Computational analysis and heat transfer on MHD transient-free convection flow in a vertical microporous channel in the existence of Hall and ion slip current

This investigation presents an analysis of the transient magnetohydrodynamic flow of Newtonian viscous fluid in a vertical microporous channel with the inclusion of ion slip-Hall current as well as an induced magnetic field (IMF) effects. Owing to the nature of the flow equations which are difficult to obtain an analytical result, a numerical scheme (PDEPE) based on finite difference approximation is adopted in solving the governing dimensional partial differential equation. The active influence of different flow parameters on velocity and IMF along the main flow and induced flow directions are visualized. Furthermore, variations of shear stress and induced current density are also presented in tabular form for active nondimensional flow quantities and later on analyzed. To establish the validity of the results obtained in this computation, values for velocity and IMF in this analysis were correlated with the steady-state existing benchmark when the values of nondimensional time are considered large. Significant results from the analysis show that at the transient time and in the simultaneous occurrence of suction/injection at the microchannel walls, higher values of ion slip current have no considerable influence on flow formation along the primary flow direction, whereas an oscillatory phenomenon is observed along the secondary flow direction. It is also significant to note that at a transient time, magnetic induction could be improved or controlled by choosing favorable values of the suction/injection parameter.     

Radiation effect on hydromagnetic convection in a vertical channel

The effect of radiation on the combined free and forced convection flow of an electrically conducting fluid inside an open-ended vertical channel and permeated by a uniform transverse magnetic field is considered. Closed form solutions for the velocity, temperature and the induced magnetic field are obtained in the optically thin limit case when the wall temperatures are varying linearly with the vertical distance. It is found that radiation tends to increase the rate of heat transport to the fluid thereby reducing the effect of natural convection. Velocity and the induced magnetic field increase and the temperature difference between the wall and the fluid decreases with increase in the radiation parameter. In the unstable situation corresponding to heating of the channel from below, both radiation and magnetic field exert stabilizing influence on the flow.     

Combined effects of variable thermal conductivity and induced magnetic field on convective Jeffrey fluid flow with nth order chemical reaction

This study addresses the impact of variable thermal conductivity and induced magnetic field on an unsteady two‐dimensional channel flow of an incompressible laminar mixed convective and chemically reacted Jeffrey fluid embedded in a non‐Darcy porous medium with an appropriate convective type boundary conditions. The suction/injection velocity distribution has been assumed to be in an exponential form. The set of transport equations is reduced into coupled ordinary differential equations by using appropriate similar variables, which are solved by shooting technique with Runge‐Kutta fourth‐order algorithm. The investigation is carried out for various emerging nondimensional parameters on the axial, radial velocities, temperature distribution, concentration, and induced magnetic fields and also with skin friction coefficient are discussed through graphs. The value of the local Sherwood and Nusselt numbers are analyzed numerically. We noticed that the effect of the induced magnetic field is increased with Strommer's number while it decreases for high magnetic Reynolds number.     

Hall current and ion‐slip effects on free convection flow in a vertical microchannel with an induced magnetic field

The steady fully developed hydromagnetic flow of a viscous incompressible and electrically conducting fluid in a vertical microchannel has been studied taking into account the influence of Hall current, ion‐slip effects and an induced magnetic field. Exact solutions for the governing equations responsible for the flow formation are obtained by the method of the undetermined coefficient and presented graphically. It is found that in the presence of the ion‐slip effect, both primary and secondary components of fluid velocity increase with the Hall parameter for symmetric as well as asymmetric heating of the microchannel surfaces. Also, the magnetic field supports flow along the secondary flow direction while the reverse impact is observed along the primary flow direction.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

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.     

Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer

In this paper, the oscillatory flow of hydromagnetic couple stress fluid-saturated porous layer with inhomogeneous wall temperatures is studied. The flow is modeled using the modified Darcy equation. The fluid is subjected to a transverse magnetic field and the velocity slip at the lower plate is taken into deliberation. The governing coupled partial differential equations of the flow are transformed to coupled ordinary differential equations and are solved analytically. The impact of the physical parameters such as the Grashof number, Prandtl number, Darcy number, Hartmann number, and couple stress parameters on velocity profiles, temperature, rate of heat transfer, and skin friction are emphasized. The velocity field increased as either the Grashof number, the Darcy number, the suction/injection parameter, and Prandtl number increased nevertheless reverse growth can be seen by increasing the Hartmann number and the couple stress parameter. The temperature field in the channel increases with increasing the suction/injection parameter and Prandtl number but a conflicting development can be seen with increasing the oscillation amplitude. It is interesting to note that skin friction increases on both channel plates as injection increases on the heated plate.     

Heat and mass transfer effect on an unsteady MHD radiative chemically reactive Casson fluid over a stretching sheet in porous medium

The objective of the present study is to investigate the effects of the variable magnetic field, chemical reaction, thermal radiation, Soret effect, and variable heat absorption on the fluid flow and heat and mass transfer of an unsteady Casson fluid past a stretching surface in a saturated porous medium. Velocity slip near the plate and conjugate heating boundary conditions in heat and mass transfer have been considered in this study. Due to the complexities in boundary conditions, the analytic solution of the governing equations of the present model is not possible. Thus, to overcome these issues, the coupled partial differential equations of the model are converted into a set of ordinary differential equations using similarity transformation. These equations have then been solved numerically using the fourth-order Runge-Kutta technique via the shooting method. The effects of various pertinent flow parameters on the velocity, concentration, and temperature field have been studied graphically. For the field of engineering, to get an insight into the physical quantities, especially Nusselt number, Sherwood number, and skin friction, their numerical values have been estimated against various parameters and presented in tables. From the tabulated values, it has been perceived that the shear stress increases with an increase in magnetic parameter, unsteadiness parameter, Casson parameter, and heat source parameter, whereas the Biot number shows the reverse trend. The mixture of porous media has justified that the heat transport process over a stretching sheet results in averting heat loss and accelerating the process of cooling, which is a significant outcome of the study. Furthermore, it has also been revealed that with the increase in the Soret effect and magnetic field, there is a reduction in the fluid velocity and temperature near the plate, whereas there is an increase in the species concentration. It has also been mentioned that the effects of the variable magnetic field have been widely applied in various engineering applications like magnetohydrodynamic (MHD) propulsion forces, rate of cooling, MHD power generation, and so on.     

Numerical investigation of induced magnetic field and variable mass diffusivity on double stratified Jeffrey fluid flow with heat and mass flux boundary conditions

The investigation explores the influence of the induced magnetic field and variable mass diffusivity on an unsteady incompressible mixed convective double stratified and chemically reactive flow of Jeffrey fluid through a porous medium with heat, and mass flux boundary conditions. The system of flow field nonlinear partial differential equations is reduced into coupled nondimensional ordinary differential equations using appropriate similar variables, then worked out a numerical solution via shooting technique along with Rung-Kutta fourth-order scheme. The results are analyzed for various physical flows, heat and mass transfers, induced magnetic field, and skin friction against disparate prominent parameters via graphs and tables. It is recognized that the temperate of the fluid is enhanced with thermal stratification; however, the concentration of the fluid is decreased with magnetic Reynold's number. The comparison of numerical values of skin friction with the existing literature for limiting sense.     

Natural MHD convection for an impulsively started infinite vertical plate with diffusion-thermo effect,induced magnetic field,and ramped wall temperature and concentration

The major motive of the current investigation is to analyze an exact solution for an unsteady magnetohydrodynamics natural convective flow of a viscous incompressible electrically conducting non-gray optically thick fluid past an impulsively started infinite vertical plate with ramped wall temperature and concentration in the presence of radiation, diffusion-thermo effect, and induced magnetic field. Laplace transform method is used to acquire the specific solutions of the dimensionless domain equations. The impact of various physical parameters on fluid velocities, temperature, concentration, and moreover on the rate of heat transfer, mass transfer, and skin friction at the wall are shown graphically. It is also found that the Dufour effect causes an increase in fluid velocity as well as temperature. The ramped condition influences the rise in Nusselt number.     

