The flow of a Jeffrey fluid in a composite horizontal channel partially filled with a deformable porous material

The flow of a Jeffrey liquid in a composite deformable porous layer is examined. The Jeffrey model governs fluid flow in the free-flow zone, while the theory of mixtures describes the fluid flow in the deformable porous region. The governing equations are transformed to dimensionless by using appropriate nondimensional quantities. The velocity field is achieved in both the clear flow and deformable porous regions. The displacement expression in the porous zone is also established. The results are discussed for various substantial parameters in detail. It is scrutinized that the flow rate accelerates with a rise in the Jeffrey parameter ${\lambda }_1$. Also, it is perceived that the flow rate is less for a Newtonian liquid than the non-Newtonian Jeffrey liquid. The fluid momentum enhances by increasing the volume fraction of the fluid phase. It is found that the magnitude of skin friction at the clear flow region and porous region grows with an increase in the Jeffrey parameter ${\lambda }_1$. Furthermore, it is noticed that the wall shear stress is less for a Newtonian liquid when compared with non-Newtonian Jeffrey liquid both in the free-flow region as well as in the porous regions.     

Entropy analysis in MHD Couette flow of chemically reacting viscoelastic fluid past a deformable porous channel

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region.     

Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer

Stability analysis of thermal convection for a Jeffrey fluid with rotation in an anisotropic porous medium is examined utilizing a modified Jeffrey–Darcy model. The linear stability theory is applied to examine how the Jeffrey parameter, rotation parameter, and anisotropic parameters affect the convective motion. It is observed that the rotation and the anisotropic in the thermal diffusivity act to delay the start of Jeffery fluid convection, while the Jeffery parameter and the anisotropic in the permeability show a dual effect in the presence of rotation. The extent of the convection cell diminishes with rotation and Jeffery parameters, while it augments with the thermal anisotropy parameter. Also, some previous outcomes are regained as special cases of the current analysis.     

Hall and ion-slip effects on MHD free convection flow of rotating Jeffrey fluid over an infinite vertical porous surface

An attempt has been made to explore Hall and ion-slip effects on an unsteady magnetohydrodynamic rotating flow of an electrically conducting, viscous, incompressible, and optically thick radiating Jeffrey fluid past an impulsively vertical moving porous plate. Analytical solutions of the governing equations are obtained by Laplace transform technique. The analytical expressions for skin friction, Nusselt number, and Sherwood number are also evaluated. The velocity, temperature, and concentration distributions are displayed graphically in detail. From engineering point of view, the changes in skin friction, Nusselt number, and Sherwood number are observed with the computational results presented in a tabular manner. It is observed that the effects of rotation and Hall current tend to accelerate secondary velocity and decelerate primary velocity throughout the boundary layer region. Thermal and concentration buoyancy forces tend to accelerate both velocity components. Thermal radiation and thermal diffusion tend to enhance fluid temperature throughout the boundary layer region. Rotation and Jeffrey fluid parameters tend to enhance both stress components.     

Channel flow of a Jeffrey fluid in a porous space with entropy generation

The present investigation reveals the Poiseuille flow of an incompressible Jeffrey fluid involving two heated parallel plates. The nonlinear model is proposed by incorporating Brownian motion vis-a-vis, viscous dissipation, and suction/injection, which are also taken into consideration. However, numerical treatment is based on fourth-order Runge–Kutta shooting integration method and applied for the solution of the system of governing equation. As a novelty, the entropy analysis due to the flow irreversibility of the system is carried out, and also a computational result of the Bejan number is also elaborated. The impacts of various thermo-physical pertinent specifications such as velocity, temperature are examined thoroughly and interpreted through graphs.     

