An unsteady MHD flow of a second-grade fluid passing through a porous medium in the presence of radiation absorption exhibits Hall and ion slip effects

In the presence of radiation absorption, we analyzed the effects of Hall and ion slip effects on an unsteady laminar magnetohydrodynamics convective rotating flow of heat-producing or absorbing second-grade fluid across an inclined moving permeable surface in the presence of chemical reaction and radiation absorption. Using the perturbation method, the nondimensional equations for the governing flow are solved to the most excellent conceivable investigative answer. The effects of various factors on velocity, temperature, and concentration are visually and explored in depth. Shear stresses, Nusselt number, and Sherwood number are calculated analytically, rendered computationally in a tabular style, and discussed concerning the essential characteristics for engineering inquiry. It is inferred that an increase in radiation absorption, Hall, and ion slip parameters across the fluid area leads to a rise in the resulting velocity. The thermal and solutal buoyancy forces contribute to the resultant velocity, constantly growing to a very high level. The rotation parameter is used to reduce skin friction, while the Hall and ion slip effects enhance it. The rate of mass transfer increases when the chemical reaction parameter is raised.     

MHD convective rotating flow of viscoelastic fluid past an infinite vertical oscillating porous plate with Hall effects

It is considered the unsteady and incompressible magnetohydrodynamic rotating free convection flow of viscoelastic fluid with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field and taking Hall current into account. The governing equations of the flow field are then solved by a regular perturbation method for a small elastic parameter. The expressions for the velocity, temperature, and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction on the boundary, the heat flux in terms of the Nusselt number, and the rate of mass transfer in terms of the Sherwood number are also obtained and their behavior discussed. The resultant velocity enhances with increasing Hall parameter and rotation parameter. The reversal behavior is observed with increasing viscoelastic parameters. The resultant velocity enhances and experiences retardation in the flow field with increasing radiation parameters, whereas the secondary velocity component increases with increasing rotation parameters. The temperature diminishes as the Prandtl number and/or the frequency of oscillations. The concentration reduces at all points of the flow field with the increase in the Schmidt number.     

Hall and ion slip effects on MHD free convective rotating flow bounded by the semi‐infinite vertical porous surface

Thermodiffusion, thermal radiation, Hall and ion slip effects on heat and mass transport of free convective MHD micropolar fluid flow bounded by a semi‐infinite absorbent plate with rotation and suction have been investigated. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The solutions are found analytically with the perturbation technique. With the help of graphic representations, the impacts of many critical parameters on velocity, temperature, and concentration within the boundary layer are discussed. In addition, local skin‐friction, Nusselt number, and Sherwood numbers are determined and computationally analyzed.     

Role of rotation and hall currents on free convection and mass transfer flow through a porous medium

Effects of Hall current and rotation on free convection and mass transfer flow through a porous medium bounded by a vertical surface have been analysed. The problem is solved analytically. The velocity profiles are shown on graphs. Effects of m (Hall parameter), K★ (permeability parameter), E (Ekman number) and Sc (Schmidt number) on velocity are discussed.     

Steady MHD Casson Ohmic heating and viscous dissipative fluid flow past an infinite vertical porous plate in the presence of Soret,Hall, and ion‐slip current

In the present study, the influence of Hall and ion‐slip current on steady magnetohydrodynamics mixed convective, Ohmic heating, and viscous dissipative Casson fluid flow over an infinite vertical porous plate in the presence of Soret effect and chemical reaction are investigated. The modeling equations are transformed into dimensionless equations and then solved analytically through the multiple regular perturbation law. Computations are performed graphically to analyze the behavior of fluid velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number on the vertical plate with the difference of emerging physical parameters. This study reflects that the incremental values of Casson fluid parameter and Schmidt number lead to reduction in velocity. However, fluid velocity rises due to enhancement of ion‐slip parameter but an opposite effect is observed in case of Hall parameter. In addition, the Sherwood number declines with enhancing dissimilar estimators of the chemical reaction, Schmidt number, as well as Soret number.     

