MHD free convective dissipative flow past a porous plate in a porous medium in the presence of radiation and thermal diffusion effects

The problem of a hydromagnetic convective flow of an electrically incompressible viscous conducting fluid past a uniformly moving vertical porous plate is investigated analytically, taking into consideration radiation and thermal diffusion effects. A constant suction velocity is applied to the plate. A uniformly strong magnetic field is supposed to be applied normally to the plate and directed into the fluid region. To find a solution to the problem, an asymptotic series expansion method is used. The effects of thermal diffusion, magnetic field, porosity parameter, thermal radiation, and Grashof number are mainly focused on the discussion of the current problem. Increasing Soret number (Sr) hikes the velocity profile and skin friction but declines Sherwood number. Also, it has been found that, when the magnetic parameter (M) increased, the fluid velocity and the concentration profile decreased. The current results show a good deal of agreement with previously published work. The findings of this study could be relevant in a variety of applications, including diffusion processes involving molecular diffusion of species with molar concentration.     

Natural convective flow past a suddenly started vertical plate with uniform mass and heat flux in the presence of radiation,thermal diffusion

An attempt has been made to investigate the problem of a natural convective radiative flow past an impulsively moving vertical plate with uniform mass and heat flux in the existence of the thermal diffusion effect. The resulting governing equations are solved by the Laplace transform technique in closed form. Effects of radiation, Prandtl number, Soret number, Grashof number, modified Grashof number, and Schmidt number are studied on temperature field, concentration field, velocity field, plate temperature, plate concentration, skin friction, and are demonstrated through graphs. The present study reveals that an intensification of the thermal radiation effect causes a downfall in the fluid temperature, plate temperature, and skin friction, but a contradictory outcome is spotted for plate concentration. One of the significant findings of this study includes that the increasing thermo-diffusion effect hikes the concentration and frictional resistance of the field.     

Effects of chemical reaction and thermal radiation on MHD free convective flow of micro polar fluid past an infinite moving vertical porous plate with viscous dissipation

This article discusses the impact of chemical reaction and radiation on an unstable two-dimensional laminar flow around a viscous fluid over a semi-infinite, vertical absorbent surface that moves progressively. The governing classification of partial differentiation was converted into an ordinary differentiation system in this case. To get numerical solutions, the Galerkin finite element technique is applied to nondimensional velocity, micro-rotation, temperature, and concentration profiles. The consequences of skin friction, the combined pressure quantity, the mass, and heat assignments at the boundary are formed using different fluid properties and flow conditions. Physical quantities and their effects Graphs depict the radiation parameter R, thermal conductivity k, Eckert number Ec, and other velocities, micro-rotation, temperature, and concentration factors. The main findings of this current problem is showing the chemical reaction effects on velocity and concentration. It is observed that both the velocity and concentration of the fluid decrease when Kr increases.     

Impact of thermal diffusion and chemical reaction on oscillatory MHD convective flow of a viscoelastic fluid through a porous medium in a slip flow regime

The purpose of the current investigation is to analyze the influence of thermal diffusion on magnetohydrodynamic viscoelastic fluid flow with concurrent heat and mass transfer near an oscillating porous plate in a slip flow Regime under the influence of a uniform transverse magnetic field. The uniqueness of the present study is to examine the effects of viscoelastic property (Walters B' model) on the flow and heat transfer phenomena when a transverse magnetic field and time-dependent fluctuating suction at the boundary surface are present in a porous medium with a uniform porous matrix. A regular perturbation technique is used to solve the governing equations for small elastic parameters. Graphical representations are used to show how different parameters affect skin friction, temperature, concentration, and velocity. It is observed that concentration distribution as well as the coefficient of friction is enhanced due to the thermal diffusion effect. It is noticed that the visco-elastic parameters reduce the velocity of the fluid. In addition, chemical reactions and suction factors cause the flow field's temperature to drop. Furthermore, the fluid concentration drops under the chemical reaction effect.     

Aspects of parabolic motion of MHD fluid flow past a vertical porous plate with cross-diffusion effects

In the presence of Soret and Dufour effects, a numerical analysis is performed for an unstable magnetohydrodynamics convective flow of parabolic motion with variable temperature and concentration. The finite-difference method is used to solve the set of nondimensional governing equations with boundary conditions numerically. Graphs are used to investigate the effect of various physical characteristics on flow quantities. Variations in skin friction, Nusselt number, and Sherwood number are also examined using tables for physical curiosity. This study is unique in that it takes into account changeable temperature as well as concentration with Soret and Dufour effects. The magnetic parameter, Prandtl number, heat source, radiation parameter, Schmidt number, and chemical reaction parameter show a significant increase in skin friction, whereas the Grashof number, modified Grashof number, permeability parameter, radiation absorption parameter, Dufour number, and Soret number show the opposite trend. As the Soret number rises, the concentration rises as well, whereas the opposite is true for the Schmidt number and the chemical reaction parameter. The current study is highly supported by previously published data that have been verified.     

