Physical aspects on unsteady MHD‐free convective stagnation point flow of micropolar fluid over a stretching surface

The unsteady magnetohydrodynamic (MHD) stagnation point flow of micropolar fluid across a vertical stretching surface with second‐order velocity slip is the main concern of the present paper. The influence of electrical energy, temperature‐dependent thermal conductivity, thermal radiation, Joule heating, and heat sink/source is investigated. The basic partial differential equations are changed into ordinary differential equations with the help of appropriate similarity variables and then solved by the fourth‐order Runge‐Kutta–based shooting technique. The impact of physical parameters on the velocity, microrotation, and temperature as well as friction factor, couple stress, and local Nusselt number is thoroughly explained with the support of graphs and tables. The results divulge that the heat source/sink and thermal radiation parameters have a propensity to enhance the fluid temperature. The distribution of velocity is an increasing function of an electric field and unsteadiness parameter. The numerical results are also compared with the results available in the literature.     

Rotation,electromagnetic field,and variable thermal conductivity effects on free convection flow past an eternity vertical porous plate

The present research may facilitate the reduction of the number of conversion steps required to include the low output voltages in an electrokinetic biomass process. Variable thermal conductivity and electroosmosis flow have already established great potential in the thermo-elastic models of various manufacturing industries and have been widely used in energy technologies. As a result, the current framework investigates the characteristics of natural convection flow with the influence of variable thermal conductivity and electroosmosis over an eternity vertical porous plate. Coriolis forces and Hall current effects are considered in the momentum equations, and also thermal radiation and variable thermal conductivity are taken as energy equations. A linear chemical reaction parameter is used in the concentration equation. The equation of Poisson–Boltzmann is exploited to depict the electric potential characteristics within the accelerated plate medium. The pdepe command in Matlab software is used to figure out the numerical solutions to equations about momentum, energy, and concentration. The expressions of fluid transverse velocity, fluid axial velocity, fluid temperature, and concentration profiles are presented as numerical results and also derived vital relevant stream parameters diagrammatically, whereas the numerical values of primary skin friction, secondary skin friction, and Nusselt number are presented in tabular form for various values of pertinent flow parameters. The temperature rises as the strength of the thermal conductivity variable parameter increases. Also, as the values of the Taylor number and the thermal conductivity variable parameter go up, the primary velocity goes down. Similarly, secondary velocity increases in the opposite direction as the Taylor number and thermal conductivity variable parameter increase.     

Thermo-electrokinetic rotating non-Newtonian hybrid nanofluid flow from an accelerating vertical surface

This paper explores the combined effects of Coriolis force and electric force on the rotating boundary layer flow and heat transfer in a viscoplastic hybrid nanofluid from a vertical exponentially accelerated plate. The hybrid nanofluid comprises two different types of metallic nanoparticles, namely silver (Ag) and magnesium oxide (MgO) suspended in an aqueous base fluid. The Casson model is deployed for non-Newtonian effects. An empirical model is implemented to determine the thermal conductivity of the hybrid nanofluid. Rosseland's radiative diffusion flux model is also utilized. An axial electrical field is considered and the Poisson–Boltzmann equation is linearized via the Debye–Hückel approach. The resulting coupled differential equations subject to prescribed boundary conditions are solved with Laplace transforms. Numerical evaluation of solutions is achieved via MATLAB symbolic software. A parametric study of the impact of key parameters on axial velocity, transverse velocity, nanoparticle temperature and Nusselt number is conducted for both the hybrid (Ag–MgO)–water nanofluid and also unitary (Ag)–water nanofluid. With increasing volume fraction of silver nanoparticles, there is a reduction in both axial velocity and temperatures, whereas there is a distinct elevation in transverse velocity for both unitary and hybrid nanofluids. Elevation in the heat absorption parameter strongly decreases axial velocity, whereas it enhances transverse velocity. Increasing the radiation parameter strongly boosts temperatures. Increasing the heat absorption parameter significantly accelerates the transverse flow. Negative values of Helmholtz–Smoluchowski velocity decelerate the axial flow whereas positive values accelerate it; the opposite behavior is observed for transverse velocity. Increasing Taylor number significantly damps both the axial (primary) and transversal (secondary) flow. Increasing thermal Grashof number strongly enhances the axial flow but damps the transverse flow. The unitary nanofluid achieves higher Nusselt numbers than the hybrid nanofluid but these are decreased with greater radiative effect (due to greater heat transport away from the plate surface), Prandtl number and heat absorption. Nusselt number is significantly reduced with greater time progression and values are consistently higher for the unitary nanofluid compared with hybrid nanofluid. The computations provide insight into more complex electrokinetic rheological nanoscale flows of relevance to biomedical rotary electro-osmotic separation devices.     

