively by using finite difference method. The study is conducted for wide range of governing parameters, such as Rayleigh-Darcy number [Formula: see text], nanoparticle volume fraction [Formula: see text] for three types of nanofluids [Formula: see text]-[Formula: see text], Cu-[Formula: see text], TiO2-[Formula: see text], the waviness of the vertical wall controlled by dimensionless length of amplitude of the wave [Formula: see text] and number of undulations per unit length ( N = 1, 3, 5). The simulated results reveals that the presence of nanoparticles enhances the convective heat transfer process at low Ra, and the wall affects the local convection rate and it also controls the overall heat transfer rate. For a cavity with N = 3, [Formula: see text] is increased by about 68% at Ra = 10, and at [Formula: see text] the increment is about 11% as the a is increased from 0.05 to 0.25 having 20% of nanoparticles volume friction.

Rotating flow thorough parallel plates with the various inclined magnetic field under the influence of hall current

PurposeThe Purpose of this study to examine the magneto hydrodynamics (MHD) using the analytical and numerical tool. In recent years, MHD growing tremendously due to the presence of multidisciplinary application in solving the tedious problems in the viscous flow.Design/methodology/approachThe flows between the parallel plates under the steady inclined magneto hydrodynamic force were studied under the presence of different hall current and pressure gradient. The system was designed with the Darcian porous medium subjected to the incompressible flow. To analyse the flow reactions through stationary parallel plates, the governing equations were used using the integral transformation.FindingsThe velocity of the flows depends on the Hall parameter. As the intensity of the magnetic field increases the velocity of the flow is affected significantly. On the other hand, the radiation parameters also affect the flow of any medium through the porous medium.Practical implicationsImplementation of the Laplace and Fourier transform increases the reliability of the obtained results and further decreases the uncertainty during the measurement of the velocity of the flow without any restraints.Originality/valueFrom the evident results, it is clear that the proposed MHD model can be applied to several operations of the fluid dynamic models. Further, the application of this technique will decrease the uncertainty in the results compared to the conventional computational models and other finite element and difference approaches.

Soret-Dufour magneto-thermal radiative convective heat and mass transfer of chemically and thermally stratified micropolar fluid over a vertical stretching/shrinking surface in a porous medium

The present article deals with Soret Dufour free convective heat and mass transfer of a micropolar fluid over vertical stretching and shrinking sheets embedded in a Darcian porous medium with thermal radiation and magnetic field. We have obtained numerical solutions for the velocity, temperature, microrotation, and solute concentration fields for various values of the thermal radiation and microrotation material parameters, Prandtl number, chemical reaction, magnetic parameter, and Soret-Dufour number. Present results are obtained by using Runge-Kutta Fehlberg method with shooting technique and they are presented graphically and in tabular form for performing a critical analysis of various parametric values. It is explored that the velocity and temperature distribution decrease with enhancement in the Prandtl number and having reverse effects on the concentration distribution. Further, it is noticed that by increasing the values of the thermal radiation parameter, there is a rise in the velocity and temperature distributions. This work would find applications in the field of chemical engineering systems and magnetic materials processing.

Darcy-Brinkman flow of a viscous fluid through a porous duct: Application in blood filtration process

This article explores the problem arising in the filtration process of blood through a membrane of hemodialyzer. The blood is assumed to behave like a viscous Newtonian fluid moving through a 2D channel with permeable boundaries containing a Darcian porous medium. The well known Brinkman model is adopted in the balance of momentum transfer during the blood filtration process. Construction of exact solutions is furnished due to the vanishing of Reynolds number in slow flow situation. The distributions of velocities, pressure, flow rate and the leakage flux are derived and analyzed. The applicability of the theoretical results during the filtration process of blood in flat plate dialyzer is also investigated categorically. The computed values of the filtration coefficient and the dialyzer mean pressure drop from the present model are found to be in excellent agreement with the existing experimental values during the filtration process. Therefore, it is hoped that the present model provides promising measurements during blood purification processes in artificial kidneys.