Chemical reaction impacts the unsteady MHD convective flow of an incompressible viscous fluid past an infinite vertical porous plate

We studied the radiation magnetohydrodynamic flow of an incompressible viscous electrically conducting fluid past an exponentially accelerated perpendicular surface under the influence of slip velocity in the revolving structure. A steady homogeneous magnetic strength is applied under the assumption of low magnetic Reynolds quantity. The ramped heat and time-altering concentration near the plate are taken into consideration. First-order consistent chemical reactions and thermal absorption were also studied. The Laplace transformation technique is used for the non-dimensional governing equations to get the closed-form solutions. Supporting these results, the phases for nondimensional shear stress, rate of thermal as well as accumulation transport are also found. Graphical profiles are represented to examine the impact of physical parameters on the important physical flow features. The computational quantities of shear stress and rate of thermal and mass transportation near the surface are tabulated with a variety of implanted parameters. The resulting velocity is growing with an increase in heat and solutal buoyancy forces, while revolution and slip parameters have reverse effects on this. The resulting velocity is falling due to an increase in the Hartmann quantity, while the penetrability parameters have the opposite impacts on this. The species concentration of fluid is reduced by an increase in Schmidt number and chemical reacting parameter.     

Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer

In this paper, the oscillatory flow of hydromagnetic couple stress fluid-saturated porous layer with inhomogeneous wall temperatures is studied. The flow is modeled using the modified Darcy equation. The fluid is subjected to a transverse magnetic field and the velocity slip at the lower plate is taken into deliberation. The governing coupled partial differential equations of the flow are transformed to coupled ordinary differential equations and are solved analytically. The impact of the physical parameters such as the Grashof number, Prandtl number, Darcy number, Hartmann number, and couple stress parameters on velocity profiles, temperature, rate of heat transfer, and skin friction are emphasized. The velocity field increased as either the Grashof number, the Darcy number, the suction/injection parameter, and Prandtl number increased nevertheless reverse growth can be seen by increasing the Hartmann number and the couple stress parameter. The temperature field in the channel increases with increasing the suction/injection parameter and Prandtl number but a conflicting development can be seen with increasing the oscillation amplitude. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate.     

Couette flow through a porous medium of a high prandtl number fluid with temperature-dependent viscosity

The velocity and temperature profiles for an impulsively started Couette flow have been derived for a fluid with a high and strongly temperature-dependent viscosity when the flow takes place through a porous medium. The steady as well as the transient state flows are discussed and the influence of the medium permeability is assessed. In the steady state the presence of the porous medium causes higher maximum temperatures only for sufficiently low permeabilities and in all cases significantly lower velocity profiles. The flow development times tend to be higher for the low permeabilities only for high Nahme numbers. For the transient state it is noticeable that, in all cases, the velocity develops much more rapidly than the temperature and that the presence of the porous medium accelerates this tendency. Finally the medium permeability produces skew temperature profiles and higher temperature time gradients at all times.     

Exploration of heat transfer effect in a magnetohydrodynamics flow of a micropolar fluid between a porous and a nonporous disk

An analysis is carried out for the flow characteristics of a conducting micropolar fluid. The fluid was passed in between two parallel disks of infinite radii. The novelty of the study is to consider one of the disks as porous and the other one as nonporous, and the external magnetic field is applied along the transverse direction of the flow. The flow phenomena for the polar fluid characterized by the magnetic effect in conjunction with the temperature equation reduce to a set of coupled nonlinear ordinary differential equations using the requisite transformations and nondimensionalization. An analytical approach such as the variation parameter method is employed to tackle the system efficiently. To emphasize the effect of various physical parameters contributing to the flow phenomena, that is, non-zero tangential slip, Reynolds number, Prandtl number, magnetic parameter, and material parameter on the flow profiles of axial and radial velocities, the microrotation and temperature profiles are presented graphically. To validate the simulated results, a comparison with established results is made, and it is concluded that both are in good correlation.     

