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.     

Heat and mass transfer on MHD convective flow over an infinite vertical porous plate with the heat source and chemical reaction

It is considered that the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid through a porous medium past a vertical absorbent surface. The homogeneous transverse magnetic field is considered in the existence of heat source and chemical reaction in the rotating frame. The accurate solutions of the velocity, temperature, and concentration are acquired systematically making use of the perturbation method. The consequences of a variety of governing flow parameters on the velocity, temperature, and concentration are analyzed through graphical profiles. Computational outcomes for the skin friction, Nusselt number, and Sherwood number through the tabular format were also examined.     

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.     

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.     

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.     

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.     

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.     

Heat and mass transfer in MHD boundary layer flow of a second-grade fluid past an infinite vertical permeable surface

Heat and mass transfer of non-Newtonian fluids is increasingly being studied by researchers due to its applications in many branches of science and engineering, such as metallurgical processes, polymer extrusion, glass blowing, crystal growing, and so forth. The present work is mainly concerned with the unsteady laminar magnetohydrodynamic flow of a heat-generating or absorbing second-grade fluid past an infinite vertical porous plate. The nondimensional governing equations are solved for the best analytical solution. Results for various flow characteristics are presented through graphs and tables delineating the effect of various parameters characterizing the flow. For engineering interest, the shear stresses, Nusselt number, and Sherwood number are computed and exchanged of views with reference to the important parameters. Our analysis explored that the influences of a chemical reaction and fluid oscillations reduced the concentration distribution in the entire liquid region. The rotation effect decreases the shear stress, whereas it is augmented through an increase in the permeability of porous medium and second-grade fluid parameters' impact.     

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.     

Thermodiffusion and chemical reaction on MHD free convective flow past a rotating vertical porous plate with constant heat and mass discharge

Simultaneous heat and mass transport have played significant roles in different substantial chemical, and biomedical processes. Heat and mass transports happen in absorptions, distillations, extractions, drying, melt along with crystallizations, moreover, evaporations, and condensations. Mass flows due to the temperature gradients are recognized as the Soret effect. The Soret effects on the unsteady hydromagnetic liberated convective flow of a non-incompressible electrically performing gelatinous liquid over the rotating perpendicular absorbent plate in the incidence of temperature amalgamation have been investigated. The effects of the first order chemical reaction along with heat radiation are considered. The scheme of partially differential equalities is rendered into ordinarily differential equalities and therefore solved systematically with the Laplace transforms methodology. The impacts of different pertinent flow parametrics on velocities, temperature as well as concentration distributions, in addition, the shear stress is examined through the graphical profiles along with tables accordingly. This is established that resultant velocity field is ascending through an increase in the Soret parameter and chemically reacting parameter. The temperature distribution is increased by an increasing heat absorption parameter. Also, when the Soret parameter increases, then concentration increases throughout the fluid region.     

Effect of thermal radiation on an unsteady MHD flow over an impulse vertical infinite plate with variant temperature in existence of Hall current

In this paper, the effects of thermal radiation on unsteady MHD flow viscous incompressible electrically conducting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion in the presence of Hall current have been presented. The dimensionless governing partial differential equations of the flow have been solved numerically by using the Galerkin finite element method. The numerical solutions for fluid velocity, angular velocity, temperature, and concentration are represented graphically whereas the numerical results of primary skin friction, rate of heat and mass transfer are presented in tabular form for various parameters involved. The current results were compared to the existing analytical solution based on the Crank–Nicolson implicit finite difference technique. The current study's findings have been shown to be extremely consistent with earlier findings.     

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.     

Soret and Dufour effects on MHD flow of viscoelastic fluid past an infinite vertical stretching sheet

Heat and mass transmission taking place in a magnetohydrodynamics fluid of substantial viscosity via a permeable object has been currently a subject of study inviting research. This transmission takes place along an infinite expanding vertical surface showing Soret and Dufour effects. Differential forms of nonlinear nature such as energy, momentum, and equations defining concentration are ascertained by means of similarity transformation with the existing buoyancy force, and by making use of the homotopy analysis method, the equations have been analytically resolved. The impacts arising out of applied factors on temperature, velocity, and concentration forms have been appropriately designed and established.     

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 effects on the hydromagnetic free convective flow and mass transfer through a porous medium bounded by an infinite vertical porous plate with constant heat flux

Effects of Hall current on free convection and mass transfer flow through a porous medium bounded by a vertical surface when a uniform magnetic field acts in a plane which makes an angle x with the plane transverse to the plate have been analysed. An analytic solution of the problem is obtained and the effects of the Hall parameter and the permeability parameter, as well as the other parameters entering into the problem, are discussed and shown graphically.     

