Thermal radiation and inclined magnetic field effects on MHD flow past a linearly accelerated inclined plate in a porous medium with variable temperature

An analysis of unsteady MHD natural convective flow, transfer of mass, and radiation past linearly accelerated slanted plate inserted in an immersed permeable medium with uniform permeability, variable temperature, and concentration within the sight of a slanted magnetic field has been done. The novelty of the current examination is to analyze the effect of a slanted magnetic field on the flow phenomena with heat source/sink and destructive reaction for linearly accelerated slanted plate. The governing equations have been solved by using Laplace transform strategy. The estimations of flow velocity, concentration, and temperature are exhibited graphically, while local skin friction, mass, and heat transfer rates are put on view in tabular form for different values of relevant stream parameters. It is fascinating to observe that the raise of inclination angle of an applied magnetic field diminishes both velocity profiles and local skin friction.     

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.     

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.     

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.     

MHD natural convection heat and mass transfer flow over an inclined porous plate with thermophoresis and nonlinear thermal radiation effects

This study examined magnetohydrodynamic natural convection mass and heat transfer flow of an electrically conducting and viscous incompressible fluid over an inclined porous plate with thermophoresis, suction/injection, and uniform magnetic field. The mathematical model governing the fluid behavior surrounding an inclined plate is solved through the Runge–Kutta–Fehlberg fourth–fifth order after utilizing the shooting method. The implication of active dimensionless parameters in the governing equations is fully discussed in detail. The results obtained show that, in the existence of nonlinear thermal radiation and suction/injection, the heat transfer rises with the increase in the angle of inclination but it decreases with the mass transfer and plate shear stress. Furthermore, the heat transfer rate experiences a serious setback due to the increase in the buoyancy force but improves the plate shear stress. The mass transfer is directly proportional to the thermophoresis effect. In addition, Particle suction increases the velocity and temperature curves while it declines the concentration profile, but the opposite is valid for injection. Nonlinear thermal radiation positively affects the temperature, velocity, and concentration profiles. The Lorentz force suppresses the fluid transport and retard the rate of particle concentration, but promotes the fluid temperature distribution. It is also deduced that increasing the rate of particle suction from 0 to 1, accounts for over 76% increase in the particle deposition at the plate surface. However, increasing the rate of particle injection from 0.004 to 0.250 accounts for an over 83% decrease in the particle deposition at the plate surface.     

Heat and mass transfer of MHD Jeffrey nanofluid flow through a porous media past an inclined plate with chemical reaction,radiation, and Soret effects

This paper investigates the heat and mass transfer of an unsteady, magnetohydrodynamic incompressible water-based nanofluid (Cu and TiO₂) flow over a stretching sheet in a transverse magnetic field with thermal radiation Soret effects in the presence of heat source and chemical reaction. The governing differential equations are transformed into a set of nonlinear ordinary differential equations and solved using a regular perturbation technique with appropriate boundary conditions for various physical parameters. The effects of different physical parameters on the dimensionless velocity, temperature, and concentration profiles are depicted graphically and analyzed in detail. Finally, numerical values of the physical quantities, such as the local skin-friction coefficient, the Nusselt number, and the Sherwood number, are presented in tabular form. It is concluded that the resultant velocity reduces with increasing Jeffrey parameter and magnetic field parameter. Results describe that the velocity and temperature diminish with enhancing the thermal radiation. Both velocity and concentration are enhanced with increases of the Soret parameter. Also, it is noticed that the solutal boundary layer thickness decreases with an increase in chemical reaction parameters. This is because chemical molecular diffusivity reduces for higher values of chemical reaction parameter. Also, water-based TiO₂ nanofluids possess higher velocity than water-based Cu nanofluids. Comparisons with previously published work performed and the results are found to be in excellent agreement. This fluid flow model has several industrial applications in the field of chemical, polymer, medical science, and so forth.     

Chemical reaction and Dufour effects on nonlinear free convection heat and mass transfer flow near a vertical moving porous plate

A theoretical analysis is made for steady fully developed free convection and mass transfer flow near an infinite vertical moving porous plate by taking into consideration the first‐order chemical reaction and Dufour effects. The mathematical model responsible for the present physical situation is based on the nonlinear density variation with temperature as well as nonlinear density variation with concentration. Exact solutions are derived for heat mass and momentum equations under relevant boundary conditions. The dimensionless velocity, temperature, and concentration are presented in terms of exponential functions. The impact of controlling parameters such as Dufour number (diffusion thermo effect), chemical reaction parameter, Prandlt number, Schmidt number, on velocity, temperature, Nusselt number, and skin friction are discussed with the aid of line graphs, contours, and tables. The analysis of the result shows that Nusselt number, skin friction, and velocity increases with increase in Dufour number. Furthermore, velocity and skin friction are higher in case of nonlinear convection in comparison to linear convection.     

