Study of an unsteady magnetohydrodynamic-free convective flow under parabolic ramped temperature and concentration in the presence of Soret and heat sink

The purpose of this paper is to investigate the effects of Soret, thermal radiation, and chemical reaction on an unsteady magnetohydrodynamic free convective flow past an impulsively initiated semi-infinite vertical plate with heat sink under parabolic ramped temperature and parabolic ramped concentration. Using some nondimensional parameters, the flow boundary equations in this case are first converted to dimensionless equations. The closed-form Laplace transform technique is employed here to solve the partial differential equations and get the solutions for fluid velocity, temperature, and concentration. The velocity, temperature, and concentration of the fluid tend to vary with the effect of various flow factors. These changes are graphically represented and analyzed. Differences in skin friction, Nusselt number, and Sherwood number for the different relevant parameters are also recorded. The Soret number hikes the fluid velocity and concentration. The rate of heat transfer, mass transfer, and momentum transfer improves due to the application of parabolic ramped conditions.     

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.     

Chemical reaction and magnetohydrodynamics effects on heat absorbing fluid past an inclined porous plate

The study of a heat-absorbing, chemically bonding fluid over a porous channel in a conducting field with ramped wall temperature is considered. The Dufour effect presence is also considered with thermal radiation. The novelty is the consideration of radiation absorption and the angle of inclination. In this approach, the dimensional governing equations and boundary forms are transformed into a dimensionless form using standard nondimensional parameters and variables. The simplified governing equations and boundary forms are then calculated using the Laplace transform method. We get accurate answers in the speed, temperature, and concentration spaces. Calculations of surface friction, the Nusselt number, and the Sherwood number are also performed. Several physical parameters' influences on the quantified flows are analysed using graphics. A comparison is also made with the results available in the literature and found a good agreement in the absence of radiation absorption. When a chemical is added to a fluid to dilute it, the velocity area and concentration area both decrease, but the temperature area increases as a result of an increase in the Schmidt Number, the Nusselt Number, and the skin friction. Our research revealed that the Dufour effect and arbitrarily ramped temperatures had a similar effect on fluid velocity.     

Thermal diffusion effect on unsteady MHD free convective flow past an impulsively started but temporarily accelerated semi-infinite vertical plate with parabolic ramped conditions

The purpose of the present study is to analyze the problem of a free convective MHD flow of incompressible, electrically conducting, and viscous fluid past an impulsively started semi-infinite moving vertical plate. The fluid is considered to be non-gray and optically thick. The parabolic ramped temperature of the plate and thermodiffusion effect are also taken into account. A magnetic field having uniform strength is applied in the transverse direction to the fluid velocity. Solutions of dimensionless governing partial differential equations are attained on the adoption of the closed-form Laplace transformation technique. Effects of different flow parameters on the velocity field, temperature field, concentration field, Nusselt number, skin friction, and Sherwood Number are discussed graphically. It is noticed that fluid concentration, temperature, and velocity decline considerably for ascending values of Prandtl Number. Increasing Ramped parameter hikes the Nusselt number and Sherwood Number but declines skin friction.     

Soret and heat source effects on the unsteady radiative MHD free convection flow from an impulsively started infinite vertical plate

The heat and mass transfer characteristics of the unsteady electrically conducting fluid flow past a suddenly started vertical infinite flat plate are taken into account in this paper. The radiation and heat absorption/generation effects for two distinct types of thermal boundary conditions are accounted for. Derivation of exact analytical solutions are aimed under different physical properties. The velocity, concentration and temperature profiles, skin friction coefficient, Sherwood number and Nusselt number are easily examined and discussed via the closed forms obtained. In particular, the Sherwood and Nusselt numbers are found evolve into their steady state case in the large time limit. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems.     

Transient MHD convective flow of a micropolar fluid past a moving vertical plate in the presence of thermal diffusion

In this article, we investigate a transient magnetohydrodynamic convective micropolar fluid flow over a semi-infinite vertical plate embedded in a porous medium in the presence of chemical reaction and thermal diffusion. The dimensionless governing equations are solved by adopting the regular perturbation technique. The impact of various parameters on the velocity, microrotation, temperature, concentration profiles, skin friction, Sherwood number, and Nusselt number over the boundary layer is analyzed using graphs. The fluid velocity and microrotation reduce under the effect of thermal diffusion and chemical reaction. Furthermore, concentration rises due to thermal diffusion (Soret) effect, but concentration falls under the effect of chemical reaction. It is found that the velocity and skin friction fall with enhancing value of magnetic parameter. But Sherwood number increases as the magnetic parameter increase.     

