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.     

Magnetohydrodynamic chemically reactive viscoelastic fluid flow through an inclined porous layer

Analysis of a time-independent magnetohydrodynamic viscoelastic fluid flow in a deformable inclined porous layer with first-order chemical reaction has been investigated. Walters' fluid model has been used to study viscoelastic fluid. The walls are suctioned/injected at a constant rate. The expression representing the solution for solid displacement, fluid velocity, temperature, and concentration distribution is obtained. The effect of applicable parameters on solid displacement, fluid velocity, temperature, and concentration are discussed graphically, while skin friction, heat transfer, and mass transfer are revealed in a tabular structure. It is noticed that solid displacement, fluid velocity, and temperature profiles decrease when the viscoelastic parameter increase. Solid displacement enhances and the velocity of the fluid reduces owing to the influence of increasing drag parameter, whereas the reverse effect is seen for the volume fraction parameter. Nusselt number at the walls shows the opposite behavior for the viscoelastic parameter and Eckert number. Sherwood number at the walls shows opposite behavior for Reynolds number, Schmidt number, and radiation parameter. Also, the entropy generation number rises as a result of the influence of viscoelasticity and Eckert number.     

Magnetohydrodynamic flow of a nanofluid due to a non‐linearly curved stretching surface with high order slip flow

This article numerically scrutinizes magnetohydrodynamic flow of a nanofluid due to a nonlinearly curved stretching surface with third order slip flow conditions. The third order slip flow condition has not yet been discussed in fluid dynamics research. The mathematical modeling of the flow problem is given in partial differential equation form. The governing partial differential equations are transformed to high order ordinary differential equations using the similarity transformation and then solved numerically using a boundary value problem solver, bvp4c from Matlab software. The effect of the governing parameters on the flow of the velocity profile, concentration, and heat transfer characteristics are studied. Also graphs of the skin friction coefficient, local Nusselt number, and Sherwood number are drawn and their numerical values are tabulated. The numerical results of the study are compared with previously published articles in the limiting condition. The velocity of the flow field is reduced as the third order slip parameter and the first order slip parameter rises, but the velocity grows as the values of the second order slip flow parameter are elevated. The findings also indicate that the local Nusselt number is depreciated but local Sherwood numbers are elevated when the Soret and Dufour numbers are larger.     

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.     

Nanofluid Flow in a Porous Channel with Suction and Chemical Reaction using Tiwari and Das's Nanofluid Model

In this paper, an analysis is made for a nanofluid flow in a porous channel by introducing the conservation equation of nanoparticle volume fraction into Tiwari and Das's nanofluid model. The suction and chemical reaction are also considered in this work. The governing partial differential equations are simplified by employing a new variable and transformed into a system of high‐order nonlinear ordinary differential equations by similarity transformations. The Keller box method is used to solve this problem numerically. In addition, the influences of significant physical parameters on the distributions of the velocity and temperature as well as nanoparticle concentration are graphically presented and discussed in detail. It is found that there exists a critical value of the permeable parameter which determines the influence law of nanoparticle volume fraction parameter on skin friction coefficient and local Sherwood number. The results also indicate that the concentration increases sharply with the Schmidt number and chemical reaction 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.     

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.     

MHD nonlinear natural convection flow of a micropolar nanofluid past a nonisothermal rotating disk

The aim of this analysis is to examine the steady, laminar boundary layer flow of a micropolar nanofluid owing to a rotating disk in the presence of a magnetic field and thermal and solutal nonlinear convection and nonisothermal parameters. The governing joined partial differential equations are converted into nonlinear ordinary differential equations by means of available transformations. The equations are calculated using the method bvp4c from Matlab software. The convergence test has been maintained; for the number of spots greater than the appropriate mesh number of points, the precision is not influenced, but the set time is boosted. Moreover, various quantities of the main parameters on skin friction coefficients, wall couple stress coefficients, Nusselt number, Sherwood number, velocities, temperature, and concentration of nanofluid are analyzed by means of tables and graphs. The results indicate that the presence of the nonisothermal parameter boosts the radial skin friction, temperature, and Sherwood number but causes decaying concentration distributions, the azimuthal skin friction coefficient, and Nusselt number that indicate the diffusion of momentum occurs more around the surface of the rotating disk.     