Numerical modelling of second‐grade fluid flow past a stretching sheet

The present numerical study reports the chemically reacting boundary layer flow of a magnetohydrodynamic second‐grade fluid past a stretching sheet under the influence of internal heat generation or absorption with work done due to deformation in the presence of a porous medium. To distinguish the non‐Newtonian behaviour of the second‐grade fluid with those of Newtonian fluids, a very popularly known second‐grade fluid flow model is used. The fourth order momentum equation with four appropriate boundary conditions along with temperature and concentration equations governing the second‐grade fluid flow are coupled and highly nonlinear in nature. Well‐established similarity transformations are efficiently used to reduce the dimensional flow equations into a set of nondimensional ordinary differential equations with the necessary conditions. The standard bvp4c MATLAB solver is effectively used to solve the fluid flow equations to get the numerical solutions in terms of velocity, temperature, and concentration fields. Numerical results are obtained for a different set of physical parameters and their behaviour is described through graphs and tables. The viscoelastic parameter enhances the velocity field whereas the magnetic and porous parameters suppress the velocity field in the flow region. The temperature field is magnified for increasing values of the heat source/sink parameter. However, from the present numerical study, it is noticed that the flow of heat occurs from sheet to the surrounding ambient fluid. Before concluding the considered problem, our results are validated with previous results and are found to be in good agreement.     

A numerical study on heat transfer and MHD flow of a Newtonian through a porous channel—Local thermal nonequilibrium model

 Vast numbers of studies concentrate on the thermal equilibrium state whereas in many real-world applications the model exists in the nonequilibrium state. Also, local thermal non-equilibrium precisely represents the thermohydroflow characteristics. Therefore, the current study examines the heat transfer and fluid flow characteristics of the magnetohydrodynamic flow of a Newtonian fluid through a local thermal non-equilibrium (LTNE) porous channel in the presence of the induced magnetic field. The mathematical model of the prescribed flow encloses the coupled nonlinear equations which are difficult to approach analytically. Hence, they are solved numerically using the shooting method with the Newton–Raphson method. The implications of various physical parameters of the problem on fluid flow, induced magnetic field, current density, temperature profiles, and heat transfer are elucidated with the aid of plots and tables. From the examination, it is clear that the porous medium significantly influences the characteristics of the fluid flow. That is, the least value of the Darcy number is related to a higher momentum field. Another interesting phenomenon is that the induced magnetic field remarkably enhances when the Darcy number is high, whereas the process is contrary to the current density. The effect of LTNE on the flow characteristics and heat transfer ceases for higher values of inter-phase heat transfer coefficient and the ratio of thermal conductivities, which gives rise to the local thermal equilibrium (LTE) situation. Furthermore, the amount of heat transport is maximum in the LTE case compared to that of the LTNE case.     

Chemically reacting mixed convective Casson fluid flow in the presence of MHD and porous medium through group theoretical analysis

This paper explores the consequences of chemically reacting magnetohydrodynamic mixed convective fluid substances driven by the porous medium, slippery, incompressible, and laminar vertical channel flow. Casson fluid model in a vertical channel is strengthened with mixed convection flow. The effects of the heat source-sink parameter, the suction-injection parameter, slips on the slide wall, and thermal radiation are also considered. A Lie group method is taken into consideration and nonlinear partial differential equations are converted into nonlinear ordinary differential equations (ODEs). The NDSolve command solves these ODEs and shows the action of the related parameters in the velocity, temperature, and concentration figures. The Casson fluid parameter increases the velocity profile but reduces the concentration profile. The parameter of suction-injection enhances the velocity, temperature, and concentration profiles. The variations in skin-friction coefficient in the heat and mass transfer rate are addressed in the diagrams. Moreover, streamlines are plotted for suction-injection parameter.     