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.     

Effect of material parameter on mixed convective fully developed micropolar fluid flow in a vertical channel

In this study, the effect of material parameter on the mixed convective fully developed micropolar fluid flow in a vertical channel has been analyzed. By considering appropriate boundary and interface conditions, the coupled nonlinear equations are solved analytically. The analytical results are plotted for various important parameters. It is found that an increase in the material parameter enhances the microrotation velocity and decreases the fluid velocity, and the results are shown graphically.     

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.     

Study of an unsteady fluctuative MHD flow of elasticoviscous liquid past a vertical porous plate

Most flows which occur in nature/practical applications are fluctuating. The fluctuating motions superimposed on the main motion are complex. Further, the unsteadiness of the flow is an added reality to applications in various fields. The free convection flow of an electrically conducting fluid past different types of vertical bodies subjected to a magnetic field is studied because of its wide range of applications in astrophysics, geophysics, aerodynamics, electromagnetic pumps, the flow of liquid metals, and so forth. In the present analysis, an attempt has been made to study the thermal radiation effect on the unsteady magnetohydrodynamic flow of an incompressible elasticoviscous liquid (Walters-B' fluid model) along an infinite hot vertical permeable surface embedded in a porous medium with heat source and chemical reaction. The governing equations of motion, energy, and concentration are solved by an approximate analytical method, that is, the successive perturbation technique and numerical method (Runge–Kutta with shooting). The solution procedure rests upon the basic assumption that the unsteady boundary layer involves a steady basic flow superimposed on an unsteady flow. The most striking outcome is that the combined effect of oscillation outflow, the elasticity of the fluid, and thermal as well as mass buoyancy overrides the resistive electromagnetic force and suction at the plate to enhance the velocity so that high values of magnetic strength are not desired. Further, a higher value of the heat source parameter accelerates the momentum diffusion resulting in the escalation of the velocity field. Fall of concentration is relatively faster in cases of heavier species as well as destructive reactions. The heat transfer coefficient assumes positive values indicating the heat flows from the plate to the fluid (cooling of the bounding surface and heating of the fluid). These observations may have industrial (design of heat exchanges) and therapeutic bearings.     

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.     

Chemical reaction effects on magnetohydrodynamic convective flow past a vertical absorbent plate with ramped wall temperature and concentration

The numerical analysis is conducted to evaluate the heat generating as well as Soret–Dufour influences on magnetohydrodynamic unsteady chemically reacting fluid. It is owing to an exponentially stimulating perpendicular porous plate entrenched in the absorbent medium by considering ramped surface temperatures and concentrations in the endurance of thermal radiating. The fundamental governing set of equations of the fluid dynamics in the flow is converted into dimensionless form by inserting suitable dimensionless parameters and variables, and the resulting equations are numerically solved by the efficient Crank–Nicolson implicit finite difference method. The influence of several important substantial parameters into the model on the velocity, temperature, and concentration of the fluid, in addition to the skin-frictions coefficient, Nusselt's number along with Sherwood's number for both thermal conditions has been studied and explored intensely by making use of graphs and tables. It is discovered that, with mounting values of Dufour, heat generating as well as thermal radiating parameters, the fluid temperatures, and velocity enhanced. Likewise, it is noticed that increasing the Soret parameter causes escalated fluid velocity and concentration, whereas the reverse result is noted with the chemical reaction parameter.     

Incidences of aligned magnetic field on unsteady MHD flow past a parabolic accelerated inclined plate in a porous medium

An exact analysis of a radiative hydromagnetic flow behavior over a tilted parabolic plate through a permeable medium along with variable species concentration and fluid temperature in the presence of a slanted magnetic field parameter, chemical reaction, and heat generation has been carried out in this study. Closed-form analytical benchmark solutions for flow-governing equations are obtained by using the Laplace transform method. Thereafter, the incidences of different important physical entities on the nondimensional velocity field, temperature distribution, and species concentration are presented using graphs, whereas impacts of various physical entities on wall shear stress, heat and mass transfer rates are presented in tables. It is worth noting that an increase in the magnetic field and its inclination angle causes the reduction in the fluid velocity. However, wall shear stress increases with the increase of magnetic field and its inclination angle. The novel results in this article can be used to improve quicker cooling and producing miniaturized heat flow systems with upgraded efficiency and cost-effectiveness.     