Pulsating flow of a micropolar-Casson fluid through a constricted channel influenced by a magnetic field and Darcian porous medium: A numerical study

The behavior of the pulsatile flow of non-Newtonian micropolar-Casson fluid in a constricted channel influenced by Lorentz force following Darcy's law is examined. The governing model of the problem is transformed into the vorticity-stream function formulation and numerically solved using a scheme based on the finite difference method. Impacts of numerous flow controlling parameters including the Hartmann, Strouhal, porosity, Casson fluid, and micropolar fluid parameters on the wall shear stress (WSS), axial velocity, and micro-rotation velocity are presented graphically and discussed. The WSS is found to increase with rising values of any of the Hartman, Casson fluid, and micropolar fluid parameters. The WSS decreases with rising values of the porosity parameter. The Hartman number is found to have a significant impact on the flow separation region, as well. The velocity profiles are parabolic at all the axial locations. At the constriction throat, the maximum value of the velocity is identified.

HEAT AND MASS TRANSFER ON UNSTEADY MHD FLOW THROUGH AN INFINITE OSCILLATING VERTICAL POROUS SURFACE

Analytical solutions of an unsteady magnetohydrodynamic (MHD) flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting, and Boussinesq fluid over a vertical oscillating plate embedded in a Darcian porous medium in the presence of a thermal radiation are presented. The fluid considered here is a gray, absorbing/emitting radiating, but nonscattering medium. At time t > 0, the plate temperature and concentration near the plate are raised linearly with time t. The dimensionless governing coupled unsteady boundary layer partial differential equations are solved by the Laplace transform technique. An increase in permeability parameter (K) is found to increase fluid velocities and shear stress in the regime. Also it was found that when the conduction-radiation parameter (R) increased, the fluid velocity and the temperature profiles decreased. Applications of the study are found in materials processing and solar energy collector systems.

Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

Bioconvection has shown significant promise for environmentally friendly, sustainable “green” fuel cell technologies. The improved design of such systems requires continuous refinements in biomathematical modeling in conjunction with laboratory and field testing. Motivated by exploring deeper the near-wall transport phenomena involved in bio-inspired fuel cells, in the present paper, we examine analytically and numerically the combined free-forced convective steady boundary layer flow from a solid vertical flat plate embedded in a Darcian porous medium containing gyrotactic microorganisms. Gyrotaxis is one of the many taxes exhibited in biological microscale transport, and other examples include magneto-taxis, photo-taxis, chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field, light, chemical concentration or gravity, respectively). The bioconvection fuel cell also contains diffusing oxygen species which mimics the cathodic behavior in a proton exchange membrane (PEM) system. The vertical wall is maintained at iso-solutal (constant oxygen volume fraction and motile microorganism density) and iso-thermal conditions. Wall values of these quantities are sustained at higher values than the ambient temperature and concentration of oxygen and biological microorganism species. Similarity transformations are applied to render the governing partial differential equations for mass, momentum, energy, oxygen species and microorganism species density into a system of ordinary differential equations. The emerging eight order nonlinear coupled, ordinary differential boundary value problem features several important dimensionless control parameters, namely Lewis number (Le), buoyancy ratio parameter i.e. ratio of oxygen species buoyancy force to thermal buoyancy force (Nr), bioconvection Rayleigh number (Rb), bioconvection Lewis number (Lb), bioconvection Péclet number (Pe) and the mixed convection parameter ([Formula: see text] spanning the entire range of free and forced convection. The transformed nonlinear system of equations with boundary conditions is solved numerically by a finite difference method with central differencing, tridiagonal matrix manipulation and an iterative procedure. Computations are validated with the symbolic Maple 14.0 software. The influence of buoyancy and bioconvection parameters on the dimensionless temperature, velocity, oxygen concentration and motile microorganism density distribution, Nusselt, Sherwood and gradient of motile microorganism density are studied. The work clearly shows the benefit of utilizing biological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems. In particular, the deployment of gyrotactic microorganisms is shown to stimulate improved transport characteristics in heat and momentum at the fuel cell wall.

