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The purpose of this paper is to study the effects of ion‐slip current and Hall current on the formation of longitudinal vortices in natural convection flow over a heated horizontal plate.

The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, the Reynolds number, the wave number, the Hall parameter, the ion‐slip parameter, and the Hartmann number.

The flow becomes more stable as the magnetic field increases. However, the destabilizing effect is found on the flow when the Hall and ion‐slip currents are presented.

The standard method of linear stability model is applied, with terms higher than first order in disturbance quantities being neglected.

The problem of MHD natural convection flow with Hall and ion‐slip currents has many important engineering applications, e.g. power generators, Hall accelerators and flows in channels and ducts.

This study is to check the validity of the assumptions that the conditions of Hall and ion‐slip currents can be ignored.

The purpose of this paper is to investigate a two dimensional problem in magneto-micropolar thermoelastic half-space with fractional order derivative in the presence of combined effects of hall current and rotation subjected to ramp-type heating.

The fractional order theory of thermoelasticity with one relaxation time derived by Sherief et al. (2010) has been used to investigate the problem. Laplace and Fourier transform technique has been used to solve the resulting non-dimensional coupled field equations to obtain displacement, stress components and temperature distribution. A numerical inversion technique has been applied to obtain the solution in the physical domain.

Numerical computed results of all the considered variables have been shown graphically to depict the combined effect of hall current and rotation. Some particular cases of interest are also deduced from the present study.

Comparison are made in the presence and absence of hall current and rotation in a magneto-micropolar thermoelastic solid with fractional order derivative.

The purpose of this study is to analyze an unsteady MHD Darcy flow of nonNewtonian hybrid nanoliquid past an exponentially accelerated vertical plate under the influence of velocity slip, Hall and ion slip effects in a rotating frame of reference. The fluids in the flow domain are assumed to be viscously incompressible electrically conducting. Sodium alginate (SA) has been taken as a base Casson liquid. A strong uniform magnetic field is applied under the assumption of low magnetic Reynolds number. Effect of Hall and ion-slip currents on the flow field is examined. The ramped heating and time-varying concentration at the plate are taken into consideration. First-order homogeneous chemical reaction and heat absorption are also considered. Copper and alumina nanoparticles are dispersed in base fluid sodium alginate to be formed as hybrid nanoliquid.

The model problem is first formulated in terms of partial differential equations (PDEs) with physical conditions. Laplace transform method (LTM) is used on the nondimensional governing equations for their closed-form solution. Based on these results, expressions for nondimensional shear stresses, rate of heat and mass transfer are also determined. Graphical presentations are chalked out to inspect the impacts of physical parameters on the pertinent physical flow characteristics. Numerical values of the shear stresses, rate of heat and mass transfer at the plate are tabulated for various physical parameters.

Numerical exploration reveals that a significant increase in the secondary flow (i.e. crossflow) near the plate is guaranteed with an augmenting in Hall parameter or ion slip parameter. MHD and porosity have an opposite effect on velocity component profiles for both types of nanoliquids. Result addresses that both shear stresses are strongly enhanced by the Casson effect. Also, hybrid nanosuspension in Casson fluid (sodium alginate) exhibits a lower rate of heat transfer than usual nanoliquid.

This model may be pertinent in cooling processes of metallic infinite plate in bath and hybrid magnetohydrodynamic (MHD) generators, metallurgical process, manufacturing dynamics of nanopolymers, magnetic field control of material processing, synthesis of smart polymers, making of paper and polyethylene, casting of metals, etc.

The originality of this study is to obtain an analytical solution of the modeled problem by using the Laplace transform method (LTM). Such an exact solution of nonNewtonian fluid flow, heat and mass transfer is rare in the literature. It is also worth remarking that the influence of Hall and ion slip effects on the flow of nonNewtonian hybrid nanoliquid is still an open question.

The purpose of this paper is to analyze the thermal-diffusion and diffusion-thermo effects on magnetohydrodynamics (MHD) natural convective flow through porous medium in a rotating system with ramped temperature.

Using the non-dimensional variables, the flow governing equations along with corresponding initial and boundary conditions have been transformed into non-dimensional form. These non-dimensional partial differential equations are solved by using finite element method. This method is powerful and stable. It provides excellent convergence and flexibility in providing solutions.

