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The purpose of this paper is to investigate the effects of thermal radiation and viscous dissipation on steady natural convection flow of a viscous incompressible fluid along a uniformly moving infinite vertical porous plate with Newtonian heating in the presence of transverse magnetic field. The governing non-linear boundary layer equations are solved by using homotopy analysis method (HAM). The effects of various system parameters on velocity and temperature fields are discussed graphically, and the numerical values for skin friction and Nusselt number are presented in tabular form.

The problem is formulated using the Boussinesq approximation under the effects of thermal radiation and transverse magnetic field. The resulting coupled system of non-linear differential equations is solved using HAM with appropriate boundary conditions for Newtonian heating of the plate. HAM is a powerful method which provides rapidly converging series solution for the velocity and temperature fields. The effects of Prandtl number, Grashof number, suction parameter, magnetic field parameter, radiation parameter and Eckert number on the fluid velocity, temperature, skin friction and Nusselt number have been investigated.

The HAM solution has been successfully applied to find the converging series solution for velocity and temperature fields in terms of pertinent system parameters. Comparison of the exact solution results agree well with the HAM solution results in the absence of Eckert number and this indicates that the HAM solutions are accurate. It is found that the velocity and temperature profiles decreases with the increase of thermal radiation and suction parameters. An increase in the magnetic field parameter leads to a rise in the fluid temperature and fall in the fluid velocity.

The present analysis is limited to steady state laminar natural convection flow only. Unsteady natural- /mixed-convection laminar flow in the presence of thermal radiation, chemical reaction and transverse magnetic field will be investigated in a future work.

The study provides very useful information for heat transfer engineers to understand the heat transfer rate when the moving vertical porous surface temperature is not known a prior. The present results have immediate relevance in the design of nuclear reactors where vertical moving porous plates are using as control rods.

The present research work is relatively original and illustrates the effects of thermal radiation, viscous dissipation and transverse magnetic field on natural convection flow past a uniformly moving infinite vertical porous plate with Newtonian heating.

The purpose of this paper is to develop and correct the problem studied by Makinde and Mhone (2005) to a rotating vertical porous channel immersed in a Darcian porous regime in presence of a strong transverse magnetic filled and with the application of thermal radiation. In this investigation, the fluid is considered to be of viscous, electrically conducting, Newtonian and radiating and is optically thin with a relatively low density. Excellent agreement is obtained for exact solutions with those of previously published works.

In this investigation, a closed form analytical method based on the complex notations for the velocity, temperature and the pressure is developed to solve the governing coupled, non-linear partial differential equations. The accuracy and effectiveness of the method are demonstrated.

Interestingly observed that, the Lorentizian body force is not act as a drag force as in conventional MHD flows, but as an aiding body force and this will serve to accelerate the flow and boost the primary velocities. Due to the large rotation of the channel, the primary velocities are become flattered and shift towards the walls of the channel. With a rise in Darcian drag force, flow velocity and shear stress are found to reduce. Moreover, increasing thermal radiation and rotation of the channel strongly depress the shear stress, and maximum flow reversal, i.e. back flow is observed due to large Darcian resistance, thermal radiation and rotation.

The analysis is valid for unsteady, two-dimensional laminar flow of an optically thick no-gray gas, electrically conducting, and Newtonian fluid past an isothermal vertical surface adjacent to the Darcian regime with variable surface temperature. An extension to three-dimensional flow case is left for future work.

Practical interest of such study includes applications in magnetic control of molten iron flow in the steel industry, liquid metal cooling in nuclear reactors, magnetic suppression of molten semi-conducting materials and meteorology and in many branches of engineering and science. It is well known that the effect of thermal radiation is important in space technology and high-temperature processes. Thermal radiation also plays an important role in controlling heat transfer process in polymer processing industry.

The paper presents useful conclusions with the help of graphical results obtained from studying exact solutions based on complex notations for Darcian drag force, rotation of the channel and conduction-radiation heat transfer interaction by unsteady rotational flow in a vertical porous channel embedded in a Darcian porous regime under the application hydromagnetic force. The results of this study may be of interest to engineers for heat transfer augmentation and drag reduction in heat exchangers as well as MHD boundary layer control of re-entry vehicles, etc.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

The purpose of this paper is to consider unsteady free convection flow of a dissipative fluid past an exponentially accelerated infinite vertical porous plate in the presence of Newtonian heating and mass diffusion.

The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A Galerkin finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. It is a powerful, stable technique which provides excellent convergence and versatility in accommodating coupled systems of ordinary and partial differential equations.

It is found that the skin friction coefficient increases with increases in either of the Eckert number, thermal Grashof number, mass Grashof number or time whereas it decreases with increases in either of the suction parameter, Schmidt number or the acceleration parameter for both air and water. The skin friction coefficient is also found to decrease with increases in the values of the Prandtl number. In addition, it is found that the rate of heat transfer increases with an increase in the suction parameter and decreases with an increase in the Eckert number for both air and water. Lastly, it is found that the rate of heat transfer increases with increasing values of the Prandtl number and decreases with increasing time for all values of the Prandtl number.

The present study has considered only Newtonian fluids. Future studies will address non-Newtonian liquids.

A very useful source of information for researchers on the subject of free convective flow over the surface when the rate of heat transfer from the surface is proportional to the local surface temperature.

This paper is relatively original and illustrates the effects of viscous dissipation on free convective flow past an exponentially accelerated infinite vertical porous plate with Newtonian heating and mass diffusion.