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.     

Numerical analysis of MHD nanofluid flow over a wedge,including effects of viscous dissipation and heat generation/absorption,using Buongiorno model

The key purpose of this article is to examine magnetohydrodynamics flow, generative/absorptive heat, and mass transfer of nanofluid flow past a wedge in the presence of viscous dissipation through a porous medium. The investigation is completely theoretical, and the present model expresses the influence of Brownian motion and thermophoresis using the nanofluid Buongiorno model. The fundamental model of partial differential equations is reframed into the structure of ordinary differential equations implementing the nondimensional similarity transformation, which are tackled through the fourth–fifth-order Runge–Kutta–Fehlberg algorithm together with the shooting scheme. The analysis of sundry nondimensional controlling parameters, such as magnetic parameter, Eckert number, heat generation/absorption parameter, porosity parameter, Brownian motion parameter, and thermophoresis parameter on velocity, temperature, and concentration profiles are discussed graphically. The effects of the physical factors on the rate of momentum and heat and mass transfer are also determined with appropriate analysis in terms of skin friction, Nusselt number, and Sherwood number. The outcomes illustrate that the local Nusselt number and local Sherwood number are reduced for higher values of the thermophoresis parameter. Besides, it is found that higher estimations of heat generation/absorption and viscous dissipation parameters increase temperature. Moreover, it is found that the temperature profile increases with the involvement of the Brownian motion parameter, while an opposite trend is observed in the concentration profile. A comparison is also provided for limiting cases to authenticate our obtained results.     

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.     

Influence of relaxation-retardation viscous dissipation on chemically reactive flow of Oldroyd-B nanofluid with hyperbolic boundary conditions

The present analysis is meant to explore the computational solution of the problem dealing with the impact of relaxation-retardation viscous dissipation and chemical reaction on the flow of Oldroyd-B nanofluid over a Riga plate. Hyperbolic time-varying boundary conditions are taken into consideration. The basic modeled problem being transformed into nonlinear differential equations are solved numerically by efficient fourth-order Runge-Kutta method along with shooting technique. Characteristics of controlling parameters on velocity, temperature, and concentration along with skin friction, Nusselt number, and Sherwood number profiles are presented with the help of well-featured graphs. The relaxation and retardation parameters affect well flow profiles. In addition, an accelerated flow pattern is accomplished due to the augmentation of the modified Hartmann number. Furthermore, the presence of relaxation-retardation viscous dissipation improves the temperature field.     

The eventuality of diffusiophoresis and chemical reaction in a flow with variable fluid properties through an upright channel

The quintessence of this article encompasses the effect of diffusiophoresis, chemical reaction, and varying viscosity as well as thermal conductivity on a fully developed dissipative flow through an upright channel. The fluid is electrically conducting undergoing mixed convection. The governing equations, after transfiguring into dimensionless formation, are solved through a numerical procedure for boundary value problems incorporating MATLAB solver. Imperative scrutiny is made to visualize associative impacts of flow parameters, namely, magnetic parameter, the Brinkmann number, the Schmidt number, variable viscosity parameter, variable thermal conductivity parameter, chemical reaction parameter, diffusiophoretic parameter, and particle diffusion parameter, on the flow. The velocity field, the temperature field, the solute concentration field, the particle concentration field, the skin friction, the Nusselt number, the Sherwood number, and the particle concentration gradient are assessed in view of alteration of the aforesaid parameters with the help of visual illustrations in graphical form and tabular form. Solute mass transposition and colloidal particle locomotion are the fresh inclusions to the scrutiny of upright channel flow in light of solving scheme of bvp4c. Chemical reaction engulfs both solute and particle concentration. Growing viscosity hinders the fluid velocity and heats up the flow encouraging interlayer friction.     