Unsteady MHD fluid flow past an inclined vertical porous plate in the presence of chemical reaction with aligned magnetic field,radiation, and Soret effects

The aim of the present paper is to investigate the Soret effect due to mixed convection on unsteady magnetohydrodynamics flow past a semi-infinite vertical permeable moving plate in the presence of thermal radiation, heat absorption, and homogenous chemical reaction subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using the perturbation technique. Graphical results for the velocity distribution, temperature distribution, and concentration distribution based on the numerical solutions are presented and discussed. Also, the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number, and rate of mass transfer in the form of Sherwood number at the surface are discussed. Velocity distribution is observed to increase with an increase in Soret number and in the presence of permeability, whereas it shows reverse effects in the case of the aligned magnetic field, inclined parameter, heat absorption coefficient, magnetic parameter, radiation parameter, and chemical reaction parameter.     

Hall effects on MHD chemically reacting flow of second grade fluid past a vertical porous plate

The scrutiny of the consequences of radiation-absorption, chemical reaction impacts on unsteady magnetohydrodynamics heat and mass transportation laminar flow of a gelatinous, electrical conducting by the heat generation or absorption second grade fluid embedded past a half-unlimited porous surface within a gyratory structure taking Hall effects into account have been discussed. The plate is assumed to as in the motion by the invariable velocity contained by the direction of fluid movement. A uniform magnetic field performed at perpendicular to the porous plate; this is engrossing the fluid with the suction velocity changing with definite instants of time. The corresponding dimensionless governing equations of current configuration are solved by making use of perturbation technique with reference to harmonic and nonharmonic idioms. The velocity, temperature, and concentration profiles are discussed and examined with references to various governing parameters in detail. The results are verified with the published work. The velocity components are increased with increasing permeability and Hall parameters. It is noticed that practical application of Hall effects is as, washing machine dial to select the type of washing moves very smoothly. This problem has also applications in biomedical and aerospace engineering.     

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.     

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation,diffusion-thermo,heat sink,and chemical reaction

An attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength $B_0$, a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.     

Numerical study on the parabolic flow of MHD fluid past a vertical plate in a porous medium

A numerical investigation on MHD fluid flow in parabolic mode has been performed to point out its significant properties. Thermal radiation, porous medium, heat generation, chemical reaction, and thermal diffusion along with variable temperature and concentration are taken into consideration in the analysis. The novelty of the work is the inclusion of heat generation and thermal diffusion along with exponentially varying temperature and concentration. The constituent governing equations are solved by using finite difference schemes in explicit form. The fluctuations in velocity, concentration, and temperature are observed and discussed with the help of graphs as well as numerical data. Their gradients are also calculated and analyzed the flow properties by using numerical tables. The existence of heat generation, as well as viscous dissipation, creates an increment in the temperature. The gradient of heat transfer rises with the impact of Prandtl number and decay in it is examined under the existence of a source of heat and viscous dissipation.     

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.     

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

The present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first-order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first-order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.     

Stability analysis on dual solutions of MHD Casson fluid flow with thermal and chemical reaction over a permeable elongating sheet

The endeavor of this study is to explore the nature of dual solutions (steady and unsteady) for the Casson fluid flow with the simultaneous consequences of both thermal and mass transmissions. The flow passes above an absorbent elongating sheet in the existence of a constant magnetic field. The supported leading equations are remodeled into a set of solvable forms with the assist of suitable similarity variables and hence deciphered utilizing the “MATLAB routine bvp4c scheme.” Due to the sudden changes in the surface with time, the temperature and flow behavior over the sheet also change, and hence dual-type flow solutions exist. Stability scrutiny is implemented to examine the less (more) stable and visually achievable solutions. From this study, we have achieved many interesting facts, among them, we can use magnetic and Casson fluid parameters to control the motion of the fluid and to enlarge of thermal transmission of the fluid. This flow model has many important applications in different physical fields, such as engineering sciences, medical sciences, and different industrial processes. One of the most important results, which has been achieved from this investigation, is that the Prandtl number enriches the heat transfer rate of the fluid at the surface during the time-independent case under the suction environment. Also, the chemical reaction parameter helps to enhance the mass accumulation rate of the fluid in both cases.