Soret‐Dufour effects in electroosmotic biorheological flow of Jeffrey fluid

The Soret and Dufour cross‐diffusion on the electrokinetic flow of Jeffrey fluid augmented with peristalsis have been presented. The fundamental equations are employed to predict the mass distribution in the two‐dimensional asymmetric electroosmotic channel. Reliable approximations such as low Peclet, low Reynolds, and large wavelength are utilized. The analytical solutions of the concentration, temperature, velocity, and stream function are obtained. To predict the effects of prominent parameters such as fluid parameter, electroosmotic parameter, Brinkman, Soret, and Schmidt number graphs are plotted. The phenomenon of trapping is also discussed to observe the behavior on streamlines. It is observed that the electroosmotic parameter enhances the temperature profile. With the increase in Jeffrey fluid parameter, the Nusselt number is decreased. Furthermore, the concentration is decreased with the elevation in Soret and Schmidt numbers. The current study can help reduce the conversion stages necessary for the integration of the low voltage output in an electrokinetic biomass process.     

The flow of non-Newtonian fluid in an inclined channel through variable permeability

A non-Newtonian fluid's Poiseuille flow in a porous medium with variable inclination and permeability is investigated. Let us assume for the sake of simplification that permeability varies as a quadratic parabolic function form. The porous medium is used by the Brinkman methodology to control the flow. The equations for velocity distribution and mass flow that result from this are evaluated using different input values. This problem describes the effect of inclination, Jeffrey parameter, and variable permeability on the classical Poiseuille flow between parallel plates. This problem can also be treated as an extension of the work of Hamdan and Kamel for non-Newtonian fluid flow in an inclined channel. Also, the effects of these variables on the variation of mass flux with Jeffrey parameter λ₁ is analyzed through graphs, and the skin friction coefficient is analyzed through table values. It is observed that the maximum permeability of the porous medium affects both the mass flow rate and the velocity, which increase with rising λ₁ and decrease with rising H_a, respectively.     

Features of Cattaneo‐Christov heat flux model for Stagnation point flow of a Jeffrey fluid impinging over a stretching sheet: A numerical study

The present work focuses on a two‐dimensional steady incompressible stagnation point flow of a Jeffery fluid over a stretching sheet. The Cattaneo‐Christov heat flux model is incorporated into this study. Simulation is conducted via the Runge‐Kutta fourth‐order cum shooting method for the transformed system of nonlinear equations. The influence of the governing parameters on the dimensionless velocity, temperature, skin friction, streamlines, and isotherms is incorporated. A significant outcome of the current investigation is that an increase in the relaxation time parameter uplifts temperature; however, a gradual decrease is observed in the velocity field. Another important outcome of the present analysis is that the momentum boundary layer augments due to an increase in the Deborah number; however, a decrease is observed in the temperature. Furthermore, it is also observed that the skin friction coefficient escalates with an increase in the relaxation time parameter for the assisting flow, but a reverse trend is observed for the opposing flow.     

On MHD and slip flow over a rotating porous disk with variable properties

The steady laminar magnetohydrodynamics (MHD) flow of a viscous Newtonian and electrically conducting fluid over a rotating disk with slip boundary condition is investigated taken into account the variable fluid properties (density, (ρ), viscosity, (μ) and thermal conductivity, (κ)). These fluid properties are taken to be dependent on temperature. The governing equations, which are partial and coupled, are transformed to ordinary ones by utilizing the similarity variables introduced by von Karman and the resulting equation system is solved numerically by using a shooting method. The resulting velocity and temperature distributions are shown graphically for different value of parameters entering into the problem. The numerical values of the radial and tangential skin-friction coefficients and the rate of heat transfer coefficient are shown in tabular form.     

Viscoelastic effects on the oscillatory flow in a fluid-saturated porous layer

The oscillating flow of the viscoelastic fluid-saturated porous layer has been useful in many areas, including the petroleum, chemical, and bioengineering industries. It is studied using the modified Darcy-Oldroyd-B model in this article. The exact solution is obtained utilizing a simpler and more reasonable method. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From the analysis, it was found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Further, velocity, temperature, shear stress, and the rate of heat transfer are exponential solutions that are obtained and analyzed for different values of known physical parameters. Finally, we recognize that the relaxation and retardation parameters in this model act in the opposite manner.     