Second law analysis of a disturbed flow in a thin slit with wall suction or injection

Fully-developed laminar flow in a horizontal thin slit having plates at different temperature is considered for the case of lower plate movement and/or the pressure gradient-and-upper plate movement. The flow under these conditions is analyzed in terms of entropy generations as function of the Prandtl number, the Eckert number, cross-flow Reynolds number and dimensionless temperature difference. In this context, the governing equations for distributions of temperature, the dimensionless entropy generation number and Bejan number are analytically derived with the aid of expressions for velocity distributions. The effect of each parameter on the temperature and the entropy generation are investigated by varying one of the parameters and keeping the rest of them constant for each flow case. The effects of viscous dissipation, rates of mass suction/injection and dimensionless temperature differences on the fluid temperature and entropy generation are examined. The magnitudes of mass suction and/or injection have a large influence on the temperature profile of the fluid. It is observed that the Prandtl number and the Eckert number affect fluid temperature in similar way. It is found that an increase in values of the cross-flow Reynolds number (mass suction/injection) enhances the entropy generation in boundary layer. The velocity profiles are found to be in agreement with the distributions of the dimensionless entropy generation number (N_S) for two flow cases.     

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.     

The research of laminar-turbulent transition in hypersonic three-dimensional boundary layer

The results of experimental investigation of laminar-turbulent transition in three-dimensional flow under the high continuous pressure gradient including the flow with local boundary layer separation are presented. The experimental studies were performed within the Mach number range from 4 to 6 and Reynolds number 10-60×106 1/m, the angles of attack were 0°and 5°. The experiments were carried out on the three-dimensional convergent inlet model with and without sidewalls. The influence of artificial tubulator of boundary layer on transition and flow structure was studied. The conducted researches have shown that adverse pressure gradient increase hastens transition and leads to decrease of transition area length. If pressure gradient rises velocity profile fullness increases and profile transformation from laminar to turbulent occurs. As a result of it the decrease of separation area length occurs. The same effect was reached with Reynolds number increase. These results are compared with the data on two-dimensional model with longitudinal curvature.     

Influence of Hall current on hydromagnetic natural convective flow between two vertical concentric cylinders in presence of heat source/sink

The fully developed laminar magnetohydrodynamic free convection between two concentric vertical cylinders with Hall currents and heat source/sink, in the presence of the radial magnetic field, are studied. The governing thermal energy and momentum equations are changed into ordinary differential equations whose solutions are determined in closed‐form expressions of the Bessel and modified Bessel functions of order zero. A parametric investigation illustrating the impacts of the Hall current, magnetic field, heat source, and radii ratio has been accomplished graphically to examine the changes in temperature as well as velocity while the Nusselt number, mass flux, and skin friction values have been presented in tabular forms. The results ensure that the Hall current has a strong and direct impact on the flow character, such that the influence of the Hall parameter enhances the velocity fields in the appearance of heat source and sink. The velocity remains almost constant as the Hall parameter value is greater than four. Moreover, the velocity and temperature fields have an increasing tendency due to the heat source and inversely for the heat sink.     

Hydromagnetic slip flow of a radiating fluid with hall currents part 1: Fully developed flow

The problem of slip flow, as provoked primarily by high temperature rather than low pressure, is considered for a thermally radiating gas in the presence of Hall currents and mass transfer in a porous medium. The general differential approximation for radiation is invoked, and the problem, which is fully developed, is tackled numerically and analytically.     

Impacts of the periodic wall conditions on the hydromagnetic convective flow of viscoelastic fluid through a vertical channel with Hall current and induced magnetic field

In this study, a mathematical analysis is presented for the hydromagnetic convective flow of an incompressible, chemically reacting, and electrically and thermally conducting viscoelastic fluid through a vertical channel bounded by the porous regime under the action of an applied magnetic field with Hall current and induced magnetic field effects. The left wall of the channel is considered to be nonmagnetic, whereas the right wall of the channel is periodically magnetized. The flow within the channel is induced due to the nonuniform wall temperature and concentration, periodic pressure gradient, and periodic movement of the right wall. The method of separation of variable is used to convert the flow governing coupled partial differential equations into the ordinary differential equations that are solved analytically, and the solution for fluid velocity, induced magnetic field, temperature, and concentration is presented in a closed form. Numerical computation has been performed to demonstrate the impact of various system parameters on the fluid flow behavior. It is observed that oscillations increase the primary flow and primary induced magnetic field. Buoyancy forces have a tendency to lessen the secondary induced magnetic field. Furthermore, it is examined that magnetic diffusivity increases the primary flow, whereas it decreases the secondary flow and primary induced magnetic field.     