Application of blade tip shroud brush seal to improve the aerodynamic performance of turbine stage

The blade tip shroud brush seal is applied to replace the labyrinth seal for the aerodynamic performance improvement of turbine stage. The leakage flow characteristics of the brush seal are numerically predicted by using the Reynolds-Averaged Navier–Stokes equations and non-linear Darcian porous medium model. The numerical leakage flow rate of the brush seal is in well agreement with the experimental data. The last and first long teeth of the labyrinth seal were designed to bristle pack named as the postposed and preposed brush seals based on the 1.5 turbine stage. The leakage flow rate and aerodynamic performance of the turbine stage with blade tip shroud labyrinth seal and brush seal are numerically investigated. The effect of the sealing clearance between bristle pack and tip shroud on the aerodynamic performance of turbine stage is conducted which ranged from 0 mm to 0.4 mm. The axial deflection of the bristle pack is analyzed with consideration of the aerodynamic forces and contact frictional force. The obtained results show that the leakage flow rate of the tip shroud brush seals with bristle tip 0.4 mm clearance which decreases by up to 18% in comparison with the labyrinth seal, and the aerodynamic efficiency increases by 0.6%. Compared to the tip labyrinth seal, tip shroud brush seals can decrease the relative deflection angle of exit flow. This flow behavior results in reducing the mixing loss between the tip leakage flow and mainstream. The similar axial deflection of the bristle pack for two kinds of brush seals is observed at the same sealing clearance. The deflection of the bristle pack under the function of the aerodynamic forces is protected by the backing plate. This work provides the theoretical basis and technical support for the brush seal application in the turbine industries.

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

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

Double diffusive effects on mixed convection Casson fluid flow past a wavy inclined plate in presence of Darcian porous medium

Abstract The aim of this research paper is to study the effect of thermal diffusion (Soret) on unsteady magnetohydrodynamic mixed convection flow through an accelerated vertical wavy plate embedded in a darcian porous medium. Fundamental coupled non-linear partial differential equations with fitting boundary conditions control the flow problem. Efficient, stable, and finite element technique providing excellent convergence and versatility in accepting coupled systems of ordinary and partial differential equations is used to obtain numerical solutions for these partial differential equations. Graphical results for velocity, temperature, and concentration fields are discussed and displayed. The effects of emerging parameters on the Skin-friction are arrived at using comprehensive parametric tests. Rate of heat and mass transfer coefficients are graphically represented and examined. The results match with a special case of previously published work. From the present analysis it is reported that the presence of angle of inclination sustains a retarding effect on velocity. The velocity decreases with increasing magnetic field parameter, while the Dufour number and Soret number increase with increasing the same and the concentration field decrease as the Schmidt number increases while the temperature field decreases with increasing Prandtl number and Dufour number.

Numerical Study for System of ODEs Obtained from MHD Flow Past a Permeable Flat Plate in a Darcian Porous Medium Using Laguerre Collocation Method

In this article, we introduce a numerical solution for the system of ODEs which governs the problem of magnetohydrodynamic boundary layer flow and heat transfer past a permeable flat plate which embedded in a porous medium by using an efficient Laguerre collocation method. The controlling parameters which affect the dimensionless velocity are the Darcy number, the Reynolds number and the magnetic number, whereas, the radiation parameter and Peclet number are the emerging parameters on the dimensionless temperature. The influence of these parameters on both the dimensionless velocity and the dimensionless temperature are analyzed graphically. The proposed method is based on replacement of the unknown function by a truncated series of the well-known Laguerre expansion of functions. An approximate formula of the integer derivative is introduced. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with Laguerre coefficients. Verification of the numerical Laguerre collocation method is tested after introducing the comparison with the previously published results.

NANOFLUID SLIP FLOW THROUGH POROUS MEDIUM WITH ELASTIC DEFORMATION AND UNIFORM HEAT SOURCE/SINK EFFECTS

The uniform heat source/sink effect on second-grade nanofluid flow over a stretching sheet embedded in Darcian porous medium is studied with elastic deformation. The partial slip, heat flux, and mass flux boundary conditions are considered. The magnetic field is applied in various directions. The nanofluid model is considered with viscoelasticity, Brownian motion and theromophosis mechanisms. Mathematical equations governing the problem are solved numerically using the fourth-order Runge-Kutta method with shooting iteration technique. The flow and heat transfer phenomena are analyzed through plots for various sets of physical parameters. It is found that the presence of elastic deformation and the uniform heat source increase the thickness of the nanofluid thermal and concentration boundary layers.