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The present study aims to investigate the effect of radiation on the unsteady magnetohydrodynamic (MHD) flow of a viscous, electrically conducting Newtonian fluid over rotating disk moving upward/downward immersed in a porous medium, considering the Hall effect. The study is motivated by the various applications in the context of solar power technology, electric power generation, Hall accelerators, MHDs generators and other industrial areas when the fluid flow is subjected to the previously mentioned effects such as MHD, Hall effect and thermal radiation.

Suitable similarity transformations are employed to reduce the governing nonlinear partial differential equations into the nonlinear ordinary ones. The solutions of the reduced system are numerically obtained using the boundary value problem (BVP) Midrich scheme in Maple. The results are presented graphically for vertical disk movement, magnetic parameter, Hall current, Darcy parameter, thermal radiation and Schmidt number. Skin frictions, mass and heat transfer rates are numerically tabulated.

It is revealed that the vertical motion of the disk significantly boosts the radial and annular flows. Moreover, the Hall parameter has contrasting effects on velocity profiles for the range of magnetic field but temperature field is oblivious of this behavior. It is observed that heat and mass transfer considerably enhance along vertical disk movement. Also magnetic field, temperature ratio and radiation parameter significantly enhance the temperature field, while reaction rate parameter and Schmidt number decrease the concentration profile. The current model is calibrated in its reduced form to an already published literature with good correlation to ensure the numerical scheme's validity.

This work is original within the best efforts of the authors.

This study aims to focus on the effect of hall currents on the thermal stability of a couple-stress fluid with a uniform horizontal magnetic field.

The thermal perturbation method is used for the analytical solution. The analysis is administered within the framework of linear stability theory and normal mode technique on the convection for a fluid layer contained between two boundaries for which an exact solution is obtained.

For the case of stationary convection, a dispersion relation governing the effect of hall currents magnetic field and couple stress are derived. Results from the current study concluded that magnetic field has stabilizing effect whereas hall currents are found to have a destabilizing effect on the system. Couple stress, however, has a dual character in contrast to its stabilizing effect in the absence of hall currents. The Oscillatory modes are introduced due to the presence of a magnetic field in the system. Graphs are plotted by giving numerical values to the parameters to depict the stability characteristics in each case.

This research paper is new and original.

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.