Effects of hall current and wall temperature oscillation on free convective and mass transfer flow in a rotating porous medium with constant heat source

The combined effects of Hall current and a constant heat source on the hydromagnetic free convective and mass transfer flow past an infinite vertical porous plate in a rotating porous medium are considered, when the temperature of the plate varies with time about a nonzero constant mean and the temperature of the free stream is constant. The problem is solved analytically and the velocity profiles are shown on graphs. Effects of m (Hall parameter) and α (heat source parameter) on velocity are discussed extensively.     

Mixed convection flows of tangent hyperbolic fluid past an isothermal wedge with entropy: A mathematical study

The nonlinear, steady, and mixed convective boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian fluid over an isothermal wedge in the presence of magnetic field are analyzed numerically using the implicit Keller-Box finite-difference technique. The entropy analysis due to MHD flow of a tangent hyperbolic fluid past an isothermal wedge and viscous dissipation is also included. The numerical code is validated with previous Newtonian studies available in the literature. Graphical and tabulated results are analyzed to study the behavior of the fluid velocity, temperature, concentration, shear stress, heat transfer rate, entropy generation number, and Bejan number for various emerging thermophysical parameters, namely Weissenberg number (We), power-law index (n), mixed convection parameter (λ), pressure gradient parameter (m), Prandtl number (Pr), Biot number (γ), Hartmann number (Ha), Brinkmann number (Br), Reynolds number (Re), and temperature gradient (Π). It is observed that velocity, entropy, Bejan number, and surface heat transfer rate are reduced with the increase in the Weissenberg number, but temperature and local skin friction are increased. An increase in pressure gradient enhances velocity, entropy, local skin friction, and surface heat transfer rate, but reduces temperature and Bejan number. An increase in an isothermal power-law index (n) is observed to increase velocity, Bejan number, and surface heat transfer rate, but it decreases temperature, entropy, and local skin friction. An increase in the magnetic parameter (Ha) is found to decrease temperature, entropy, surface heat transfer rate, and local skin friction, and it increases velocity and Bejan number. The research is applicable for coating materials in chemical engineering, for instance, robust paints, production of aerosol deposition, and water-soluble solution thermal treatment.     

Flow of three-dimensional radiative Williamson fluid over an inclined stretching sheet with Hall current and nth-order chemical reaction

In the current communication, three-dimensional Williamson fluid flow past a bidirectional inclined stretching plate with novel Hall current, nonuniform heat source/sink, and nth-order chemical reaction features are investigated. Rosseland's diffusion model is defined for the radiation heat transfer. The nonlinear governing derivative equations satisfying the flow are transmuted to the coupled derivative equations by employing the local similarity quantities and then solved numerically through the Runge–Kutta–Fehlberg method utilizing the shooting quadrature. An inclusive analysis is reported via graphs for the flow rate field, temperature, and concentration distributions for different evolving terms of immense concern. Wall dragging effect and wall heat gradient and wall concentration gradient have been examined, plotted, and described. The detailed geometry reveals that dimensionless velocity field is monotonically rising as the Hall parameter rises. The chemical reaction concentration for the Williamson fluid is enhanced with expanding values of the magnetic field parameter. Transitional values of wall stress components upturn with an increase in Hall parameter while the Williamson term is boosted. Nusselt number is reduced as the Williamson term rises and the Sherwood number enhances with a rising chemical reaction term. The results are verified for limiting cases by comparing with various investigations and found to have excellent accuracy.     

Hall and ion-slip effects on MHD natural convective flow past an unbounded vertical porous channel with thermodiffusion

The consequences of Soret in addition to Dufour of natural convection heat and mass transfer for the unsteady three-dimensional boundary layer flow through a perpendicular condition of the existence of viscous dissipation, invariable suction, Hall as well as ion slip consequences into relation. The prevailing partial differential equation is dissolved digitally utilizing the implicit Crank–Nicolson finite difference method. The velocity, temperature, as well as concentration dispensations, is addressed computationally and demonstrated by the graphs. Numerical values of the Nusselt number, skin friction as well as Sherwoods numbers nearby the plate are discussed for a choice of values of substantial parameters and are displayed in a tabular manner. It is noticed that the temperature of the fluid diminishes with higher Prandtl numbers. The resulting velocity diminishes with the growing Hartmann number. Rotation, Soret, and Dufour parameters strengthen the velocity and momentum boundary layer thickness. The velocity intensifies through growing Hall and ion-slip parameters and the revoke trend is acquired with enhancement in suction parameter.     

