Differential transform solution for Hall and ion‐slip effects on radiative‐convective Casson flow from a stretching sheet with convective heating

Magnetohydrodynamic (MHD) materials processing is becoming increasingly popular in the 21st century as it offers significant advantages over conventional systems, including improved manipulation of working fluids, reduction in wear, and enhanced sustainability. Motivated by these developments, the present work develops a mathematical model for Hall and ion‐slip effects on non‐Newtonian Casson fluid dynamics and heat transfer toward a stretching sheet with a convective heating boundary condition under a transverse magnetic field. The governing conservation equations for mass, linear momentum, and thermal (energy) are simplified with the aid of similarity variables and Ohm's law. The emerging nonlinear‐coupled ordinary differential equations are solved with an analytical technique known as the differential transform method. The impact of different emerging parameters is presented and discussed with the help of graphs and tables. Generally, aqueous electroconductive polymers are considered, for which a Prandtl number of 6.2 is employed. With increasing Hall parameter and ion‐slip parameter, the flow is accelerated, whereas it is decelerated with greater magnetic parameter and rheological (Casson) fluid parameter. Skin friction is also decreased with greater magnetic field effect, whereas it is increased with stronger Hall parameter and ion‐slip parameter values.     

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.     

Induced magnetic field effect on MHD free convection flow in nonconducting and conducting vertical microchannel walls

The current examination employs a numerical analysis to ascertain the effect of the Eckert number along with the Prandtl number on a magnetohydrodynamic natural convection flow of an incompressible viscous fluid in which it is electrically conducting, passing through a perpendicular microchannel. Conduction along with non-conducting immeasurable perpendicular walls within the existence of temperature and velocity slip at the microchannel is analyzed. The induced magnetic field (IMF) generated by the motion of an electrically conducting fluid in the presence of a transverse magnetic field is considered. The momentum and induction equations are coupled in the presence of an induced magnetic field. A set of similar variables are used to convert the governing set of equations to nonlinear-coupled ordinary differential equations. With the aid of MATLAB in built solver is carried out to get the numerical solutions. The influences of Hartman number, Prandtl number, and Eckert number along with some physical parameters are explained through graphs. The results indicate that increasing the Hartmann and magnetic Prandtl numbers results in a significant decrease in volume flow rate.     

Hall and ion slip effects on MHD laminar flow of an elastico‐viscous (Walter's‐B) fluid

We investigated the magnetohydrodynamic (MHD) laminar flow of an elastico‐viscous electrically conducting (Walter's‐B) fluid through a circular cylinder or pipe, loosely packed with a porous material subjected to Hall and ion‐slip effects. The innovation of the study is to consider the entire flow domain without boundary layer approximation in the governing equations. Fully developed solutions of the velocity and pressure drop are obtained making use of perturbation approximation and computationally discussed with reference to flow governing parameters. It is quite exciting that the elastic parameter almost reduces the speed of the liquid in the center of the channel and then continuously expands into the cylinder. For engineering interest, we found the analytical solution and then computationally discussed for skin friction. The occurrence of a magnetic field and a porous matrix gives a fairly uneven flow between the pipes. Elasticity and suction are resistant to experience greater skin friction and are therefore useful for controlling flow separation. A porch has been made to include studies of non‐Newtonian fluids with Hall and ion‐slip effects due to the vast number of possible engineering applications, like power generators, MHD accelerators, refrigeration coils, electric transformers, and heating elements.     

Second law analysis for chemically reacting natural convective second‐grade fluid flow between porous parallel plates with Hall and Ion slip

In this article, we performed the entropy generation of free convective chemically reacting second‐grade fluid confined between parallel plates in the influence of the Hall and Ion slip with heat and mass fluxes. Let there be a periodic suction/injection along with the plates, the governing flow field equations are reduced as a set of coupled nonlinear ordinary differential equations by using appropriate similarity transformations then solved numerically with shooting method based on Runge‐Kutta 4th order scheme. The results are analyzed for velocity in axial and radial directions, temperature distribution, concentration distribution, entropy generation number, Bejan number, mass and heat transfer rates with respect to distinct geometric, and fluid parameters and shown graphically and tables. It is observed that the entropy generation is enhanced with Prandtl number, whereas decreases with a second‐grade parameter, the effects of Hall and Ion slip parameters on velocity components, temperature and entropy generation number are the same. The entropy generation number the fluid is enhanced with the suction‐injection parameter whereas, the concentration of the fluid decreases with the increasing of chemical reaction parameter.     

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.     

