Increase In Porosity Parameter Research Articles

Dispersion of solute in a packed cylindrical tube with wall reaction

Abstract The study aims to investigate the transport of solute in a packed cylindrical tube, analytically. At the wall, the solute experiences an irreversible chemical reaction of order-one.The combined action of moments method with integral transform technique has been introduced to employ the Gill’s generalized dispersion model. The main goal is to investigate a full time evaluation of various transport coefficients in different superficial flow through porous media together with wall reaction. This study provides a perspective on how porous media influences the migration of solutes in the presence of wall reactions. Exchange coefficient is shown to be solely dependent on wall absorption. In the presence of porosity, wall absorption causes an increase in the advection coefficient's magnitudes; however, the dispersion coefficient exhibits the reverse behavior. Fluid velocity is always suppressed by damping factor, and thus advection and dispersion coefficients both controlled by damping factor. Increase in porosity parameter will reduces the axial concentration distribution. This work could have applications in areas such as groundwater flow, contaminant transport, or chemical reactions within porous materials.

Neural artificial networking for a nonlinear darcy–forchheimer chemically reactive flow: Levenberg marquardt analysis

In this paper, the 3D Darcy–Forchheimer flow model (TDDF-FM) is discussed by utilizing the artificial intelligence-based backpropagated neural networks with the algorithm of Levenberg–Marquardt (BNN-ALM) along with the convective conditions. The effects of Brownian diffusion and thermophoresis are also examined. The governing partial differential equations are transformed into a system of ODEs. Lobatto IIIA method is used to interpret the reference dataset of BNN-ALM for different scenarios of TDDF-FM by variation of porosity parameter, Forchheimer parameter, ratio parameter, Prandtl number, Biot number, Brownian motion parameter, Schmidt number, strength parameter of homogeneous reaction and thermophoresis parameter. The solutions are computed for the designed TDDF-FM by testing, training and validation processes of BNN-ALM. The performance analysis of the designed BNN-ALM is validated by histogram analysis, regression studies and the results of mean square error (MSE). Graphs are presented for temperature profile, concentration profile and concentration rate profile. The increasing values of porosity parameter, Forchheimer parameter and Biot number enhance the temperature distribution, whereas the temperature profile shows a decreasing behavior with the increase in Prandtl number and ratio parameter. The concentration profile increases with the increase in porosity parameter, Forchheimer parameter and thermophoresis parameter and it decreases with the increasing behavior of Brownian motion parameter, ratio parameter and Schmidt number. The concentration rate profile decreases with the increase in porosity parameter, Forchheimer parameter and strength parameter of homogeneous reaction and it increases with the ratio parameter. The best performance values for different cases of scenarios are 1.42E−08, 1.70E−08, 1.78E−08, 1.61E−08, 2.43E−08, 1.05E−08, 1.30E−08, 1.59E−08 and 2.31E−08, attained at 215, 186, 178, 99, 125, 213, 187, 190 and 191 epochs. The values for the Gradient factor are 9.93E−08, 9.86E−08, 9.99E−08, 2.97E−07, 1.23E−07, 9.94E−08, 9.94E−08, 9.87E−08 and 9.94E−08, where the value of regression is [Formula: see text] for the training, testing and validation data.

Cattaneo-Christov heat and mass flux models on time-dependent swirling flow through oscillatory rotating disk

This analysis emphasis on the time invariant impressions of Cattaneo-Christov heat and mass flux theories are implemented to overcome the initial instant disturbances throughout whole medium. The motion of three-dimensional, incompressible, magnetized viscous fluid flow induced by the oscillatory disk. Porous media is used to saturate the rotating disk. Similarity transformations are accomplished to normalize the flow problem. Successive over Relaxation (SOR) technique is implemented to discuss the new findings of normalized non-linear resulting system. It is perceived that increase in porosity parameter results in decrease of oscillatory velocity profiles. The characterization of porous media is useful in geothermal and petroleum reservoirs. Time varying oscillatory curves for concentration and temperature decay for varying concentration and thermal relaxation times parameters, respectively. Moreover, an interesting nature of phase-log shift is also observed in temperature and concentration profiles. Three-dimensional flow features are also labeled for velocity, temperature and concentration fields.

