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.     

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.     

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.     

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.     

Stagnation flow of hybrid nanoparticles with MHD and slip effects

The flow of hybrid nanoparticles with significant physical parameters with different base fluids in the presence of Biot number, velocity slip, and MHD effects has not been explored so far, particularly for a circular cylinder. Therefore, the current report is presented to offer a numerical solution for hybrid nanoparticles with base fluids (water and ethylene glycerol) via a circular cylinder. The physical situation is interpreted in terms of partial differential equations and is converted into ordinary differential equations after applying the similarity transformation. The results are presented in both tabular and graphical forms. The impact of physical parameters on velocity distribution is examined through graphs. The comparative results of hybrid nanoparticles for distinct base fluids as ethylene glycol and water are proposed and the hybrid nanoparticles with base fluid water seems to be greater than that of the hybrid nanoparticles with base fluid EG. The temperature profile of hybrid nanoparticles is found to be a decreasing function with growth in velocity slip parameter but an opposite trend is noted in case of nanoparticles . The skin friction and Nusselt number augmented for the increase in magnetic field, velocity slip, and nanoparticle while it shows a decreasing trend toward thermal slip parameter. For the both cases, improvement in Biot number helps enhance the heat transfer constantly.     

Cubic B-splines method for Hall and ion slip impacts on unsteady MHD rotating flow past a vertical moving porous plate

The heat and mass transfer of unsteady magnetohydrodynamic (MHD) flow of Newtonian fluid with Hall current and ion-slip currents due to vast possible engineering applications is very important in areas like power generators, MHD accelerators, refrigeration coils, electric transformers, and heating elements. A quality-based research on Hall and ion-slip consequences on the rotating unsteady MHD flow past an infinite perpendicular moving absorbent plate have not been performed. Therefore, the Hall and ion-slip consequences on rotating unsteady MHD flow past an infinite perpendicular moving absorbent plate have not been performed. The similarity transformations are engaged to transfer the governing partial differential equations within favor of the scheme of nonlinear ordinary differential equations and elucidated numerically making use of cubic B-splines collocation mechanism. The influences of felicitous parameters on basic equations are remarked on through graphical profiles. Even though the computational estimations of frictional forces, Nusselt number, and Sherwood number for various parameters are distributed in tabular format and exchanged of views comparatively.     

Hall current and ion‐slip effects on free convection flow in a vertical microchannel with an induced magnetic field

The steady fully developed hydromagnetic flow of a viscous incompressible and electrically conducting fluid in a vertical microchannel has been studied taking into account the influence of Hall current, ion‐slip effects and an induced magnetic field. Exact solutions for the governing equations responsible for the flow formation are obtained by the method of the undetermined coefficient and presented graphically. It is found that in the presence of the ion‐slip effect, both primary and secondary components of fluid velocity increase with the Hall parameter for symmetric as well as asymmetric heating of the microchannel surfaces. Also, the magnetic field supports flow along the secondary flow direction while the reverse impact is observed along the primary flow direction.     

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 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.     

Second law analysis for chemically reacting natural convective second‐grade fluid flow between porous parallel plates with Hall and Ion slip

In this article, we performed the entropy generation of free convective chemically reacting second‐grade fluid confined between parallel plates in the influence of the Hall and Ion slip with heat and mass fluxes. Let there be a periodic suction/injection along with the plates, the governing flow field equations are reduced as a set of coupled nonlinear ordinary differential equations by using appropriate similarity transformations then solved numerically with shooting method based on Runge‐Kutta 4th order scheme. The results are analyzed for velocity in axial and radial directions, temperature distribution, concentration distribution, entropy generation number, Bejan number, mass and heat transfer rates with respect to distinct geometric, and fluid parameters and shown graphically and tables. It is observed that the entropy generation is enhanced with Prandtl number, whereas decreases with a second‐grade parameter, the effects of Hall and Ion slip parameters on velocity components, temperature and entropy generation number are the same. The entropy generation number the fluid is enhanced with the suction‐injection parameter whereas, the concentration of the fluid decreases with the increasing of chemical reaction parameter.     

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.     

Mixed convection flow of a Maxwell nanofluid with Hall and ion‐slip impacts employing the spectral relaxation method

This article investigates the Hall and ion‐slip impacts on the mixed convection flow of a Maxwell nanofluid over an expanding surface in a permeable medium. The impacts of Brownian movement and thermophoresis parameters, Soret, Dufour, viscous dissipation, chemical reaction, and suction parameters, are, moreover, considered. Using the similitude changes, the partial differential equations with regard to the momentum, energy, and concentration equations are transformed to an arrangement of nonlinear ordinary differential equations, which are handled numerically utilizing a spectral relaxation method (SRM). The impacts of noteworthy physical parameters on the velocities, thermal, and concentration distributions are investigated graphically. Moreover, the numerical values of skin‐friction coefficients, local Nusselt number, and Sherwood number for different values of the mixed convection parameter $\left(\gamma \right),$ Deborah number $\left(\lambda \right),$ Hall parameter $({\beta }_{\mathrm{H}}),$ ion‐slip parameter $({\beta }_{\mathrm{i}}),$ Dufour number (Du), and Soret number $\left(\mathit{Sr}\right)$ are computed and tabulated. It is discovered that ascent in Deborah number reduces both the stream and transverse velocity profiles, while the inverse pattern is seen with augmentation in the mixed convection parameter. In addition, inverse patterns of the stream and transverse velocity profiles are seen with expansion in magnetic, Hall, and ion‐slip parameters. Besides this, the temperature and concentration disseminations decline with augmentation in Dufour number and chemical reaction parameters, respectively. It is likewise seen that both the skin‐friction coefficients lessen with expansion in Deborah number, and they ascend with upgrade in blended convection and ion‐slip parameters, while the opposite condition is noticed with augmentation in Hall parameter. Furthermore, the reverse trends of local Nusselt and Sherwood numbers are discovered with expansion in the Dufour and Soret numbers.     