Hall current effect on the peristaltic motion of synovial nanofluid with magnetohydrodynamics

This paper examines the influence of magnetic field on peristaltic flow of synovial nanofluid in an asymmetric channel. Hall current, thermophoresis, and Brownian motion effects are taken into account. Our problem is discussed for two models, in the first model which referred as Model (I), viscosity is considered exponentially dependent on the concentration, and Model (II) Shear thinning index is considered function of concentration. The governing problem is reformulated under the assumption of low Reynolds number and high wavelength. Resulting system of equations are solved numerically with the aid of Parametric ND Solve. Detailed comparisons have been made between Model (I) and Model (II) and found unrealistic results between them. Results for velocity, temperature and nanoparticle concentration distributions as well as pressure gradient and pressure rise are offered graphically for different values of various physical parameters. It is found that the velocity of fluid decreases in semi‐curved lines in case of Model (I) with the increase of while, in Model (II) it decreases in the left side of the channel and increases in the right side of that channel. Such models are applicable to rheumatoid arthritis treatment.     

An improvement on the efficiency of a single rotor transonic compressor by reducing the shock wave strength on the blade suction surfaces

It is well known that increasing the rotational velocity is an effective way to increase the total pressure ratio. With increasing flow velocity especially under the condition of transonic flow in the supersonic region, where exist strong shock waves, the shock wave loss becomes main and important. Simultaneously, there occurs boundary layer separation due to the shock wave / boundary layer interaction. In the present paper the transonic compressor blades were studied and analyzed to find a proper and simple way to reduce the shock wave loss by optimizing the suction surface configuration or controlling the gradient of isentropic Mach number on the suction surface. A Navier-Stokes solver combined with a modified design algorithm was developed and used. The NASA single rotor for transonic flow compressor was served as a numerical example to show the effectiveness of this method. Two cases for both original and modified rotors were analyzed and compared.     

Effect of inclined and low magnetic field in gaseous slip flow in two‐dimensional rectangular microchannel using first‐order boundary conditions

In the present work, the effect of an oriented low magnetic field on near‐continuum gaseous slip flow inside a two‐dimensional rectangular microchannel has been studied using first‐order boundary conditions. The flow was assumed to be compressible, laminar, and steady. The governing equations were solved analytically to obtain the solutions of velocity, temperature, and the pressure of the flow. The influence of different parameters such as Knudsen number, aspect ratio, Hartmann number, and pressure ratio were studied and analyzed. It was found that the electric and magnetic field with an inclined angle had significant effects on the flow properties. The results showed that the velocity increases and the temperature decreases as the inclination angle of the magnetic field decreases. The velocity increases as the Knudsen number, pressure ratio, and aspect ratio increase, while it decreases with increasing of the Hartmann number. The temperature decreases with increasing of the Knudsen number, pressure ratio, and aspect ratio, while the temperature increases as the Hartmann number increases. The results of the present study were validated with published results in the literature.     

Analytical Solution of Viscoelastic Fluid Flow and Heat Transfer through an Annulus

Abstract

Forced convection heat transfer to a fully developed laminar flow of simplified Phan-Thien-Tanner fluid in an annulus was studied analytically. Inner and outer cylinders were stationary and subjected to constant heat flux. The results of the velocity and temperature distributions, dimensionless pressure gradient, and Nusselt number were obtained for a wide range of aspect ratios and dimensionless viscoelastic groups. Results indicated the gap between two cylinders as well as viscoelastic behavior of the fluid have noticeable effects on flow and heat transfer.     

The transpired turbulent boundary layer in an adverse pressure gradient

An experimental program was carried out to study the effect of transpiration on a turbulent boundary layer in an adverse pressure gradient. A wind tunnel with a porous test wall was designed so that the blowing velocity and the strength of the pressure gradient could be varied in the course of the experiments. The effect of transpiration on the location of the separation point was observed. Measurements of mean velocity profiles and heat transfer rates were compared with predictions of a boundary layer calculation method based on an effective viscosity model. Predictions of skin friction were satisfactory, but there was noticeable error in the predicted velocity profile shapes near separation. It was also found that a form of the law of the wake provides a good representation of velocity profiles with blowing and could be used as the basis tor an integral method of prediction.