Slip Flow of Casson Rheological Fluid Under Variable Thermal Conductivity with Radiation Effects

This paper investigates the radiation and chemical reaction effects on Casson non‐Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non‐Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing.     

Numerical solution of MHD,Soret, Dufour,and thermal radiation contributions on unsteady free convection motion of Casson liquid past a semi-infinite vertical porous plate

In this paper, the unsteady motion of Casson liquid over a half-infinite penetrable vertical plate with MHD, thermal radiation, Soret, and Dufour contributions have been explored numerically. In the physical geometry, the Casson liquid flows to the layer from the penetrable vertical plate. At the layer, Casson liquid is set into motion and the flow equations are illustrated using coupled partial differential equations (PDEs). This set of PDEs is simplified to form dimensionless PDEs with the use of normal nondimensional transformation. The controlling parameters' effects on the working fluid are extensively discussed on velocity, concentration, and temperature and presented graphically. Computational values of Nusselt plus Sherwood number and skin friction for controlling parameters are depicted in a tabular form. Our outcomes show that a raise in the Casson term depreciates the velocity because of the magnetic parameter influence on the fluid flow. The Soret parameter was found to accelerate the skin friction along with the Sherwood number coefficients. An incremental value of the Dufour parameter was detected to hike the skin friction alongside the Nusselt number. Results of this study were found to be in conformity with previously published work.     

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.     

Viscous dissipation and radiation absorption effects on unsteady MHD free convective fluid flow past an inclined porous plate with chemical reaction

The current scrutinization concentrated on the consequences of viscous dissipation and chemical reaction on unsteady MHD two-dimensional free convective fluid flow past a semi-infinite inclined permeable plate with radiation absorption and heat generation. The governing equations are determined analytically by employing the perturbation technique. The impact of various physical estimators on velocity, temperature, concentration, skin friction, and Nusselt number along with Sherwood number were exemplified quantitatively through graphs. It was concluded that velocity declined with the incremental values of Eckert number, but contradictory impact occurred in the case of skin friction. In addition temperature, Nusselt number, as well as velocity, declined with the progressive values of radiation absorption. However, skin friction was accelerated with the augmented values of radiation absorption. Velocity accelerated, with the progressive values of angle of inclination. Concentration declined with the various augmentation values of chemical reaction as well as Schmidt number.     

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.     

Influence of nonlinear radiation on MHD micropolar fluid flow with viscous dissipation

This study takes account of the impact of the convective boundary conditions. The energy equation consists of Joule heating and thermal nonlinear radiation impacts. Contact between the solid and the fluid is also susceptible to a velocity slip. The resultant differential equations system is solved using homotopy analysis method. To find all numerical computations, Mathematica is utilized. The behavior, with graphical results, of pertinent parameters in micropolar fluid flow characteristics is studied. We look at the impact of the material parameter, magnetic parameter, slip parameter, and electrical parameter to grasp the physics of the problem better. Different values of skin friction, wall couple stress, and Nusselt and Sherwood numbers are discussed.     

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.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Hydromagnetic mixed convection unsteady radiative Casson fluid flow towards a stagnation-point with chemical reaction,induced magnetic field,Soret effect,and convective boundary conditions

This article presents the two-dimensional mixed convective MHD unsteady stagnation-point flow with heat and mass transfer on chemically reactive Casson fluid towards a vertical stretching surface. This fluid flow model is influenced by the induced magnetic field, thermal radiation, viscous dissipation, heat absorption, and Soret effect with convective boundary conditions and solved numerically by shooting technique. The calculations are accomplished by MATLAB bvp4c. The velocity, induced magnetic field, temperature, and concentration distributions are displayed by graphs for pertinent influential parameters. The numerical results for skin friction coefficient, rate of heat, and mass transfer are analyzed via tables for different influential parameters for both assisting and opposing flows. The results reveal that the enhancement of the unsteadiness parameter diminishes velocity and induced magnetic field but it rises temperature and concentration distributions. Moreover, higher values of magnetic Prandtl number enhance Nusselt number and skin friction coefficient, but it has the opposite impact on Sherwood number. We observe that the amplitude is higher in assisting flow compared to opposing flow for skin friction coefficient and Nusselt number whereas opposite trends are noticed for Sherwood number. Our model will be applicable to various magnetohydrodynamic devices and medical sciences.     

Model for MHD viscoelastic nanofluid flow with prominence effects of radiation

Present phenomenon is dedicated to analyze the problem of steady state flow of an incompressible fluid model pertained to as magnetohydrodynamics viscoelastic nanofluid through a permeable plate. Continuity, momentum, energy, and concentration expressions are elaborated to comprehend nature of the fluid flow. Numerical solutions are presented. The arising mathematical problem is governed by interesting parameters which include viscoelastic parameter, magnetic field parameter, nanofluid parameter, radiation parameter, skin friction, Prandtle number, and Sherwood number. Solutions for the dimensionless velocity, temperature, and concentration fields and the corresponding skin friction, Nusselt number, and Sherwood number are determined and canvassed with the help of graphs for the distinct values of pertinent parameters.     