Thermal analysis of buoyancy-motivated Casson fluid flow with time-independent chemical reaction under Lorentz forces

The present research study examines the magneto-hydrodynamic natural convection visco-elastic boundary layer of Casson fluid past a nonlinear stretching sheet with Joule and viscous dissipation effects under the influence of chemical reaction. To differentiate the visco-elastic nature of Casson fluid with Newtonian fluids, an established Casson model is considered. The present physical problem is modeled by utilizing the considered geometry. The resulting system of coupled nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations by applying suitable similarity transformations. Numerical solutions of these reduced nondimensional governing flow field equations are obtained by applying the Runge-Kutta integration scheme with the shooting method (RK-4). The physical behavior of different control parameters is described through graphs and tables. The present study describes that the velocity and temperature profiles decreased for increasing values of Casson fluid parameter. Velocity field diminished for the increasing nonlinear parameter whereas velocity profile magnified for increasing free convection parameter. Thermal field enhanced with increasing magnetic parameter in the flow regime. The concentration profile decreased for the rising values of the chemical reaction parameter. The magnitude of the skin-friction coefficient enhanced with increasing magnetic parameter. Increasing Eckert number increases the heat transfer rate and increasing chemical reaction parameter magnifies the mass transfer rate. Finally, the similarity results presented in this article are excellently matched with previously available solutions in the literature.     

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values.     

Impact of Soret and Dufour on MHD mixed convective flow of non-Newtonian fluid over a coagulated surface

In the present study, we investigated the steady, two-dimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo-diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth-order Runge–Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter.     

Numerical study on the conjugate effect of joule heating and magnato-hydrodynamics mixed convection in an obstructed lid-driven square cavity

Conjugate effect of joule heating and magnetic force, acting normal to the left vertical wall of an obstructed lid-driven cavity saturated with an electrically conducting fluid have been investigated numerically. The cavity is heated from the right vertical wall isothermally. Temperature of the left vertical wall, which has constant flow speed, is lower than that of the right vertical wall. Horizontal walls of the cavity are adiabatic. The physical problem is represented mathematically by sets of governing equations and the developed mathematical model is solved by employing Galerkin weighted residual method of finite element formulation. To see the effects of the presence of an obstacle on magnetohydrodenamic mixed convection in the cavity, we considered the cases of with and without obstacle for different values of Ri varying in the range 0.0 to 5.0. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the magnetic parameter, Ha and Joule heating parameter J. The results showed that the obstacle has significant effects on the flow field at the pure mixed convection region and on the thermal field at the pure forced convection region. It is also found that the parameters Ha and J have notable effect on flow fields; temperature distributions and heat transfer in the cavity. Numerical values of average Nusselt number for different values of the aforementioned parameters have been presented in tabular form.     

Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow

The effect of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field has been studied in the case of unsteady flow. The plate is moved with a constant velocity, which is in the same or opposite direction to the free stream velocity. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The effect of the induced magnetic field has been included in the analysis. The governing partial differential equations have been solved numerically using the finite difference method. The velocity, the x-component of the induced magnetic field and heat transfer characteristics of the flow are determined     

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.     

Peristaltic motion with heat and mass transfer of nano-Williamson fluids in two layers

In this paper, we have investigated the peristaltic motion with heat and mass transfer through a vertical channel divided into two equal regions, the right region filled with a clear non-Newtonian fluid obeying the Williamson model and the left region with a nano-Williamson fluid. The system is stressed by a gravity force with a uniform external magnetic field. The problem is modulated mathematically with a system of coupled nonlinear partial differential equations that describe the velocities, temperatures, and concentration of the fluids. The system of nondimensional, nonlinear, and partial differential equations is solved analytically with the homotopy perturbation method after using the approximations of low Reynolds number and long wavelength. The obtained solutions are functions of the physical parameters of the problem. Then, the effects of these parameters on velocities, temperatures, and concentration are discussed numerically and illustrated graphically through a set of figures. It is found that the parameters play an important role in controlling the solutions. It is shown that the stream function decreases on the left side and increases on the right side with an increase in the Wissenberger parameter and thermal conductivity ratio. Also, the temperature in the two regions increases with an increase in the thermophoretic parameter, whereas it decreases with an increase in the Brownian motion parameter. Furthermore, the concentration increases with an increase in the Brownian motion parameter and decreases with an increase in the thermophoretic parameter.