An unsteady MHD flow of a second-grade fluid passing through a porous medium in the presence of radiation absorption exhibits Hall and ion slip effects

In the presence of radiation absorption, we analyzed the effects of Hall and ion slip effects on an unsteady laminar magnetohydrodynamics convective rotating flow of heat-producing or absorbing second-grade fluid across an inclined moving permeable surface in the presence of chemical reaction and radiation absorption. Using the perturbation method, the nondimensional equations for the governing flow are solved to the most excellent conceivable investigative answer. The effects of various factors on velocity, temperature, and concentration are visually and explored in depth. Shear stresses, Nusselt number, and Sherwood number are calculated analytically, rendered computationally in a tabular style, and discussed concerning the essential characteristics for engineering inquiry. It is inferred that an increase in radiation absorption, Hall, and ion slip parameters across the fluid area leads to a rise in the resulting velocity. The thermal and solutal buoyancy forces contribute to the resultant velocity, constantly growing to a very high level. The rotation parameter is used to reduce skin friction, while the Hall and ion slip effects enhance it. The rate of mass transfer increases when the chemical reaction parameter is raised.     

Irreversibility analysis of micropolar nanofluid flow using Darcy–Forchheimer rule in an inclined microchannel with multiple slip effects

The present work explores the consequence of the flow of micropolar fluid in an inclined microchannel when exposed to linear radiation in presence of a magnetic field. The microchannel is embedded with a porous medium and the Darcy–Forchheimer model is implemented. The walls of the microchannel facilitate the simultaneous suction and injection of the micropolar fluid. A multiple slip regime and temperature jump conditions were assumed at the boundaries. The equations are modeled and nondimensionalized using nondimensional entities and further solved with the aid of the Runge–Kutta–Fehlberg method. Entropy generated in the medium and ratio of irreversibilities is also computed. Results so obtained deliberate that enhancement in Darcy number has caused an increment in entropy generation rate whereas the opposite nature is attained for the Bejan number. Magnifying the radiation parameter has resulted in diminishing the profile of entropy generation rate and Bejan number.     

Numerical investigation of nonuniform transverse magnetic field effects on the flow and heat transfer of magnetic nanofluid in a sintered porous channel

In this paper, fluid flow and convective heat transfer of a ferrofluid (water and 4 vol% Fe₃O₄) in sintered Aluminum porous channel, which is subjected to a nonuniform transverse magnetic field have been studied. The numerical simulations supposed an ordinary cubic and staggered arrangement organized by uniformly sized particles with a small contact area for the porous media and constant heat flux at the surface of the microchannel. A wire, in which the electric current passes creates a nonuniform magnetic field, which is perpendicular to the flow direction. To do this simulation, the control volume technique and the two‐phase mixture model have been employed. The results show that the obtained local heat transfer coefficient on the channel surface increased with increasing mass flow rate and decreased slightly along the axial direction. Moreover, exerting the above‐mentioned magnetic field increases the Nusselt number that enhances the heat transfer rate while it has no effect on the pressure drop along the channel.     

Exploration of heat transfer effect in a magnetohydrodynamics flow of a micropolar fluid between a porous and a nonporous disk

An analysis is carried out for the flow characteristics of a conducting micropolar fluid. The fluid was passed in between two parallel disks of infinite radii. The novelty of the study is to consider one of the disks as porous and the other one as nonporous, and the external magnetic field is applied along the transverse direction of the flow. The flow phenomena for the polar fluid characterized by the magnetic effect in conjunction with the temperature equation reduce to a set of coupled nonlinear ordinary differential equations using the requisite transformations and nondimensionalization. An analytical approach such as the variation parameter method is employed to tackle the system efficiently. To emphasize the effect of various physical parameters contributing to the flow phenomena, that is, non-zero tangential slip, Reynolds number, Prandtl number, magnetic parameter, and material parameter on the flow profiles of axial and radial velocities, the microrotation and temperature profiles are presented graphically. To validate the simulated results, a comparison with established results is made, and it is concluded that both are in good correlation.     

Effect of inclined and low magnetic field in gaseous slip flow in two‐dimensional rectangular microchannel using first‐order boundary conditions

In the present work, the effect of an oriented low magnetic field on near‐continuum gaseous slip flow inside a two‐dimensional rectangular microchannel has been studied using first‐order boundary conditions. The flow was assumed to be compressible, laminar, and steady. The governing equations were solved analytically to obtain the solutions of velocity, temperature, and the pressure of the flow. The influence of different parameters such as Knudsen number, aspect ratio, Hartmann number, and pressure ratio were studied and analyzed. It was found that the electric and magnetic field with an inclined angle had significant effects on the flow properties. The results showed that the velocity increases and the temperature decreases as the inclination angle of the magnetic field decreases. The velocity increases as the Knudsen number, pressure ratio, and aspect ratio increase, while it decreases with increasing of the Hartmann number. The temperature decreases with increasing of the Knudsen number, pressure ratio, and aspect ratio, while the temperature increases as the Hartmann number increases. The results of the present study were validated with published results in the literature.     