Numerical solution for Sisko nanofluid flow through stretching surface in a Darcy–Forchheimer porous medium with thermal radiation

AbstractThe heat transfer assessments in a Sisko nanofluid flow over a stretching surface in a Darcy–Forchheimer porous medium with heat generation and thermal radiation are studied. The numerical analysis technique is used to assess the governing nonlinear equations of the model. The influence of Forchheimer number, porosity, heat generation, radiation, and material parameters is examined. The outlines of Nusselt number and skin friction coefficient corresponding to pertinent parameters are revealed. The comparison of Nusselt number outlines of working fluid and Newtonian fluid is depicted. From the analysis, it has been examined that with the increase in Forchheimer number and material parameter values, heat transfer function decreases, whereas heat transfer characteristics of Sisko nanofluid increase with heat generation and material parameters. Moreover, working fluid velocity outlines depreciate when there is an increase in porosity parameter for both shear‐thinning and shear‐thickening. The comparison of this study with previous research has been conducted.

Marangoni convective flow of hybrid nanofluid (MnZnFe2O4-NiZnFe2O4-H2O) with Darcy Forchheimer medium

This communication discusses the Marangoni convection of hybrid nanofluid. Hybrid nanofluid is made up of two nanoparticles ( M n Z i F e 2 O 4 - N i Z n F e 2 O 4 ) and one base fluid ( H 2 O ) . Darcy Forchheimer porous medium effect is inserted in momentum equation. Entropy generation in the flow due to heat transfer irreversibility, mass transfer irreversibility and viscous dissipation irreversibility is calculated and examined against pertinent parameters. Activation energy effect is applied in concentration equation. Bejan number effect is calculated to examine that which irreversibility factor is dominant. Transformations are applied to form the required governing equations from PDE’s. Effect of pertinent parameters on velocity, concentration, skin friction, temperature, entropy generation, Nusselt number and Bejan number are studied graphically. Velocity of the fluid is decreasing due to increase in porosity parameter, Forchheimer number and Marangoni ratio parameter. Temperature rises for Eckert number and nanoparticles volume fraction of both nanoparticles. Concentration rises for activation energy parameter and reduces for chemical reaction parameter. Entropy generation increases for Marangoni ratio parameter, diffusion parameter and Brinkman number.

Thermal drift and force convection analysis of nanofluid due to partially heated triangular fins in a porous circular enclosure

The main emphasis of this article is to analyze the simultaneous effects of thermal drift and force convection on water based single wall carbon nanotubes (SWCNTs) in a porous circular duct. Equilateral triangular fins which are enclosed in a circular cavity having vertical and horizontal side of triangular fins are moving. Internal heat generation/absorption is considered to determine the thermal drift. Impact of inclined Magnetohydrodynamics (MHD) has been introduced. The governed equations are solved through weighted residue method of Finite Element Method (FEM). Effect of various parameters, that is: Reynolds number, nanoparticles, porous medium and absorption/generation on flow patterns and heat transfer were worked out. The heat transfer rate at different heated fins has been investigated for various parameters. This study carries out significant impact of Q on temperature profile and Local Nusselt. Local Nusselt number against heated walls decreases with increase of porosity parameter and increases in case of heat generation. Streamlines decreases with increase of quantity of solid volume fraction in enclosure. Significant effect of Re observed in transformation of heat in circular duct.

Thermal Radiation Effects on MHD Unsteady Couette Flow Heat and Mass Transfer Free Convective in Vertical Channels due to Ramped and Isothermal Temperature

Numerical investigations were carried out to study thermal radiation effects on magneto-hydrodynamics (MHD) unsteady Couette flow heat mass transfer free-convective in vertical channels due to ramped and isothermal temperature. The governing coupled non-linear partial differential equations of the flow were transformed into non-dimensional form using suitable dimensional quantities. Finite element method (FEM) was employed to find numerical solution of the dimensionless governing coupled boundary layer partial differential equations. The expressions of velocity, temperature, concentration, skin friction, Nusselt number as well as Sherwood number have been obtained and discussed using line graph. From the outcome of the result it was revealed that, increase of porosity parameter K, ratio of mass transfer parameter N, Time parameter t, Eckert number Ec enhances the velocity and temperature while reverse is the case with the with increase of Magnetic parameter M, Radiation parameter tern R and Prandtl number Pr. At y = 0, the fluid skin friction gets enlarged with increase in porosity parameter K, Nusselt number gets increased with increase of Prandtl number Pr and Sherwood number gets boosted with increase of Eckert number Ec. Similarly, at y = 1 skin friction gets enhanced with increase of porosity parameter K, Nusselt number diminishes with increase of Prandtl number Pr and Sherwood number gets enlarged with increase of Eckert number Ec.

