Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Free convection effects on HMD horizontal channel flow with Hallcurrents

An exact solution of MHD channel flow between two horizontal parallel plates taking into account free convection currents and the Hall currents is presented. Solutions for the primary and secondary velocity, the induced magnetic field, the skin friction, and the temperature are derived. The velocity field and magnetic field are shown on graphs, and the values of the skin friction and the rate of heat transfer are indicated on tables. The results are discussed in terms of the hall parameter, the Hartmann number, and the Grashof number     

Free convection effects and radiative heat transfer in MHD Stokes problem for the flow of dusty conducting fluid through porous medium

The present note deals with the effects of radiative heat transfer and free convection in MHD for a flow of an electrically conducting, incompressible, dusty viscous fluid past an impulsively started vertical non-conducting plate, under the influence of transversely applied magnetic field. The heat due to viscous dissipation and induced magnetic field is assumed to be negligible. The governing linear partial differential equations are solved by finite difference technique. The effects of various parameters (like radiation parameter N, Prandtl number Pr, porosity parameter K) entering into the MHD Stokes problem for flow of dusty conducting fluid have been examined on the temperature field and velocity profile for both the dusty fluid and dust particles.     

Theoretical solution of impulsively started vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation

An analysis is performed to study the free convective flow over a moving vertical porous plate with variable temperature under the influence of magnetic field and thermal radiation. The fluid considered here is a gray, absorbing-emitting radiation, but a nonscattering medium. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature, skin friction and Nusselt number are studied for different parameters like the radiation parameter, Grashof number, Prandtl number, magnetic field parameter, permeability parameter, and time. It is observed that the velocity decreases with increasing radiation parameter.     

Existence of a Hartmann layer in the peristalsis of Sisko fluid

Analytical solutions for the peristaltic flow of a magneto hydrodynamic(MHD) Sisko fluid in a channel, under the effects of strong and weak magnetic fields, are presented. The governing nonlinear problem, for the strong magnetic field,is solved using the matched asymptotic expansion. The solution for the weak magnetic field is obtained using a regular perturbation method. The main observation is the existence of a Hartman boundary layer for the strong magnetic field at the location of the two plates of the channel. The thickness of the Hartmann boundary layer is determined analytically. The effects of a strong magnetic field and the shear thinning parameter of the Sisko fluid on the velocity profile are presented graphically.     

Second law analysis of the flow of two immiscible micropolar fluids between two porous beds

This work investigates the effect of entropy generation rate within the flow of two immiscible micropolar fluids in a horizontal channel bounded by two porous beds at the bottom and top. The flow is considered in four zones. Zone IV contains the flow of viscous fluid in the large porous bed at the bottom, zone I and zone II contain the free flow of two immiscible micropolar fluids, and zone III contains the flow of viscous fluid in the thin porous bed at the top. The flow is assumed to be governed by Eringen’s micropolar fluid flow equations in the free channel. Darcy’s law and Brinkman’s model are used for flow in porous zones, namely, zone IV and zone III, respectively. The closed form expressions for entropy generation number and Bejan number are derived in dimensionless formby using the expressions of velocity, microrotation and temperature. The effect of physical parameters like a couple stress parameter and micropolarity parameter on velocity, microrotation, temperature, entropy generation number and Bejan number are investigated.     

Hydromagnetic free convection flow through a porous medium between two parallel plates

Steady hydromagnetic free convective flow of a conducting fluid through a porous medium bounded by two parallel plates is considered and effects of G (Grashof number) and the K (permeability parameter) on the velocity field are discussed.     

MHD Maxwell flow modeled by fractional derivatives with chemical reaction and thermal radiation

Heat transfer in a time-dependent flow of incompressible viscoelastic Maxwell fluid induced by a stretching surface has been investigated under the effects of heat radiation and chemical reaction. The magnetic field is applied perpendicular to the direction of flow. Velocity, temperature, and concentration are functions of z and t for the modeled boundary-layer flow problem. To have a hereditary effect, the time-fractional Caputo derivative is incorporated. The pressure gradient is assumed to be zero. The governing equations are non-linear, coupled and Boussinesq approximation is assumed for the formulation of the momentum equation. To solve the derived model numerically, the spatial variables are discretized by employing the finite element method and the Caputo-time derivatives are approximated using finite difference approximations. It reveals that the fractional derivative strengthens the flow field. We also observe that the magnetic field and relaxation time suppress the velocity. The lower Reynolds number enhances the viscosity and thus motion weakens slowly. The velocity initially decreases with increasing unsteadiness parameter δ. Temperature is an increasing function of heat radiation parameter but a decreasing one for the volumetric heat absorption parameter. The increasing value of the chemical reaction parameter decreases concentration. The Prandtl and Schmidt numbers adversely affect the temperature and concentration profiles respectively. The fractional parameter changes completely the velocity profiles. The Maxwell fluids modeled by the fractional differential equations flow faster than the ordinary fluid at small values of the time t but become slower for large values of the time t.     

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Negative electrorheological responses of micro-polar fluids in the finite spin viscosity small spin velocity limit. I. Couette flow geometries

Negative electrorheological responses induced by micro-particle electrorotation in two-dimensional Couette flow geometries are analyzed by a set of continuum modeling field equations originating from anti-symmetric/couple stress theories in the finite spin viscosity small spin velocity (FSV) limit. Analytical solutions are obtained for the first time to express the spin velocity, linear velocity, and effective viscosity in terms of the electric field strength, driving shear rate, boundary condition selection parameter, and spin viscosity. Good agreement is achieved between the FSV theoretical predictions presented herein and the experimental measurements reported in recent literature for the effective viscosity for low driving shear rates.     

