An unsteady magnetohydrodynamic natural convection transfer of mass and heat flow over a vertical porous sheet under the influence of thermal radiation and thermo-diffusion effect. The dimensionless governing equations are solved analytically by employing Laplace transform technique. The impact of various physical parameters on momentum, energy and concentration are discussed and analyzed with the aid of graphs. Furthermore, the numerical values for local Skin friction, Nusselt number and Sherwood number are noted and examined. Increasing the values of thermal diffusion results in increasing of the concentration, but it decreases with Schmidt number. Skin friction reduces for increasing values of thermo-diffusion are discussed with the help of tables.

The present study investigates the steady three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet under the influence of Lorentz force. Heat transfer effects have been carried out for constant heat flux and Newtonian heating systems. The transformed governing equations of the flow model are solved by using the spectral relaxation method (SRM), taking into account similarity transformations. The effects of controlling parameters on flow and derived quantities have been presented in the form of graphs and tables. Numerical benchmarks are used to characterise the effects of skin friction and heat transfer rates. It is noticed that in the case of Newtonian heating, the rate of heat transfer is higher than that in the constant heat flux case. As the stretching parameter increases, the fluid temperature decreases in both Newtonian heating and constant heat flux. It was discovered that successive over (under) relaxation (SOR) approaches will considerably boost the convergence speed and stability of the SRM system. The current findings strongly agree with earlier studies in the case of Newtonian fluid when the magnetic field is absent.

Purpose: The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH). Design/methodology/approach: The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically. Findings: It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH. Research limitations/implications: This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids. Practical implications: Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production. Social implications: Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration. Originality/value: The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

In this manuscript an investigation is done to analyze various properties of fully developed free convective flow of a viscous incompressible electrically conducting visco-elastic and dissipative fluid past a vertical porous plate bounded by a porous medium in the presence of thermal radiation and variable permeability. A magnetic field of uniform strength is applied perpendicular to the plate and the presence of heat source is also considered. The coupled dimensionless non-linear partial differential equations are solved numerically by finite difference method. The numerical computations have been studied through graphs. The presence of thermal radiation decreases the temperature and an opposite nature is shown in the case of Eckert number.

In this study, effects of numerous physical quantities like dissipation, thermal radiation, and induced magnetic field on magnetohydrodynamic Casson fluid flow through a vertical plate is addressed. The non-dimensional multivariable governing equations are solved numerically by by means of Runge-Kutta method along with shooting technique. The behavior of velocity, temperature and induced magnetic fields for different physical aspects is discussed through graphical illustrations. The influence of physical constants like Casson fluid (β), Magnetic parameter Μ, Soret number Sc, Prandtl number Pr, Magnetic Prandtl number etc., on induced magnetic field, temperature and velocity is analyzed. Interesting observation of this study is that the effect of velocity distribution obeys the physical nature of well-known Newtonian and all other Non-Newtonian fluids.