A comprehensive study for mechanical behavior of functionally graded porous nanobeams resting on elastic foundation

In this paper, a comprehensive study is presented for mechanical analysis of functionally graded porous (FGP) nanobeams resting on an elastic foundation. The nanobeam is modeled according to different beam theories along with nonlocal strain gradient theory and Gurtin–Murdoch surface elasticity theory. Using Hamilton’s principle, the set of governing equations are derived, and exact solutions are presented using Navier’s method for the static bending, mechanical buckling and free vibration analyses of simply supported FGP nanobeams. The effects of various parameters on static deflection, critical buckling load and fundamental natural frequency of FGP nanobeams are studied. It is shown that for all types of porosity distribution patterns, an increase in porosity parameter leads to an increase in static deflection, and a decrease in critical buckling load and effect of porosity parameter on fundamental natural frequency is dependent on the porosity distribution pattern. Numerical results confirm that tensional residual surface stress decreases static deflection and increases both critical buckling load and fundamental natural frequency, but compressive residual surface stress has opposite effects.

Unsteady MHD Flow of Nanofluid with Variable Properties over a Stretching Sheet in the Presence of Thermal Radiation and Chemical Reaction

The unsteady magnetohydrodynamics (MHD) flow of nanofluid with variable fluid properties over an inclined stretching sheet in the presence of thermal radiation and chemical reaction is studied taking into account the effect of variable fluid properties in thermal conductivity and diffusion coefficient. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation. The numerical solutions of the problem are obtained by using the fourth order Runge-Kutta method in line with the shooting technique. It is found that the increase in both thermal conductivity and radiative heat flux decreases the heat transfer rate but increases the skin friction and mass transfer rates. It is further observed that the increase in porosity parameter and magnetic field reduces the skin friction, heat, and mass transfer rates.

Numerical treatment for fluidic system of activation energy with non-linear mixed convective and radiative flow of magneto nanomaterials with Navier’s velocity slip

A novel application of Lobatto IIIA computing solver is presented for the solution of nanofluidic Buongiorno model in the porous space. Incompressible electrically conducting fluid mixed with nanomaterial is considered. Flow expression is modelled via nonlinear mixed convection and Navier’s slip condition. Activation energy, Joule heating and non-liner thermal radiation characterise the heat/mass transport. The governing PDEs of the considered problem are transformed into an equivalent system of ODEs using similarity variables. The resulting system is solved numerically by exploiting the strength of Lobatto IIIA computing solver. Numerical and graphical illustrations are utilized to interpret the behaviour of sundry physical parameters on velocity, concentration and temperature profiles. Skin friction, temperature and concentration gradients for different scenarios of embedding variables are tabulated and analysed. Furthermore, numerical data for mesh points, error analysis, ODEs and boundary conditions evaluation are also displayed. Our computed analysis indicates that velocity of nanofluid increases for large value of slip parameter while it decreases with the increase of porosity parameter. In addition, concentration distribution is decaying and increasing functions of chemical reaction and activation energy parameters respectively.

Nonlinear bending analysis of porous FG thick annular/circular nanoplate based on modified couple stress and two-variable shear deformation theory using GDQM

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

Thermal performance analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation

In this study, thermal performance analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation is carried out using Galerkin’s method of weighted residual. The developed symbolic heat transfer models are used to investigate the effects of various parameters on the thermal performance of the porous fin. It is found that increase in porosity parameter, Nusselt, Darcy and Rayleigh numbers and the thickness-length ratio of the fin increase the rate of heat transfer from the base of the fin and consequently improve the efficiency of the fin. Also, decreasing thermal conductivity parameter results in an increase in the rate of heat transfer from the base of the fin. However, an optimum value is reached beyond which further increase in porosity, Nusselt, Darcy and Rayleigh numbers, thermal conductivity ratio and thickness-length ratio has no significant influence on the rate of heat transfer. For the purpose of verification of the results, exact analytical solutions are developed. The results of the Galerkin’s method for the second-order approximation function are found to be in excellent agreements with the results of the exact analytical solutions and also with that of the numerical methods and homotopy perturbation method.

MHD flow of carbon in micropolar nanofluid with convective heat transfer in the rotating frame

Abstract This article addresses the MHD flow of micropolar carbon-water nanofluid in the presence of rotating frame. Two types of carbon nanotubes (single and multi-walls) are homogeneously dispersed in the base fluid (water). Convective heat transfer phenomenon is also retained in this study. With the help of the similarity transformation, a mathematical model is developed by transforming the partial differential equation into ordinary differential equation. Further it is then solved analytically by using homotopy analysis method HAM. The impact of emerging parameters, skin friction coefficient and Nusselt number are also discussed in detail. It is observed that temperature profile decreases with the increase in porosity parameter and nanoparticle volume fraction while enhances for higher values of Biot number. Further Micro rotation profile increases with the increase in coupling parameter N 1 and Reynolds number R while decreases with increase in Biot number Bi and volume fraction ϕ .

