Influence of ramped pressure gradient on transient flow formation in a horizontal porous channel

The transient flow formation in a horizontal porous channel assuming a ramped pressure gradient is presented. The equation governing the flow is modeled into a partial differential equation (PDE) which is solved by employing the Laplace transformation technique to transform the PDE to an ordinary differential equation (ODE). The obtained ODE is solved by employing the method of undetermined coefficients to obtain the velocity profile in the Laplace domain. The Riemann sum approximation technique is then adopted to change the obtained solution from the Laplace domain into the time domain. For accuracy checks, the numerical results of the obtained equation are reckoned with previously published work, and an excellent agreement is found. For a clearer understanding of the impact of various flow parameters entering the solutions obtained, graphical and tabular representations are offered using MATLAB software. We noticed that the velocity is slower with ramped pressure gradient compared to a constant pressure gradient. This is because the motion of the fluid occurs gradually with ramped pressure gradient.     

The effects of thermal radiation on unsteady MHD free convective flow through the porous medium between two vertical plates with Hall effects

The effects of thermal radiation and Hall current on magnetohydrodynamic free convection three-dimensional flow in a vertical channel filled with a porous medium have been studied. We consider an incompressible viscous and electrically conducting incompressible viscous fluid in a parallel plate channel bounded by a loosely packed porous medium. The fluid is driven by a uniform pressure gradient parallel to the channel plates, and the entire flow field is subjected to a uniform inclined magnetic field of strength inclined at an angle of inclination $\alpha$ with the normal to the boundaries in the transverse xy-plane. The temperature of one of the plates varies periodically, and the temperature difference between the plates is high enough to induce radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, the temperature field, and the rate of heat transfer in terms of their amplitude and phase angles are shown graphically.     

Integral transform analysis of MHD flow and heat transfer in parallel-plates channels

A hybrid solution through the so-called Generalized Integral Transform Technique (GITT) is obtained for the MHD flow and heat transfer of a Newtonian fluid in parallel-plates channels. A simple mathematical formulation for the problem is adopted, which evidences both the transient regime flow sustainable only by a constant pressure gradient; and the steady state situation that considers both a constant pressure gradient and a movement of the upper plate, as well as the action of an inflow and outflow perpendicular to the porous plates. Results for the velocity and temperature fields are computed within the governing parameters, namely, pressure gradient, suction velocity, upper plate velocity and Hartmann numbers, for typical situations. A convergence analysis is also performed showing the consistency of the results. In addition, the present results are confronted with those previously reported ones in the literature showing excellent agreements.     

Hall effects on magnetohydrodynamic rotating flow through porous medium in a parallel plate channel with various oscillations of pressure gradient

We explored the unsteady flow of an incompressible electrically conducting viscous fluid in a gyratory porous medium with a changeable pressure gradient by taking Hall currents into account. The governing equations are then solved analytically with the help of the Laplace transforms methodology. It is regarded as three dissimilar cases, namely, an impulsive change, cosine as well as sine oscillations of the pressure gradient. The physical significances of different dimensionless parameters on velocity distributions are explored analytically and computationally. It is observed that a thin boundary layer is formed near the plate of the channel and the thicknesses of the layer increase with the increase in either the Hall parameter or Reynolds number while it decreases with an increase in Hartmann number. It is interesting to note that the rotation and Lorentz forces are having noteworthy effects on velocity profiles with pressure gradient and Hall currents.     

Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.     

Unsteady couette flow and heat transfer in a dusty gas

Unsteady flow of a dusty fluid, filling the gap between two infinite parallel plates kept at arbitrary temperatures, has been considered. The flow is induced by the impulsive start of one of the plates. The number density of the particles has been considered to be uniform throughout the motion and the solution for any time has been obtained by using Laplace transform followed by its numerical inversion. It has been observed that initially there is oscillation in both the fluid velocity and temperature distribution. Also the particles slip on the moving plate at the initial stage. Further Nusselt number increases with the increase of the concentration parameter.     

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.     