Influence of an inclined stretching cylinder over MHD mixed convective nanofluid flow due to chemical reaction and viscous dissipation

This paper analyzed the steady two‐dimensional magnetohydrodynamic mixed convective viscous nanofluid and heat transfer toward an inclined stretching cylinder with chemical reaction and uniform magnetic field. The governing partial differential equation in a cylindrical form is reduced to a set of nonlinear ordinary differential equations by using appropriate similarity transformation and solved numerically by spectral quasilinearization methods (SQLMs). A new approach of this method is employed to derive numerical expressions for velocity, temperature, and concentration profile. The convergence and accuracy of our numerical scheme are observed. The SQLM is employed to find out the convergent series solution. There is an increase in the temperature profiles due to the increase in the thermophoresis parameter. The increase in effective Eckert number results in the increase of the temperature profile.     

Radiation and Hall effects on a 3D flow of MHD Williamson fluid over a stretchable surface

Magnetohydrodynamics (MHD) three-dimensional flow of an unsteady Williamson fluid on an enlarging surface with Hall current, radiation, heat source/sink, and chemical reaction is investigated in this article. The basic governing equations are transformed into a system of ordinary differential equations by using an appropriate similarity transformation. The system is deciphered using the shooting method. The properties of influential parameters such as parameters of magnetic field, Hall current, radiation, and so forth, on the flow are discussed with the help of graphs and tables. We noticed that the increase in the magnetic field reduces the velocity in x-direction and the rate of heat and mass transfer. We also acknowledged that the growing values of Hall current parameter boost the velocity in z-direction but it reduce the temperature and concentration distributions, respectively. The results of this study represent many applications in biomedical engineering and these results are helpful for further study of non-Newtonian fluids in various circumstances.     

Hall current impacts on unsteady MHD free convective flow past an infinite vertical porous surface

In this paper, the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid over a vertical plate embedded in a porous medium is considered. A homogeneous transverse magnetic field is applied in the presence of a heat source and chemical reaction in a rotating frame, taking Hall current effects into account. The momentum equations for the fluid flow in a porous medium were determined by Brinkman modeling. At the undisturbed state, both the plate and fluid have an rigid body rotation due to the constant angular velocity, perpendicular to the infinite vertical plane surface. The vertical surface is subject to the homogeneous constant suction and the heat on the surface vary by time about a nonzero constant rate whereas the temperature of free stream is engaged to be constant. The accurate solutions for the velocity, temperature, and concentration distributions were acquired systematically using the perturbation method. The consequences of an assortment of governing flow parameters on the velocity, temperature, and concentration were analyzed through graphical profiles. The computational results for the skin friction, Nusselt number, and Sherwood number in a tabular format were also examined.     

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     

Differential transform solution for Hall and ion‐slip effects on radiative‐convective Casson flow from a stretching sheet with convective heating

Magnetohydrodynamic (MHD) materials processing is becoming increasingly popular in the 21st century as it offers significant advantages over conventional systems, including improved manipulation of working fluids, reduction in wear, and enhanced sustainability. Motivated by these developments, the present work develops a mathematical model for Hall and ion‐slip effects on non‐Newtonian Casson fluid dynamics and heat transfer toward a stretching sheet with a convective heating boundary condition under a transverse magnetic field. The governing conservation equations for mass, linear momentum, and thermal (energy) are simplified with the aid of similarity variables and Ohm's law. The emerging nonlinear‐coupled ordinary differential equations are solved with an analytical technique known as the differential transform method. The impact of different emerging parameters is presented and discussed with the help of graphs and tables. Generally, aqueous electroconductive polymers are considered, for which a Prandtl number of 6.2 is employed. With increasing Hall parameter and ion‐slip parameter, the flow is accelerated, whereas it is decelerated with greater magnetic parameter and rheological (Casson) fluid parameter. Skin friction is also decreased with greater magnetic field effect, whereas it is increased with stronger Hall parameter and ion‐slip parameter values.     

MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation,slip condition,and viscous dissipation

This study presents the problem of MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation, slip condition, and viscous dissipation. The partial differential equations with the corresponding boundary conditions that govern the fluid flow are reduced to a system of highly nonlinear ordinary differential equations using scaling group transformations. The fourth-order method along shooting technique is applied to solve this system of boundary value problems numerically. The effects of flow parameters on the velocity, temperature, and concentration profiles are presented via graphs. The impact of the physical parameters on the skin friction coefficient reduced Nusselt numbers and reduced Sherwood numbers are investigated through tables. Comparison of the present findings with the previously published results in the literature shows an excellent agreement. It is also noted that a rise in the Eckert number results in a drop in the temperature of the fluid in the thermal boundary layer region of the fluid flow.     

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.     

Three‐dimensional visualization of an electrically conducting and viscous dissipative fluid flow over a moving permeable vertical cylinder

This study numerically scrutinizes the boundary layer flow of an electrically conducting and viscous dissipative fluid past an impulsively started permeable vertical cylinder together with thermal radiation. The solutions of the governing problem are accomplished using the Crank‐Nicholson scheme. The impressions of pertinent parameters on the flow patterns of the fluid particles as well as on the velocity, temperature, and distributed regions are captured and visualized three‐dimensionally.