Nanofluid flow over three different geometries under viscous dissipation and thermal radiation using the local linearization method

This study deals with the transfer of mass and heat of nanofluid flow over three different geometries of the non‐Darcy permeable vertical cone/wedge/vertical plate. Influence of the Brownian motion and thermophoresis takes place due to the nanofluid. Boundary condition on the temperature is introduced at the surface where the thermal conductivity of the fluid obeys a linear relation with the temperature. The local linearization method is introduced for solving the governing equations, and is based on spectral discretization. To verify the numerical scheme, we compared our results with those in the existing literature. The impact of the governing parameters on the fluid velocity, temperature distribution, and concentration distribution of nanoparticles along with the Nusselt number and Sherwood number is discussed. Some important outcomes of the present study are that the Nusselt number is higher for the plane plate than that for the vertical cone and it significantly decreases with introduction of the radiation parameter. The nanofluid Lewis number decreases the diffusivity of mass of the nanofluid, and as a result it helps enhance the Sherwood number.     

Chemically reactive and radiative flow of ferro-aluminum (AA7075) hybrid nanofluid past a stretching cylinder

The present investigation throws light on the heat transfer behavior of hybridized (ferro-aluminum alloy [AA7075]) nanofluid. In addition to that, influences of thermal radiation, magnetic effect, and chemical reaction are also considered for the exploration. Here, the flow is deliberated due to a porous stretching cylinder. The equations that portray the fluid flow are transfused to simple ordinary differential equations by applying similarity elements. Then, the procured equations have been solved by adopting the Runge–Kutta–Fehlberg 4th–5th order tool. The extracted solution are exported to plot graphs for velocity, thermal, and solutal profiles with the concerned parameters, and using these plots, the discussion has been produced for the behavior of all flow fields. The behavior of the thermal profile shows substantial enhancement with an increase in the solid volume fraction of hybrid nanofluid. The velocity and concentration panel de-escalates for larger values of Reynolds number. A significant discussion on the skin friction drag, Nusselt number, and Sherwood number has been produced.     

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.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Influence of nonlinear thermal radiation on mixed convective hybrid nanofluid flow about a rotating sphere

The present study investigates the mixed convective hybrid nanofluid flow over a rotating sphere under the impact of nonlinear thermal radiation. A model is built to examine the heat transport performance of ferrimagnetic magnetite and copper nanoparticles over a rotating sphere. Nonsimilar transformations are used to nondimensionalize the coupled nonlinear governing equations and the flow model's boundary conditions. Furthermore, the nondimensional governing equations were solved using implicit finite difference approximation and the quasilinearization technique. The impacts of the flow regime on many controlling parameters are then thoroughly addressed. Temperature patterns improve when nonlinear thermal radiation and hybrid nanofluid values increase. The fluid velocity and skin friction coefficient increase in the streamwise direction while decreasing in the rotating direction. The separation of the boundary layer is delayed as the sphere's rotation weakens. The stationary sphere has a larger boundary layer separation than the revolving sphere. The velocity distribution improves with increasing rotation parameter values while decreasing with increasing combined convection parameter values in the rotating direction. An increase in the temperature ratio parameter makes the fluid get hotter, and the Nusselt number goes down simultaneously. Nusselt number and skin friction coefficient in the rotation direction increase, while skin friction coefficient in streamwise direction reduces for increasing values of hybrid nanofluid. The velocity of the fluid enhances in the stream-wise direction while reducing in the rotational direction with the increasing values of the combined convection parameter.     

Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet

The unsteady boundary layer flow of a nanofluid over a permeable stretching/shrinking sheet is theoretically studied. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. The results are obtained for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle fraction profiles for some values of the governing parameters, namely, the unsteadiness parameter, the mass suction parameter, the Brownian motion parameter, the thermophoresis parameter, Prandtl number, Lewis number and the stretching/shrinking parameter. It is found that dual solutions exist for both stretching and shrinking cases. The results also indicate that both unsteadiness and mass suction widen the range of the stretching/shrinking parameter for which the solution exists.