Effect of radiation absorption and chemical reaction on MHD-free convective flow through a porous medium past an infinite vertical porous plate in the presence of constant heat flux

An incompressible, electrically conducting, and viscous fluid flowing steadily and freely across a uniformly porous media that is partially constrained by an infinitely long vertical porous plate is studied in the present article. Additionally, chemical reaction and radiation absorption effects are seen. Here, a magnetic field of uniform strength is applied transversely to the plate, a normal suction velocity is imposed on the fluid, and the heat flux is considered to be constant. The non-dimensional momentum and energy equations are solved using the method of perturbation. The problem has been analytically resolved, and several parameters, including the Hartmann number, porosity parameter, thermal Grashof number, mass Grashof number, and transport properties like the Sherwood number, skin friction, and plate temperature, are graphically represented. The current study reveals a spike in the radiation absorption effect causes skin friction to drop, but on the other hand, a contrary effect is observed for plate temperature. One of the notable findings of this investigation is that the Sherwood number increases as chemical reaction parameter influence increases.     

Hall current,radiation absorption,and diffusion thermoeffects on unsteady MHD rotating chemically reactive second-grade fluid flow past a porous inclined plate in the presence of an aligned magnetic field,thermal radiation,and chemical reaction

In this paper, we analyze the effects of Hall current, radiation absorption and diffusion thermo on unsteady magnetohydromagnetic free convection flow of a viscous incompressible electrically conducting and chemically reacting second-grade fluid past an inclined porous plates in the presence of an aligned magnetic field, thermal radiation, and chemical reaction. An exact analytical solution of the governing equations for fluid velocity, fluid temperature, and species concentration subject to appropriate initial and boundary conditions is obtained using the perturbation technique. Expressions for shear stress, rate of heat transfer, and rate of mass transfer at the plate are derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically, whereas those of shear stress and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. In addition, the skin friction on the boundary, the heat flux expressed in terms of the Nusselt number, and the rate of mass transfer described in the Sherwood number are all derived, and their behavior is studied computationally. It can be deduced that an increase in radiation absorption and hall current parameters over the fluid region increases the velocity produced. The resulting velocity continually increases to a very high level, with contributions coming from thermal and solutal buoyancy forces. Skin friction may decrease by manipulating the rotation parameter, but the Hall effect can worsen it. When the parameter for the chemical reaction increases, there is a concomitant rise in the mass transfer rate.     

Radiation effect on MHD flow past a porous vertical plate in the presence of heat sink

This study investigates heat and mass transfer in MHD convective flow through a vertical plate via porous media in the presence of radiation and a heat source/sink. It is assumed that a uniform magnetic field of strength is imposed perpendicular to the plate and directed into the fluid area. The governing nondimensional equations are solved using the perturbation technique. We further derived the skin friction, Nusselt number, and Sherwood number. The computation of results is performed with the aid of mathematical software and results are presented in graphical and tabular forms for distinct flow impacting parameters. It is observed that fluid motion is retarded due to the application of the magnetic field. Furthermore, the fluid temperature comprehensively falls under the Prandtl number as well as the thermal radiation effect. It is important to note that the heat sink causes fluid velocity and fluid temperature to fall drastically.     

Aspects of second-order velocity slip and radiation absorption on hydromagnetic stagnation point flow of Jeffrey fluid with chemical reaction

The present article describes the magnetohydrodynamic flow of a moving Jeffrey fluid along a convectively heated porous stretching surface with second-order velocity slip and radiation absorption effects. Furthermore, chemical reactions and viscous dissipation impacts are also taken into account. The governing equations are converted into dimensionless ordinary differential equations (ODEs) using appropriate similarity transformations. The highly nonlinear ODEs are solved numerically by employing a shooting technique based on the Runge–Kutta Cash–Karp formula. The figures are used to study the variations in temperature, velocity, and concentration profiles for several physical factors. The numerical values of the local skin friction, Sherwood number, and Nusselt number are explained and shown in tables. The analysis reveals that the velocity profile is enhanced for amplifying values of velocity ratio parameter and first-order velocity slip parameter. However, the temperature profile of Jeffrey nanofluid is highlighted w.r.t. Eckert number and radiation absorption parameter. This study may find significant applications in polymer production, food processing, instrumentation, combustion modeling, catalytic chemical reactors, and so on.