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

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

Effects of variable electric conductivity and non-uniform heat source (or sink)on convective micropolar fluid flow along an inclined flat plate with surfaceheat flux

Numerical simulations have been carried out to investigate the effects of the fluid electric conductivity and non-uniform heat source (or sink) on two-dimensional steady hydromagnetic convective flow of a micropolar fluid (in comparison with the Newtonian fluid) flowing along an inclined flat plate with a uniform surface heat flux. The local similarity solutions are presented for the non-dimensional velocity distribution, microrotation, and temperature profiles in the boundary layer. The significance of the physical parameters on the flow field is discussed in detail. The results show that the values of the skin-friction coefficient and the Nusselt number are higher for the case of constant fluid electric conductivity compared with those for the variable fluid electric conductivity. The effect of temperature dependent heat generation is much stronger than the effect of surface dependent heat generation. The results also show that effects of the fluid electric conductivity and non-uniform heat generation in a micropolar fluid are less pronounced than that in a Newtonian fluid.     

Analysis of dissipative non-Newtonian magnetic polymer flow from a curved stretching surface with slip and radiative effects

The convective–radiative magnetohydrodynamic non-Newtonian second-grade fluid boundary layer flow from a curved stretching surface has been scrutinized in the present study. The Reiner–Rivlin second-grade viscoelastic model is deployed which provides a good approximation for certain magnetic polymers. High temperature invokes the presence of radiative heat transfer, which is simulated with the Rosseland diffusion approximation. Viscous dissipation and Joule heating are also featured in the model and hydrodynamic (velocity) slip at the wall is also incorporated in the boundary conditions. The emerging nonlinear coupled dimensionless transport equations are solved with a Runge–Kutta method and a shooting numerical scheme. The influence of emerging multiphysical flow parameters on the dimensionless profiles is examined with the help of plots for comparative analysis of both non-Newtonian fluid and Newtonian fluid. The numerical solutions are validated for special cases with existing works. The velocity declines for a higher magnetic field, whereas the reverse trend is noted for the temperature function. The augmentation in the thermal field is noted with increments in radiation parameters. Furthermore, the fluid temperature of the second-grade fluid is higher with increasing Brinkmann number. The wall slip induces deceleration. Contour plots for streamlines and isotherms are also visualized and analyzed.     

Flow and thermal analysis of Oldroyd 8 constant fluid in a porous channel

The present research is based on the thermal and flow properties of the viscoelastic Oldroyd 8 constant fluid in an upright microchannel. The energy and momentum equations were solved with the support of temperature Jump and velocity slip boundary conditions. To measure the irreversibility rate of the flow system, the acquired results of velocity and thermal equations were used. To crack the current mathematical model problem, the numerical Runge–Kutta–Fehlberg method was used. With the aid of graphs, the effect of physical parameters such as thermal radiation, thermal-dependent heat source, Joule heating, fluid parameters, velocity slip, and temperature Jump parameters on the fluid flow, thermal energy, and system entropy generation was discussed. Fluid parameters have different effects on the velocity profile. The Grashof and Hartmann numbers demonstrate opposite effects on the momentum field. The thermal energy of the system reduces with thermal radiation and temperature Jump factor. The thermal radiation, Hartmann number, and temperature Jump parameters reduce the system's irreversibility rate. With the Brinkman number and temperature Jump parameter, the irreversibility ratio increases.     

Entropy analysis of MHD flow of Jeffrey fluid in an inclined channel

This study is aimed at investigating the influence of entropy analysis of magnetohydrodynamic flow of Jeffrey fluid in an inclined micro-channel in the presence of thermal radiation and field suction/injection. We have improved the mathematical model of the physical problem under consideration. The designed equations have been solved by applying the shooting-based fourth-order, Runge–Kutta method with the boundary conditions, which describe velocity slip and temperature jump conditions at the fluid–wall inter-face. Numerical efforts are described graphically and mentioned quantitatively concerning different parameters such as Jeffery parameter, Bejan number, and entropy generation embedded in the problem. The numerical results for the expression of the irreversibility ratio are obtained. It is observed that the wall inclination strengthens the entropy production rate in the micro-channel, and the thermal buoyancy layer induces an increase in fluid velocity as suction.     

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

Radiation Effects on Turbulent Mixed Convection in an Asymmetrically Heated Vertical Channel

The purpose of present study is to numerically investigate the radiation effects on turbulent mixed convection flow between two differentially heated vertical parallel plates. Two flow situations known as aiding and opposing flow are considered. Frictional Reynolds number and Grashof number are assumed to be 150 and 1.6 × 10⁶, respectively. Both hydrodynamically and thermally developing and fully developed regions in the channel are investigated. Three Reynolds-averaged Navier–Stokes-based low Reynolds turbulence models are evaluated and the model with better overall performance is applied to the simulations. The radiative transfer equation for the gray and participating fluid is solved using the discrete-ordinates method, adopting its eighth-order quadrature scheme. The effects of two radiative parameters, namely, wall emissivity and optical thickness, on the flow and thermal fields, Nusselt number, and friction factor are addressed. Present results indicate that the presence of thermal radiation has a significant influence on flow and thermal fields. With an increase in wall emissivity and optical thickness, influence of radiation on the mean velocity, mean temperature, and turbulence kinetic energy profiles grows in both aiding and opposing regions. This results in an increase in bulk temperature, centerline velocity, and Nusselt number and a decrease in friction factor on both sides.     