The effects of Soret number, Dufour number, rotation parameter, magnetic parameter, Hall current parameter, permeability parameter, thermal Grashof number, solutal Grashof number, Prandtl number, thermal radiation parameter, heat absorption parameter, Schmidt number, chemical reaction parameter and time on the fluid velocities, temperature and concentration are represented graphically in a significant way and the influence of pertinent flow governing parameters on the skin frictions and Nusselt number are presented in tabular form. On the other hand, a comparison for validation of the numerical code with previously published work is performed, and an excellent agreement is observed for the limited case existing literature.

A very useful source of information for researchers on the subject of MHD flow through porous medium in a rotating system with ramped temperature.

The problem is moderately original, as it contains many effects like thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects and chemical reaction.

This paper aims to assess the effectiveness of Hall currents and power-law slip condition on the hydromagnetic convective flow of an electrically conducting power-law fluid over an exponentially stretching sheet under the effect of a strong variable magnetic field and thermal radiation. Flow formation is developed using the rheological expression of a power-law fluid.

The nonlinear partial differential equations describing the flow are transformed into the nonlinear ordinary differential equations by employing the local similarity transformations and then solved numerically by an effective numerical approach, namely, fourth-order Runge–Kutta integration scheme, along with the shooting iteration technique. The numerical solution is computed for different parameters by using the computational software MATLAB bvp4c. The bvp4c function uses the finite difference code as the default. This method is a fourth-order collocation method. The impacts of thermophysical parameters on velocity and temperature distributions, skin friction coefficients and Nusselt number in the boundary layer regime are exhibited through graphs and tables and deliberated with proper physical justification.

Our investigation conveys that Hall current has an enhancing behavior on velocity profiles and reduces skin friction coefficients. An increase in the power-law index is observed to deplete velocity and temperature evolution. The temperature for the pseudo-plastic (shear-thinning) fluid is relatively higher than the corresponding temperature of the dilatant (shear-thickening) fluid. The streamlines are more distorted and have low intensity near the surface of the sheet for the dilatant fluid than the pseudo-plastic fluid.

The study is pertinent to the expulsion of polymer sheet and photographic films, hydrometallurgical industry, electrically conducting polymer dynamics, magnetic material processing, solutions and melts of polymer processing, purification of molten metals from nonmetallic. The results obtained in this work can be relevant in fluid mechanics and heat transfer applications.

The present problem has, to the authors' knowledge, not communicated thus far in the scientific literature. A comparative study with the published works is conducted to verify the accuracy of the present study. The results obtained in this analysis are significant in providing the standards for validating the accuracies of some numerical or empirical methods.

This paper addresses the three-dimensional flow of viscous nanofluid bounded by two plates. The lower plate stretches while the upper plate remains stationary. The fluid is electrically conducting in the presence of an applied magnetic field. In addition, the Hall, ion slip and Joule heating effects are retained. Governing equations for the considered physical happening are modeled under the phenomenon of boundary layer analysis.

Both analytical and numerical solutions for the resulting nonlinear system are derived. Numerical solutions have been presented by using bvp4c and NDSolve techniques. The homotopy analysis method is utilized for the development of convergent analytical solutions. A comparative study for the presented solutions is made. An excellent agreement between analytical and numerical solutions is noticed.

The dimensionless velocities, temperature and concentration are examined physically by two-dimensional plots, stream plot and tabular values. It is observed that Hall and ion slip parameters reduce the velocity field and temperature profile increases for the mounting values of the Eckert number.

This manuscript contains the novel contents which comprise the Hall and ion slip effects for the transportation of heat and mass for the flow of viscous nanofluid.

The purpose of this paper is to deal with an unsteady natural convection flow of a rotating fluid past an exponential accelerated vertical plate. The effect of Hall current, ion-slip and magnetic field is considered. Two types of plate temperature, namely, uniform and ramped temperature are considered to model heat transfer analysis.

The Laplace transform technique is employed to find the closed form solutions for velocity, temperature and concentration.

The effects of flow governing parameters on the velocity profile, temperature profile, concentration profile, skin friction, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. It is found that fluid velocity in the primary flow direction decreases with the increase in the magnetic parameter.

First time in the literature, the authors obtained closed form solution to natural convection flow of a rotating fluid past an exponential accelerated vertical plate.