Numerical Analysis of Unsteady Magneto-Biphase Williamson Fluid Flow with Time Dependent Magnetic Field

Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter,heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter,volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.     

Comparative study on electroosmosis modulated flow of MHD viscoelastic fluid in the presence of modified Darcy’s law

Magnetic field plays an important role in numerous fields such as biological, chemical, mechanical and medical research. In clinical and medical research the high field magnets are extremely important to create 3D images of anatomical and diagnostic importance from nuclear magnetic resonance signals. In view of these applications, the purpose of present work is to explore the impact of an external magnetic field on the viscoelastic fluid flow in the existence of electroosmosis, porous medium and slip boundary conditions. The governing equation is modified under the suitable dimensionless quantities. The resulting non-dimensional differential equation is evaluated by analytical as well as numerical (finite difference and cubic B-spline) methods. The convergence analysis is also presented for the numerical methods. The variations of sundry parameters on velocity, volume flow rate and skin friction are presented through graphical representations. The current analysis depicts that, the higher velocities are noticed in viscoelastic fluid as compared with Newtonian fluid. The velocity enhances with rising of slip and Darcy parameters. Volume flow rate rises with the slip and viscoelastic parameters. Skin friction is a decreasing function of zeta potential, Darcy number and Hall current parameter. The limiting solutions can be captured for the Newtonian fluid model by setting the viscoelastic parameter to zero.     

Effect of heat generation on transient flow of micropolar fluid in a porous vertical channel

The present work is performed to study the effect of heat generation on fully developed flow and heat transfer of micropolar fluid between two parallel vertical plates. The rigid plates are assumed to exchange heat with an external fluid by convection. The governing equations are solved by using Crank–Nicolson implicit finite difference method. The effects of governing parameters such as transient, heat generation, micropolar parameter, Prandtl number, Biot number, and Reynolds number on the velocity and temperature profiles are discussed. It is found that the presence of heat generation enhances the velocity and temperature of the micropolar fluid at the middle of the channel.     

Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid bounded by a vertical infinite surface under the action of a transverse magnetic field. Approximate solutions of the coupled nonlinear governing equations are obtained for different values of the microrotation- and the magnetic-parameters. Numerical calculations are carried out for the various parameters entering into the problem. Velocity, angular velocity, temperature and concentration profiles are shown graphically. The numerical values of the skin friction, the wall couple stress, the rate of heat transfer and the concentration gradient at the wall are entered in tables.     

MHD oscillatory flow on free convection–radiation through a porous medium with constant suction velocity

Unsteady two-dimensional hydromagnetic free convection and thermal radiation flow of an electrically conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature are presented. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Expressions for the velocity and temperature are obtained. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Effects of varying R (radiative parameter), G (Grashof number), k′ (permeability of the porous medium) and M (magnetic parameter upon the velocity field and the effect of varying R and Pr (Prandtl number) on the temperature are discussed.     

Hydromagnetic Blood Flow of Sisko Fluid in a Non-uniform Channel Induced by Peristaltic Wave

In this paper, a smooth repetitive oscillating wave traveling down the elastic walls of a non-uniform twodimensional channels is considered. It is assumed that the fluid is electrically conducting and a uniform magnetic field is perpendicular to flow. The Sisko fluid is grease thick non-Newtonian fluid can be considered equivalent to blood. Taking long wavelength and low Reynolds number, the equations are reduced. The analytical solution of the emerging non-linear differential equation is obtained by employing Homotopy Perturbation Method(HPM). The outcomes for dimensionless flow rate and dimensionless pressure rise have been computed numerically with respect to sundry concerning parameters amplitude ratio ?, Hartmann number M, and Sisko fluid parameter b1. The behaviors for pressure rise and average friction have been discussed in details and displayed graphically. Numerical and graphical comparison of Newtonian and non-Newtonian has also been evaluated for velocity and pressure rise. It is observed that the magnitude of pressure rise is maximum in the middle of the channel whereas for higher values of fluid parameter it increases. Further, it is also found that the velocity profile shows converse behavior along the walls of the channel against multiple values of fluid parameter.     

Study of couple stresses and wall permeability effects on the flow in permeable membranes

This study focused on investigating wall permeability, and couple stresses effects on the fluid flow between two permeable membranes. These flows are encountered in a variety of industrial and applied biological processes, particularly in the fluid filtration process through dialyzer membranes. Darcy’s law is employed to define the fluid suction and injection via surface of the membrane. Fluid motion is assumed to be steady and Stokesian, where the flow Reynolds number is low. The exact solution for the fluid flow field is obtained in conjunction with the lubrication approximation. Explicit expressions are derived for some useful quantities of flow interest. A significant change in the flow field is noticed for the presented non-Newtonian fluid model. Graphical results show that the flow field has prominent deviations when the inlet pressure, membrane permeability, and the couple stress parameters are changed. In order to validate results, numerical values of the filtration constant and the average pressure drop for a dialyzer membrane are computed. A comparison of the derived results with existing data reveals a good agreement with experimental and empirical results. The presented results are new and can be reduced to existing results in the literature for specified values of the couple stress parameters.     

Numerical study of unsteady MHD oblique stagnation point flow and heat transfer due to an oscillating stream

The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.