Thermodiffusion,chemical reaction,and Hall and ion-slip impacts on MHD rotating flow past an infinite vertical porous plate

The current scrutiny explores the impacts of thermodiffusion, chemical reaction, and Hall and ion-slip impacts lying on unsteady heat and mass transport of free convective hydromagnetic flow enclosed past a semi-infinite porous plate within a gyratory frame under the accomplishment of a transverse magnetic field and convective boundary conditions. The nondimensional governing equations are solved systematically by means of the finite element method. Through the facilitation of graphical profiles, the outcomes of a variety of significant parameters within the boundary layer are addressed. In addition, the local skin friction coefficient and rates of heat and mass transports in expressions of the local Nusselt number and local Sherwood number are presented digitally in tabulation form, although it is originated that the Nusselt number and Sherwood number remain constant with varying all pertinent parameters. It is found that the porous medium impact on the boundary layer growth is significant due to the increase in the thickness of the hydrodynamic boundary layer and the decrease in the thickness of the thermal and concentration boundary layers. The resultant velocity enhances with increasing rotation, Hall and ion-slip parameters.     

Transient free convection in cold water past an infinite vertical porous plate

A finite-difference solution of the transient free convection flow of water near 4°C past an infinite vertical porous plate has been carried out. The most appropriate relation for the density in terms of the temperature, as derived by Gebhart and Mollendorf, is employed. It has been observed that, when the buoyancy force is in the upward direction, the velocity profiles are positive and opposite to those in the case where the buoyancy force is in the downward direction. Also, the skin friction is more when the buoyancy force is in the upward direction than when the buoyancy force is in the downward direction.     

Impact of viscous dissipation and Dufour on MHD natural convective flow past an accelerated vertical plate with Hall current

The present research work concentrates on viscous dissipation, Dufour, and heat source on an unsteady magnetohydrodynamics natural convective flow of a viscous, incompressible, and electrically conducting fluid past an exponentially accelerated infinite vertical plate in the existence of a strong magnetic field. The presence of the Hall current induces a secondary flow in the problem. The distinguishing features of viscous dissipation and heat flux produced due to gradient of concentration included in the model along with heat source as they are known to arise in thermal-magnetic polymeric processing. The flow equations are discretized implicitly using the finite difference method and solved using MATLAB fsolve routine. Numerical values of the primary and secondary velocities, temperature, concentration, skin friction, Nusselt number, and Sherwood number are illustrated and presented via graphs and tables for various pertinent parametric values. The Dufour effect was observed to strengthen the velocity and temperature profile in the flow domain. In contrast, due to the impact of viscous dissipation, the local Nusselt number reduces. The study also reveals that the inclusion of the chemical reaction term augments the mass transfer rate and diminishes the heat transfer rate at the plate.     

Transient free convective hydromagnetic flow in an infinite vertical cylinder with Hall current and heat source/sink

The analysis of hydromagnetic flow has been a concern of consideration for research scientists and engineers. In this treatise, the unsteady hydromagnetic free convective flow of an incompressible, viscous, and electrically conducting fluid and heat transfer in a vertical cylinder with Hall effects and transverse magnetic field, in the presence of heat source and sink, is studied. Exact solutions of dimensionless unsteady governing equations are obtained by using the Laplace transform technique. Transient fluid velocity and temperature field are depicted by graphs, whereas heat transfer rate, mass flux, and skin-friction are computed in a tabular form for different physical parametric values, such as the source/sink parameter, Hall current parameter, Prandtl number, and Hartmann number. The valuable result from the investigation is that the Hall parameter slightly accelerates the fluid velocity and it provides resistance to the skin friction at the cylindrical surface. Moreover, it is noticeable that temperature as well as velocity enhances and finally gets to its steady state with time. To be noted, the Hall effects have been widely applied in numerous experimental engineering applications, such as constrictions of turbines, Hall accelerators, Hall sensors.     

Heat transport on steady MHD flow of copper and alumina nanofluids past a stretching porous surface

An attempt is made to investigate the steady magnetohydrodynamic convective flow of the viscous nanofluid due to a permeable exponentially stretching porous surface. Water is used as a traditional fluid while nanoparticles include copper and alumina. The fluid is electrically conducting, subject to an applied magnetic field with a constant strength. Convective type boundary conditions are employed in modeling the heat transfer process. The nonlinear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations and then solved using the Runge‐Kutta fourth‐order method. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity and temperature, as well as local shear stress and local Nusselt number, is presented graphically. Hartman number increase diminishes the velocity and has the contrary result in the subjective sense for the mass transfer parameter. An increase in the Prandtl number Pr lessens the temperature and thickness of the thermal boundary layer. The main conclusions have been indicated.