The purpose of this paper is to provide an insight into the influence of gyrotactic microorganisms and Hall effect on the boundary layer flow of 29 nm CuO-water mixture on the upper pointed surface of a rocket, over the bonnet of a car and upper pointed surface of an aircraft. This is true since all these objects are examples of an object with variable thickness.

The simplification of Rosseland approximation (Taylor series expansion of T⁴ about T_∞) is avoided; thus, two different parameters relating to the study of nonlinear thermal radiation are obtained. The governing equation is non-dimensionalized, parameterized and solved numerically.

Maximum vertical and horizontal velocities of the 29 nm CuO-water nanofluid flow is guaranteed at a small value of Peclet number and large value of buoyancy parameter depending on the temperature difference. When the magnitude of thickness parameter χ is small, cross-flow velocity decreases with the velocity index and the opposite effect is observed when the magnitude of χ is large.

Directly or indirectly, the importance of the fluid flow which contains 29 nm CuO nanoparticle, water, and gyrotactic microorganisms in the presence of Hall current has been pointed out as an open question in the literature due to its relevance in imaging, ophthalmological and translational medicine informatics.

The article focuses on the magnetohydrodynamic (MHD) convective flow of MoS₂-SiO₂ /ethylene glycol (EG) hybrid nanofluid. The effectiveness of Hall current, periodically heating wall and shape factor of nanoparticles on the magnetized flow of hybrid nanocomposite molybdenum disulfide- silicon dioxide (MoS₂-SiO₂) suspended in ethylene glycol (EG) in a vertical rotating channel under the influence of strong magnetic dipole (Hall effect) and thermal radiation is assessed. One of the channel walls has an oscillatory temperature gradient. Four different shapes (i.e. brick, cylinder, platelet and blade) of nanoparticles disseminated in base fluid (EG) are considered for simulation of the flow.

The analytical solution of governing equations has been presented. Influences of emerging physical parameters on the velocity and temperature profiles, the shear stresses and the rate of heat transfer are pointed out and discussed via graphs and tables.

The analysis revealed that Hall parameter has suppressing behavior on the velocity profiles within the rotating channel. The impact of nanoparticle shape factor advances the temperature characteristics significantly in the rotating channel. Brick-shape nanoparticles put up relatively low-temperature distribution in the rotating channel. The Hall parameter reduces the amplitudes of the shear stresses at the channel wall. However, the radiation parameter enhances the amplitude of the rate of heat transfer at the channel wall.

The important technical advantage of hybrid composition of nanoparticles as a drug carrier is its stability, high thermal conductivity, high load carrying capacity, etc. The proposed model may be beneficial in biomedical engineering, automobile parts, mineral and cleaning oils manufacturing, rubber and plastic industries.

To the best of our knowledge, there is little or no report on the aspects of assessment of the effectiveness of Hall current and nanoparticle shape factor on an MHD flow and heat transfer of an electrically conducting MoS₂-SiO₂/EG ethylene glycol-based hybrid nanofluid confined in a vertical channel with periodically varying wall temperature subject to a rotating frame. The present work furnishes a robust benchmark for the dynamics of nanofluids.

The study of novel exponential heat source (EHS) phenomena across a flowing fluid with the suspension of nanoparticles over a rotating plate in the presence of Hall current and chemical reaction has been an open question. Therefore, the purpose of this paper is to investigate the impact of EHS in the transport of nanofluid under the influence of strong magnetic dipole (Hall effect), chemical reaction and temperature-dependent heat source (THS) effects. The Khanafer-Vafai-Lightstone model is used for nanofluid and the thermophysical properties of nanofluid are calculated from mixture theory and phenomenological laws. The simulation of the flow is also carried out using the appropriate values of the empirical shape factor for five different particle shapes (i.e. sphere, hexahedron, tetrahedron, column and lamina).

Using Laplace transform technique, exact solutions are presented for the governing nonlinear equations. Graphical illustrations are pointed out to represent the impact of involved parameters in a comprehensive way. The numeric data of the density, thermal conductivity, dynamic viscosity, specific heat, Prandtl number and Nusselt number for 20 different nanofluids are presented.

It is established that the nanofluid enhances the heat transfer rate of the working fluids; the nanoparticles also cause an increase of viscous. The impact of EHS advances the heat transfer characteristics significantly than usual thermal-based heat source (THS).

The effectiveness of EHS phenomena in the dynamics of nanofluid over a rotating plate with Hall current, chemical reaction and THS effects is first time investigated.