Dispersion in composite porous medium with homogeneous and heterogeneous chemical reactions

The effect of homogeneous and heterogeneous reactions on the dispersion of a solute in a composite porous medium between two parallel plates is studied. The solution approach suggested by Taylor [ 2 ] is generalized for the present model. The Brinkman model is used to define the flow through the porous medium. The fluids in both the regions of the parallel‐plate channel are incompressible and transport properties are assumed to be constant. The closed‐form solutions are obtained in both the regions of the channel. The results are tabulated for various values of viscosity ratio, pressure gradient, and porous parameter on the volumetric flow rate and the effective Taylor dispersion coefficient. It is found that for a homogeneous chemical reaction, the effective Taylor dispersion coefficient decreases as the reaction rate parameter and porous parameter increase. The validity of the results obtained for a composite porous medium is compared with the available porous medium results for a one‐fluid model and the values tallied for the small values of porous parameter. Also a two‐fluid model in the absence of a porous matrix is compared with the available one‐fluid model and good agreement is found. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20364     

Free Convective Flow in an Open‐Ended Vertical Porous Wavy Channel with a Perfectly Conductive Thin Baffle

The problem of steady two‐dimensional free convective flow of a Walters fluid (model B ′) in a porous medium between a long vertical wavy wall and parallel flat wall in the presence of a heat source is discussed. The channel is divided into two passages by means of a thin, perfectly conductive plane baffle and each stream will have its own pressure gradient and hence the velocity will be individual in each stream. The governing equations of the fluid and the heat transfer have been solved subject to the relevant boundary conditions by assuming that the solution consists of two parts: a mean part and disturbance or perturbed part. Exact solutions are obtained for the mean part and the perturbed part is solved using long wave approximation. Results are presented graphically for the distribution of velocity and temperature fields for varying physical parameters such as Grashof number, wall temperature ratio, porous parameter, heat source/sink parameter, product of non‐dimensional wave number, and space‐coordinate and viscoelastic parameter at different positions of the baffle. The relevant flow and heat transfer characteristics, namely, skin friction and the rate of heat transfer at both walls, has been discussed in detail. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21118     

Fractal analysis of Herschel–Bulkley fluid flow in porous media

The Herschel–Bulkley (HB) fluid is the representative fluid which may be reduced to the power-law fluid, Bingham and Newtonian fluids in appropriate conditions. In this paper, fractal models for velocity and the starting pressure gradient for HB fluid in porous media are derived based on fractal characteristics of porous media and capillary model. The proposed models are expressed as a function of fractal dimensions, porosity, maximum pore size and representative length of porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of HB fluid to the structural parameters of porous media. The variation trends of fractal velocity and starting pressure gradient versus different impact factors are shown, and the analytical expressions reveal the physical principles for flow velocity and starting pressure gradient in porous media.     

Impact of the electromagnetic flow of an MHD Casson fluid over an oscillating porous plate

This study deals with the effect of electric force and magnetohydrodynamics (MHD) of the transient state on natural convection flow past an oscillating vertical plate. In addition to this, thermal radiation and porous media are also examined in the Casson fluid flow. The Poisson-Boltzmann equation is employed to show the electric potential character within the fluid region, which is put into a linear form by the implementation of Debye–Hückel linearization. It is possible to compute the precise solution to the governing equations using the Laplace transform approach. The expression of fluid velocity, fluid concentration, and temperature are exposed graphically, and numerical results for Nusselt and Sherwood numbers are also derived for vital pertinent flow constraints. Increasing electroosmosis parameters strongly boosts fluid velocity. The nonnegative values of the Helmholtz–Smoluchowski velocity highly induce the axial velocity and the negative value decelerates. With increasing radiation strength and Prandtl number, the fluid's temperature distribution diminishes. These more intricate electrokinetic rheological flows associated with electroosmotic separators, such as biomedical absorbers, are illuminated by these models.     