The purpose of this paper is to examine the effects of Darcian drag force and radiation-conduction on unsteady two-dimensional magnetohydrodynamic flow of viscous, electrically conducting and Newtonian fluid over a vertical plate adjacent to a Darcian regime in presence of thermal radiation and transversal magnetic field. A well-tested, numerically stable Crank-Nicolson finite-difference procedure is employed for the conservation equations. Excellent agreement is obtained for numerical solutions with previously published work.

In this investigation, an efficient, accurate, extensively validated and unconditionally stable finite-difference scheme based on the Crank-Nicolson model is developed to solve the governing coupled, non-linear partial differential equations. The accuracy and effectiveness of the method are demonstrated.

Different numerical results are obtained and presented graphically to explain the effect of various physical parameters on the velocity and temperature profiles, local, as well as average, skin friction and Nusselt number. It is found that, with a rise in Darcian drag force, flow velocity and temperature are reduced, but increased for all times. Both average and local skin frictions are reduced considerably with an increase in Darcian drag force, but reversed behavior is observed for the local Nusselt number. Increasing the thermal radiation effects accelerated the flow velocity as well as the fluid temperature and wall local skin friction in a saturated porous medium, but effectively reduced the local Nusselt number and average Nusselt number at the wall. Comparison with previously published works in the limits shows excellent agreement.

The analysis is valid for unsteady, two-dimensional laminar flow of an optically thick no-gray gas, electrically conducting, and Newtonian fluid past an isothermal vertical surface adjacent to the Darcian regime with variable surface temperature. An extension to three-dimensional flow case is left for future work.

Practical interest of such study includes applications in electromagnetic lubrication, boundary cooling, bio-physical systems and in many branches of engineering and science. It is well known that the effect of thermal radiation is important in space technology and high temperature processes. Thermal radiation also plays an important role in controlling heat transfer process in polymer processing industry.

The purpose of this paper is to conduct a theoretical study on steady fully developed non-linear natural convection and mass transfer flow past an infinite vertical moving porous plate with chemical reaction and thermal diffusion effect. Closed-form expressions for dimensionless velocity, concentration, Sherwood number and skin-friction are obtained by solving the present mathematical model.

The fully developed steady non-linear natural convection and mass transfer flow near a vertical moving porous plate with chemical reaction and thermal diffusion effect is investigated. The non-linear density variation and Soret effect were taken into consideration. The dimensionless velocity, temperature and concentration profiles were obtained in terms of exponential functions, and were used to compute the governing parameters, skin-friction and Sherwood number.

The effect of coefficient of the non-linear density variation with the temperature (NDT) and concentration (NDC) parameter, chemical reaction parameter, thermal diffusion parameter are discussed with the aid of line graphs and tables. The analysis of the result shows that the velocity as well as skin-friction having higher values in the case of non-linear variation of density with temperature and concentration in comparison to linear variation of density with temperature and concentration. It is observed that the velocity and skin-friction increase with an increase in the Soret parameter.

The aim of this paper is to extend the work of Muthucumaraswamy (2002) by incorporating the thermal diffusion (Soret) effect and non-linear density variation with temperature (NDT) and concentration (NDC), on which, to the best knowledge of the authors, no studies have been carried out.

The hydromagnetic mixed convection flow of an incompressible viscous electrically conducting fluid and mass transfer over a vertical porous plate with constant heat flux embedded in a porous medium is investigated.

Using the Boussinesq and boundary‐layer approximations, the fluid equations for momentum, energy balance and concentration governing the problem are formulated. These equations are solved numerically by using the most effective Newton–Raphson shooting method along with fourth‐order Runge–Kutta integration algorithm.

It was found that for positive values of the buoyancy parameters, the skin friction increased with increasing values of both the Eckert number (Ec) and the magnetic field intensity parameter (M) and decreased with increasing values of both the Schmidt number (Sc) and the permeability parameter (K).

A very useful source of information for researchers on the subject of hydromagnetic flow in porous media.

This paper illustrates the effects of magnetic field on mixed convective boundary layer flow past a vertical plate embedded in a saturated porous medium with mass transfer and a constant heat flux.

The problem of steady, laminar, heat and mass transfer by mixed convection from a semi‐infinite, isothermal, vertical and permeable plate embedded in a uniform porous medium in the presence of temperature‐dependent heat source or sink and magnetic field effects is considered. A mixed convection parameter for the entire range of free‐forced‐mixed convection is employed and non‐similar equations are obtained. These equations are solved numerically by an efficient implicit, iterative, finite‐difference scheme. The obtained results are checked against previously published work on special cases of the problem and are found to be in good agreement. Useful correlations for the local Nusselt number are obtained for various physical parameters. A parametric study illustrating the influence of the magnetic field, porous medium inertia effects, heat generation or absorption, concentration to thermal buoyancy ratio, and the Lewis number on the fluid velocity, temperature and concentration as well as the Nusselt and the Sherwood numbers is conducted. The obtained results are shown graphically and the physical aspects of the problem are discussed.

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.

Steady-state mixed convection boundary layer flow, heat and mass transfer characteristics of Buongiorno's model nanofluid over an inclined porous vertical plate with thermal radiation and chemical reaction are presented in this analysis.

The governing nonlinear partial differential equations represent the flow model that can be converted into system of nonlinear ordinary differential equations using the similarity variables and are solved numerically using finite element method.

The rates of nondimensional temperature and concentration are both decelerate with the higher values of thermophoresis parameter (N_t).

The work carried out in this paper is original.