Impacts of the periodic wall conditions on the hydromagnetic convective flow of viscoelastic fluid through a vertical channel with Hall current and induced magnetic field

In this study, a mathematical analysis is presented for the hydromagnetic convective flow of an incompressible, chemically reacting, and electrically and thermally conducting viscoelastic fluid through a vertical channel bounded by the porous regime under the action of an applied magnetic field with Hall current and induced magnetic field effects. The left wall of the channel is considered to be nonmagnetic, whereas the right wall of the channel is periodically magnetized. The flow within the channel is induced due to the nonuniform wall temperature and concentration, periodic pressure gradient, and periodic movement of the right wall. The method of separation of variable is used to convert the flow governing coupled partial differential equations into the ordinary differential equations that are solved analytically, and the solution for fluid velocity, induced magnetic field, temperature, and concentration is presented in a closed form. Numerical computation has been performed to demonstrate the impact of various system parameters on the fluid flow behavior. It is observed that oscillations increase the primary flow and primary induced magnetic field. Buoyancy forces have a tendency to lessen the secondary induced magnetic field. Furthermore, it is examined that magnetic diffusivity increases the primary flow, whereas it decreases the secondary flow and primary induced magnetic field.     

Electroosmotic flow of a fractional second-grade fluid with interfacial slip and heat transfer in the microchannel when exposed to a magnetic field

We investigated the time-dependent viscoelastic fluid flow through a parallel-plate microchannel under the influence of a transversely applied magnetic field and an axially imposed electric field. We performed the analysis by employing the Poisson-Boltzmann equation under the Debye-Huckel approximation. The generalized second-grade fluid model with a fractional-order time derivative is used to observe the non-Newtonian and fractional behavior rates of deformation employing the Riemann-Liouville fractional operator. We considered the asymmetric zeta potentials and different slip effects at the walls to study the flow behavior near the vicinity of the channel. We obtained an analytical solution in terms of Mittag-Leffler function, applying Fourier and Laplace transformations. We imposed the heat transfer phenomena with the dissipation of energy and Joule heating effects on the model. The governing equations were also solved numerically by employing an implicit finite difference scheme. The numerical solution was compared with the analytical results, considering the influence of the pertinent parameters involved in the problem. The study delineates that the flow rate decreases with a rise in the fractional-order parameter, while the opposite trend is observed with the electroosmotic parameter. Due to the application of sufficient strength of the magnetic field and the Joule heating effects, the temperature increases within the channel.     

Entropy generation analysis of natural convective chemically reacting squeezing flow of Casson fluid between parallel disks with Hall and Ion slip currents

This paper concerns the second law analysis of free convective squeezing flow of a chemically reacting Casson fluid confined between two parallel disks with Hall and Ion slip effects. The upper one is impermeable and the lower disk is porous. The linear momentum, energy balance and mass partial differential equations converted as system of ODEs by similarity transformations and tackled with shooting method via fourth order Runge‐Kutta scheme. The impact of various dimensionless geometric and fluid parameters on the velocity fields, temperature and concentration fields, entropy generation and Bejan numbers are studied and presented in the form of pictorially. The present results are correlated with already published outcomes for viscous case and found to be good agreement. The Bejan number of the fluid enhances with Ion slip parameter, whereas the concentration profile of the fluid is decreases with increasing of the Casson fluid parameter. The entropy generation of the fluid is enhanced with Eckert number whereas the Bejan number is decreased with suction/blowing parameter     

Gaseous slip flow affected by inclined low magnetic field using second‐order boundary conditions

In this study, asymptotic solutions of a near continuum gaseous slip flow in two‐dimensional rectangular microchannels under the effect of electromagnetic force are presented. An inclined magnetic field was assumed in this study. Nondimensional equations were obtained that relate the pressure ratio, Mach number, magnetic Reynolds number, magnetic force number, and Reynolds number. The asymptotic solutions for the compressible, laminar, and steady flow were obtained by applying second‐order slip velocity and temperature jump wall boundary conditions. It was found that the electric and magnetic field with inclined angle had significant effects on the flow properties. The solutions obtained here using the second‐order boundary conditions result in tangible improvement over those obtained using first‐order boundary conditions. We compared our solutions against the numerical solutions that were provided in the literature and showed that our solutions were in good agreement with the numerical solution.     