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.     

Effects of chemical reaction,Soret and Lorentz force on Casson fluid flow past an exponentially accelerated vertical plate: A comprehensive analysis

The aim of the current study is to explore the effects of heat and mass transfer on unsteady chemically reacted Casson liquid flow over an exponentially accelerated vertical plate in a porous medium. It is assumed that the bounding plate has varying temperatures as well as concentrations in a porous medium under a uniform magnetic field. This phenomenon is modeled in the form of a system of partial differential equations (PDEs) with boundary conditions. The governing dimensionless PDEs are solved using Laplace transform method for velocity, temperature, and concentration. The impact of nondimensional parameters, which are controlling the flow like Casson parameter, Soret number, magnetic parameter, heat generation parameter, Prandtl number, radiation parameter, and Schmidt number is analyzed through graphs. The incremental values of the Casson fluid parameter lead to a reduction in velocity and discovered that for large values of the Casson parameter, the fluid is near to the Newtonian fluid. Also, the Sherwood number increases with enhancing dissimilar estimators of the Schmidt and Soret numbers. A comparison has been made with the published work (Kataria et al.) for a particular case, which was in good agreement.     

Effect of Dufour and chemical reaction on an unsteady magneto hydrodynamics flow past an exponentially moving plate

The aim of the study is to measure the Dufour number effects on the flow patterns and heat transfer in an exponentially accelerated infinite vertical plate embedded in a porous medium in the presence of heat source and chemical reaction. Time-dependent variations in temperature, velocity, and other factors should be taken into consideration due to the flow's unsteadiness. The fluid considered is a gray, absorbing/emitting radiation but nonscattering medium. Using the finite element method, a set of nondimensionless equations is solved analytically. Results are discussed graphically for concentration, temperature, and velocity profiles. Skin friction, Sherwood number, and Nusselt number are also explained for flow parameters through graphs.     

Unsteady thermally radiative and chemically reactive viscoelastic fluid flow past a vertical porous plate with a heat source

An analytical study is performed to investigate the thermal radiation effect on the unsteady two-dimensional magnetohydrodynamic flow of a viscoelastic incompressible fluid (Walters $B\prime$ fluid model) along an infinite hot vertical sheet embedded in a porous medium. Further, the addition of a heat source in the energy equation as well as a chemical reaction in the concentration equation renders the present analysis realistic in the field of engineering and technology. The governing equations of mass, momentum, energy, and concentration are solved with successive perturbation techniques. The effects of pertinent parameters on fluid velocity, temperature, concentration, and bounding surface coefficients are shown graphically and in tabular form. The salient feature of the present study is to impose control on magnetic field strength vis-à-vis electromagnetic force by regulating voltage in the electric circuit. The important findings are: the elasticity property of the fluid is more sensitive to heated bounding surface consequently free convection current in enhancing the velocity near the plate than the inherent property viscosity. This outcome contributes to the design requirement to control the flow near the heated surface, higher values of frequency parameters contribute to the attainment of a free stream state in temperature distribution. Besides the aforesaid outcome, the present model is conducive to thinning of boundary layer as the elasticity, magnetic as well as free convection parameters enhance the force coefficients at the bounding surface.     

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.     

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.     

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.     

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.     

Soret and Dufour effects on free convection heat and mass transfer from an arbitrarily inclined plate in a porous medium with constant wall temperature and concentration

The free convection boundary layer flow over an arbitrarily inclined heated plate in a porous medium with Soret and Dufour effects is studied by transforming the governing equations into a universal form. The generalized equations can be used to derive the similarity solutions for limiting cases of horizontal and vertical plates and to calculate the heat and mass transfer characteristics between these two limiting cases. The heat and mass transfer characteristics are presented as functions of Soret parameter, Dufour parameter, inclination variable, Lewis number, and buoyancy ratio. Results show that an increase in the Dufour parameter tends to decrease the local heat transfer rate, and an increase in the Soret parameter tends to decrease the local mass transfer rate. As the inclination variable increases, the local Nusselt number and the local Sherwood number decrease from their respective values for horizontal plates, reach their respective minima, and then increase to their respective values for vertical plates. The minima are where the tangential and normal components of buoyancy force are comparable.     

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.     

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.