Numerical/Laplace transform analysis for MHD radiating heat/mass transport in a Darcian porous regime bounded by an oscillating vertical surface

Analytical and numerical solutions of a non-linear MHD flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Boussinesq’s fluid over a vertical oscillating plate embedded in a Darcian porous medium in the presence of thermal radiation effect have been presented. The fluid considered here is gray, absorbing/emitting radiating, but non-scattering medium. At time t>0, the plate temperature and concentration near the plate raised linearly with time t. The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient, accurate, extensively validated and unconditionally stable finite difference scheme of the Crank–Nicolson type as well as by the Laplace Transform technique. An increase in porosity parameter (K) is found to depress fluid velocities and shear stress in the regime. Also it has been found that, when the conduction-radiation (R) increased, the fluid velocity and the temperature profiles decreased. Applications of the study arise in materials processing and solar energy collector systems.

Analytical and Numerical Study for MHD Radiating Flow over an Infinite Vertical Surface Bounded by a Porous Medium in Presence of Chemical Reaction

The study of non-linear MHD flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Newtonian fluid over a vertical oscillating porous plate embedded in a porous medium in presence of homogeneous chemical reaction of first order and thermal radiation effects have been analyzed. The fluid considered here is a gray, absorbing/emitting radiation, but a non-scattering medium. At time , the plate temperature and concentration levels near the plate raised linearly with time . The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank-Nicolson type as well as by the Laplace Transform technique. An increase in porosity parameter is found to depress the fluid velocities and shear stress in the regime. Also it has been found that, when the conduction-radiation increased, the fluid velocities as well as temperature profiles were decreased. It has been found that, when the chemical reaction parameter increased, the fluid velocities as well as concentration profiles were decreased. Applications of the study arise in materials processing and solar energy collector systems.

Oscillatory flow due to eccentrically rotating porous disk and a fluid at infinity embedded in a porous medium

An oscillatory flow due to non-coaxial rotations of an oscillating porous disk and a fluid at infinity rotating about an axis parallel to the axis of rotation of the disk through a fixed point has been investigated. An analytical solution of the unsteady Navier-Stokes equations is obtained for three cases when the frequency parameter is less than, equal to or greater than the rotation parameter. The influences of the physical parameters acting on the flow are explained with the help of the figures. It is found that the depth of the penetration or the wave length of the layers decreases with an increase in porosity parameter.

Unsteady Couette Flow through a Porous Medium in a Rotating System

An investigation has been made on an unsteady Couette flow of a viscous incompressible fluid through a porous me- dium in a rotating system. The solution of the governing equations has been obtained by the use of Laplace transform technique. It is found that the primary velocity decreases and the magnitude of the secondary velocity increases with an increase in rotation parameter. The fluid velocity components are decelerated by an increase of Reynolds number. An increase in porosity parameter leads to increase the primary velocity and the magnitude of the secondary velocity. It is also found that the solution for small time converges more rapidly than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of rotation parameter and Reynolds number. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the boundary layer increases with an increase in porosity parameter.

Hydrodynamic Flow between Two Non-Coincident Rotating Disks Embedded in Porous Media

Hydrodynamic viscous incompressible fluid flow through a porous medium between two disks rotating with same angular velocity about two non-coincident axes has been studied. An exact solution of the govern-ing equations has been obtained in a closed form. It is found that the primary velocity decreases and the sec-ondary velocity increases with increase in porosity parameter to the left of the z-axis and the result is re-versed to the right of the z-axis. It is also found that the torque on the disks increases with increase in either rotation parameter or porosity parameter. For large rotation, there exist a thin boundary layer near the disks and the thickness of this boundary layer decreases with increase in porosity parameter.

UNSTEADY FLOW DUE TO NON-COAXIAL ROTATION OF A POROUS DISK AND A FLUID AT INFINITY THROUGH POROUS MEDIUM

An exact solution of the unsteady hydrodynamic flow in a porous medium due to non-coaxial rotations of a porous disk and a fluid at infinity has been obtained. An analytical solution of the problem is obtained at small and large times by the Laplace transform method. It is found that the primary velocity decreases while the secondary velocity increases with the increase in porosity parameter σ. It is also found that the porosity takes more time to reach the steady state than that in the case of no porosity.