Effect of viscous heating on heat transfer performance in microchannel slip flow region

Based on the superposition principle, an analytical solution for steady convective heat transfer in a two-dimensional microchannel in the slip flow region is obtained, including the effects of velocity slip and temperature jump at the wall, which are the main characteristics of flow in the slip flow region, and viscous heating effects in the calculations. The cases of constant heat flux boundary conditions and one wall as adiabatic and the other wall at constant heat flux input are studied. The solution method is verified for the cases where micro-scale effects are neglected. The effects of viscous heating on the temperature profiles and on the heat transfer performance are analyzed in detail. It is concluded that the effect of viscous heating, like an internal energy source, heats the fluid along the flow direction and severely distorts the temperature profiles. The effects of key parameters, such as the Brinkman and Knudsen numbers, on the Nusselt number, which expresses the heat transfer performance are investigated.     

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

This investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.     

Influence of variable viscosity and thermal conductivity,hydrodynamic, and thermal slips on magnetohydrodynamic micropolar flow: A numerical study

Thermophysical and wall‐slip effects arise in many areas of nuclear technology. Motivated by such applications, in this article, the collective influence of variable‐viscosity, thermal conductivity, velocity and thermal slip effects on a steady two‐dimensional magnetohydrodynamic micropolar fluid over a stretching sheet is analyzed numerically. The governing nonlinear partial differential equations have been converted into a system of nonlinear ordinary differential equations using suitable coordinate transformations. The numerical solutions of the problem are expressed in the form of nondimensional velocity and temperature profiles and discussed from their graphical representations. The Nachtsheim‐Swigert shooting iteration technique together with the sixth‐order Runge‐Kutta integration scheme has been applied for the numerical solution. A comparison with the existing results has been done, and an excellent agreement is found. Further validation with the Adomian decomposition method is included for the general model. Interesting features in the heat and momentum characteristics are explored. It is found that a greater thermal slip and thermal conductivity elevate thermal boundary layer thickness. Increasing Prandtl number enhances the Nusselt number at the wall but reduces wall couple stress (microrotation gradient). Temperatures are enhanced with both the magnetic field and viscosity parameter. Increasing momentum (hydrodynamic) slip is found to accelerate the flow and elevate temperatures.     

Forced convective heat transfer between assemblages of spherical particles and power‐law non‐Newtonian liquids with velocity slip at the interface

Heat transfer from spheres can be influenced by a varying degree of slip at the fluid‐particle interface along with the rheology of the surrounding continuous liquid and adjacent spheres. Thus in this study, the effects of dimensionless velocity slip parameter (λ) along with power‐law fluid rheology and other pertinent kinematic flow and heat transfer parameters on isotherm contours, local and average Nusselt numbers of assemblages of spherical slip particles are presented. This is done by adopting a segregated approach where dimensionless momentum and energy equations are solved by SMAC algorithm formulated in spherical coordinates within the finite difference formulation. Before obtaining new results, grid independence studies for either extreme values of power‐law consistency index of non‐Newtonian fluids are carried out. Finally, the major contribution of this study is the development of a correlative equation for the average Nusselt number of assemblages of spherical slip particles in power‐law fluids based on the present results (5880 data points) as a function of pertinent dimensionless parameters.     

Heat and mass transport performance of MHD elastico-viscous fluid flow over a vertically oriented magnetized surface with magnetic and thermo diffusions

The key objective in this study is to examine the heat and mass transport behavior of magnetohydrodynamic elastic-viscous fluid flow over a vertically oriented magnetized surface placed in a uniform permeable regime with magnetic and thermo diffusions. The fluid is partially ionized and permeated to flow in the presence of a strong magnetic field domain. Hence the Hall current effect is considered in this investigation. The significance of rotation and induced magnetic field on the flowing nature are also scrutinized in this study. The mathematical model of the problem is converted to a similar model by introducing suitable nondimensional variables. To obtain the closed-form solutions of the flow leading equations, the regular perturbation analysis is utilized. For the exhibition of results, figures and tables are generated with the assistance of scientific computation software MATHEMATICA. Computed results are validated with the existing result in the limiting case. Such an investigation is important in evaluating the flow characteristics of low magnetic diffusive viscoelastic fluid. A noteworthy result seen is that magnetic diffusion significantly controls the fluid flow by altering the magnetic drag force. Mass diffusion factor brings an increase in the fluid velocity. Furthermore, we observed that the surface current density along the principal flow direction is significantly reduced by magnetic diffusion and mass diffusion factor.