Impact of thermal diffusion and chemical reaction on oscillatory MHD convective flow of a viscoelastic fluid through a porous medium in a slip flow regime

The purpose of the current investigation is to analyze the influence of thermal diffusion on magnetohydrodynamic viscoelastic fluid flow with concurrent heat and mass transfer near an oscillating porous plate in a slip flow Regime under the influence of a uniform transverse magnetic field. The uniqueness of the present study is to examine the effects of viscoelastic property (Walters B' model) on the flow and heat transfer phenomena when a transverse magnetic field and time-dependent fluctuating suction at the boundary surface are present in a porous medium with a uniform porous matrix. A regular perturbation technique is used to solve the governing equations for small elastic parameters. Graphical representations are used to show how different parameters affect skin friction, temperature, concentration, and velocity. It is observed that concentration distribution as well as the coefficient of friction is enhanced due to the thermal diffusion effect. It is noticed that the visco-elastic parameters reduce the velocity of the fluid. In addition, chemical reactions and suction factors cause the flow field's temperature to drop. Furthermore, the fluid concentration drops under the chemical reaction effect.     

Heat and mass transfer effects on MHD flow of a couple‐stress fluid in a horizontal wavy channel with viscous dissipation and porous medium

This paper looks at heat and mass transfer effects on an unsteady MHD flow of a couple‐stress fluid in a horizontal wavy porous space with travelling thermal waves in the presence of a heat source and viscous dissipation. Initially the temperatures of the walls are maintained at different constant temperatures. The analytical expressions for velocity, temperature, and concentration field are obtained by the regular perturbation technique. The results are presented graphically for various values of emerging dimensionless parameters of the problem and are discussed to show interesting aspects of the solution. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21040 PACS: 44.15.+a, 44.30.+f, 44.27.nd, 47.50.Cd     

Magnetohydrodynamic chemically reactive viscoelastic fluid flow through an inclined porous layer

Analysis of a time-independent magnetohydrodynamic viscoelastic fluid flow in a deformable inclined porous layer with first-order chemical reaction has been investigated. Walters' fluid model has been used to study viscoelastic fluid. The walls are suctioned/injected at a constant rate. The expression representing the solution for solid displacement, fluid velocity, temperature, and concentration distribution is obtained. The effect of applicable parameters on solid displacement, fluid velocity, temperature, and concentration are discussed graphically, while skin friction, heat transfer, and mass transfer are revealed in a tabular structure. It is noticed that solid displacement, fluid velocity, and temperature profiles decrease when the viscoelastic parameter increase. Solid displacement enhances and the velocity of the fluid reduces owing to the influence of increasing drag parameter, whereas the reverse effect is seen for the volume fraction parameter. Nusselt number at the walls shows the opposite behavior for the viscoelastic parameter and Eckert number. Sherwood number at the walls shows opposite behavior for Reynolds number, Schmidt number, and radiation parameter. Also, the entropy generation number rises as a result of the influence of viscoelasticity and Eckert number.     

Transient free convective flow through a vertical cylinder filled with a porous material

This article aims to explore the impressive impact of emerging parameters on transient fully evolved free convective flow inside a vertical cylinder containing a porous material. The mathematical formulation of the model related to the considered physical circumstance is presented under compatible boundary conditions. Closed‐form solutions are received for the velocity field, the temperature distribution, mass flux, skin friction, and the Nusselt number in terms of Bessel functions and modified Bessel functions of the first kind. Impressive effects of parameters such as the Darcy number $Da$, Prandtl number $\text{Pr}$, viscosity ratio $M$, and also time $t$ on both the velocity and temperature distribution have been explored employing graphs and tables. It is irradiated by analysis that flow erection, heat transfer rate, skin friction, and mass flux are admirably impacted by the Prandtl number, the Darcy number, viscosity ratio parameter, and time. It is found that both the velocity and temperature field profiles rise with the rising value of time and ultimately attain their steady state. Moreover, the Prandtl number and the viscosity ratio parameter reduce the velocity profiles, while the reverse phenomenon occurs with the Darcy number.