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.     

Significance of Dufour and Soret effects on the non-Darcy flow of Cross fluid by a tilted plate with radiation and chemical reaction: A Cattaneo–Christov heat flux model

The Darcy–Forchheimer flow model is substantial in the fields where a high flow rate effect is a common phenomenon, for instance, in petroleum engineering. In this paper, we aim to scrutinize the aspects of cross-diffusion effects on the non-Darcy flow of Cross fluid by a tilted plate with thermal radiation and chemical reaction. Metamorphosed equations are resolved with the combination of shooting and Runge–Kutta fourth-order procedures. The correlation coefficient is used to discuss the impact of pertinent parameters on friction factor and transfer rates (heat and mass). The main findings of this study are that the Dufour number escalates fluid temperature and the Soret number ameliorates the fluid concentration. It is observed that the fluid velocity minifies with the elevation in the Forchheimer number. And also, it is perceived that the heat transfer rate has a generous positive relationship with the thermal relaxation parameter. Furthermore, validation of current results with the earlier results under specified conditions is performed and an adequate concord is seen.     

A study of electro-osmotic and magnetohybrid nanoliquid flow via radiative heat transfer past an exponentially accelerated plate

This paper explores the electro-osmotic flow with a uniform magnetic transverse field and thermal radiation. An investigation has been conducted on electromagnetohydrodynamics (EMHD) boundary layer past a moving upright accelerated plate in hybrid nanoliquids. Two specific water-based hybrid nanoliquids are taken into account, which include copper and aluminum oxide. To define the electrical potential distribution in the fluid medium, the Poisson–Boltzmann distribution is used and linearized by Debye–Huckel. The control equations are solved by the transformation technique of Laplace and results are obtained in a closed shape. The quantitative analysis of the nanoliquid temperature, axial velocity, and Nusselt number on the accelerated plate for several values of the related parameters is shown by a graph. Hybrid nanoliquids are known to create fluid flows significantly larger than nanoliquids, which are very helpful in cleaning the contaminated water in a nuclear plant.     

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.     

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.     

Radiation and mass transfer effects on flow of an incompressible viscous fluid past a moving vertical cylinder

The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past a moving vertical cylinder with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations are solved using an implicit finite-difference scheme of Crank-Nicolson type. Numerical results for the transient velocity, the temperature, the concentration, the local as well as average skin-friction, the rate of heat and mass transfer are shown graphically. It is found that at small values of the Prandtl number and radiation parameter N, the velocity and temperature of the fluid increases sharply near the cylinder as the time t increase, which is totally absent in the absence of radiation effects.     

Significance of thermal radiation on dusty fluid flow over a stretching rotating disk with convective boundary condition

This paper explores the flow of dusty fluid over a stretching rotating disk with thermal radiation. Further, the convective boundary condition is considered in this modeling. The described governing equations are reduced to ordinary differential equations by using apt similarity transformations and then they are numerically solved using Runge–Kutta–Fehlberg-45 scheme. To gain a clear understanding of the current boundary layer flow problem, the graphical results of the velocity and thermal profiles, shear stresses at the disk, and Nusselt number are drawn. Results reveal that the increase in the value of the porosity parameter reduces the velocity of both particle and fluid phases. The increase in the value of the Biot number improves the temperature gradient of both particle and fluid phases. The rise in the value of the radiation parameter advances the heat transference of both phases. The rise in the value of the Biot number improves the rate of heat transfer. Finally, increasing the value of the radiation parameter improves the rate of heat transfer.     

MHD Eyring–Powell nanofluid past over an unsteady exponentially stretching surface with entropy generation and thermal radiation

This study's primary objective is to analyze the entropy generation in an unsteady magnetohydrodynamics (MHD) Eyring–Powell nanofluid flow. A surface that stretched out exponentially induced flow. The influences of thermal radiation, thermophoresis, and Brownian motion are also taken into consideration. The mathematical formulation for the transport of mass, momentum, and heat described by a set of partial differential equation is used, which is then interpreted by embracing the homotopy analysis method and with a fourth-order precision program (bvp4c). Graphical results display the consequences of numerous parameters on velocity, temperature, concentration, and entropy generation. Moreover, escalating amounts of the magnetic parameter, thermal radiation parameter, Reynolds number, and Brinkman number improve the entropy profile of the nanofluid. The rate of heat flux and the mass flux conspicuously improves for non-Newtonian fluid as compared to Newtonian fluid.     

Mixed convection heat transfer in inclined rectangular ducts with radiation effects

A numerical study was carried out to investigate the radiation effect on the characteristics of the mixed convection fluid flow and heat transfer in inclined ducts. The three-dimensional Navier–Stokes equations and energy equation are solved simultaneously with the vorticity–velocity method. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The effects of the thermal buoyancy and the radiative transfer on the distributions of the bulk fluid temperature, the friction factor and the Nusselt number are emphasized in detail. Results indicate that radiation effects have a considerable impact on the heat transfer and tend to reduce the thermal buoyancy effects. In addition, the development of the bulk fluid temperature is enhanced by the radiation effects.     

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.