Two-dimensional Darcy–Forchheimer flow of a dusty hybrid nanofluid over a stretching sheet with viscous dissipation

The main objective of the present examination is to design a stable mathematical model of a two-phase dusty hybrid nanofluid flow over a stretching sheet with heat transfer in a porous medium, and the Darcy–Forchheimer flow is taken into account with viscous dissipation and melting effect. The equations of motion are reduced to nonlinear ordinary differential equations by considering suitable similarity variables. These dimensionless expressions are solved by a well-known numerical technique known as Runge–Kutta–Fehlberg fourth–fifth order method. The behavioral study and analysis of the velocity and thermal profile in dual phases (fluid phase and dust phase) for diverse values of parameters are estimated using graphs and tables. The result outcome reveals that the velocity gradient declines in the fluid phase and increases in the dust phase for a rise in values of the velocity interaction parameter. Also, the velocity gradients of the both phases diminish for increasing values of the porosity parameter. Furthermore, it is determined that the increase in the value of melting parameter leads to a decline in the thermal gradient of both phases.     

Influence of relative motion of magnetic field on time‐dependent MHD natural convection flow

The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature‐dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well‐known Laplace transform. The time‐domain solution is obtained using the Riemann‐sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.     

Free convective flow of heat generating/absorbing fluid between vertical porous plates with periodic heat input

This study investigates the free convective flow of heat generating/absorbing fluid between vertical parallel porous plates due to periodic heating of the porous plates. The analysis is performed by considering fully developed flow and steady-periodic regime. The momentum and energy equations, which arise from the definition of velocity and temperature, are written in dimensionless form. Separating the temperature and velocity fields into steady and periodic parts, the resulting second order differential equations are solved to obtain the expressions for velocity, temperature, skin friction and the rate of heat transfer. The effects of various flow parameters such as the suction/injection (s), heat source/sink (δ), Strouhal (St) and Prandtl (Pr) numbers on the skin friction coefficient, rate of heat transfer, velocity and temperature profiles are discussed with the aid of line graphs and contour maps.     

Hall and ion-slip effects on steady MHD free convective flow through a porous medium in a vertical microchannel

We have considered the steady fully developed magnetohydrodynamic free convection flow through a porous medium in a microchannel bounded by two infinite vertical parallel plates due to asymmetric heating of plates taking Hall and ion-slip effects into account. Effects of velocity slip and temperature jump have been considered on the microchannel surfaces, and the exact solutions have been obtained for momentum and energy equations under relevant boundary conditions. The influence of governing parameters on flow formation is discussed with the aid of graphs. The significant result from the study is that an increase in the value of rarefaction parameter leads to enhancement in volume flow rate. Furthermore, it is evident that the volume flow rate is found to be an increasing function of the Hall current parameter.     

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

The present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first-order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first-order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.     

The Couette flow of a conducting Jeffrey fluid when the walls are lined with deformable porous material

The paper deals with the flow, past a deformable porous channel bounded by finite deformable porous layer with moving rigid parallel plates. Transverse magnetic field is also applied and incorporated in the momentum equation. The coupled nonlinear equations are transformed to ordinary differential equations (ODEs) with suitable choice of similarity transformation. Further, these sets of nonlinear ODEs are solved analytically and are used to get results for the flow phenomena. The effects of the porous layer thickness and the drag on the flow phenomena are discussed graphically. It is observed that rigid velocity decreases with increasing in the drag, whereas the decrease in the deformable is noted. It is clear to see that the retards in solid displacement are shown with enhancing viscosity parameter η.     

Entropy analysis of unsteady flow on flat plate

The flow generated due to the motion of flat plate is an important problem in fluid mechanics, since it gives insight into the unsteady boundary layer generation. The entropy analysis of such flow problems can provide enlightening information on the viscous dissipation in the fluid flow. In the present study, an impulsively started Couette flow is studied, where a flow between two parallel plates is moved impulsively by moving the lower plate from rest to a finite velocity in the half‐space y > 0. Development of velocity and entropy profiles, at different time scales, has been numerically obtained; the development of total entropy with time, in the space between the plates, has been determined. It is found that entropy generation in the space between the plates is more considerable at initial times of motion than at later times. Copyright © 2001 John Wiley & Sons, Ltd.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

Transient free-convective flow of reactive viscous fluid in a vertical channel

A numerical study is reported to investigate the transient free-convective flow of reactive viscous fluid in a vertical channel formed by two infinite vertical parallel plates. A theoretical analysis is also presented to find the expressions for temperature, velocity, skin-friction and Nusselt number for the steady fully developed flow using perturbation technique. During the course of numerical computation, an excellent agreement is found between steady state solutions and transient solution at large value of time.