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In the presence of viscous dissipation and radiation effects, a numerical analysis is performed for an unsteady‐free convective, radiative, chemically reactive, radiation absorption, viscous, incompressible, and electrically conducting fluid passing through an exponentially accelerating vertical porous plate. Numerical methods are used to solve the collection of nondimensional governing equations and their boundary conditions. Graphs are used to study the effects of different physical characteristics on flow quantities. Tables are used to study the differences in skin friction, the Sherwood number, and the Nusselt number for the physical interest. The analysis and explanation of the fluctuation in radiation and flow parameters on velocity and temperature gradient profiles through graphs using the Galerkin technique is the novelty of this work. For the magnetic, Prandtl, heat sink, radiation, Schmidt, and chemical reaction parameters, skin friction is significantly higher; however, for the Grashof, modified Grashof, permeability, radiation absorption, Dufour, and Soret numbers, skin friction has the opposite tendency. [ABSTRACT FROM AUTHOR]

The aim of the study is to measure the Dufour number effects on the flow patterns and heat transfer in an exponentially accelerated infinite vertical plate embedded in a porous medium in the presence of heat source and chemical reaction. Time‐dependent variations in temperature, velocity, and other factors should be taken into consideration due to the flow's unsteadiness. The fluid considered is a gray, absorbing/emitting radiation but nonscattering medium. Using the finite element method, a set of nondimensionless equations is solved analytically. Results are discussed graphically for concentration, temperature, and velocity profiles. Skin friction, Sherwood number, and Nusselt number are also explained for flow parameters through graphs. [ABSTRACT FROM AUTHOR]

This article discusses the impact of chemical reaction and radiation on an unstable two‐dimensional laminar flow around a viscous fluid over a semi‐infinite, vertical absorbent surface that moves progressively. The governing classification of partial differentiation was converted into an ordinary differentiation system in this case. To get numerical solutions, the Galerkin finite element technique is applied to nondimensional velocity, micro‐rotation, temperature, and concentration profiles. The consequences of skin friction, the combined pressure quantity, the mass, and heat assignments at the boundary are formed using different fluid properties and flow conditions. Physical quantities and their effects Graphs depict the radiation parameter R, thermal conductivity k, Eckert number Ec, and other velocities, micro‐rotation, temperature, and concentration factors. The main findings of this current problem is showing the chemical reaction effects on velocity and concentration. It is observed that both the velocity and concentration of the fluid decrease when Kr increases. [ABSTRACT FROM AUTHOR]

In this paper, the effects of thermal radiation on unsteady MHD flow viscous incompressible electrically conducting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion in the presence of Hall current have been presented. The dimensionless governing partial differential equations of the flow have been solved numerically by using the Galerkin finite element method. The numerical solutions for fluid velocity, angular velocity, temperature, and concentration are represented graphically whereas the numerical results of primary skin friction, rate of heat and mass transfer are presented in tabular form for various parameters involved. The current results were compared to the existing analytical solution based on the Crank–Nicolson implicit finite difference technique. The current study's findings have been shown to be extremely consistent with earlier findings. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The significance of this article lies in explaining the influence of Soret and Dufour numbers on an unsteady MHD free convection of flow of heat and mass transfer through porous media. The substances and radiation along the viscous, incompressible, and conductive compounds respond to the unstable convection of the liquid. Using physical quantities, the dimensional governing equations are converted to non-dimensional equations. Finite element Galerkin method is applied to numerically solve the resulting partial differential equations. Flow parameters on velocity, temperature, and concentration are studied and explained graphically to reflect their effects. Similarly, the skin friction number and Nusselt number are also observed and recorded in tables. [ABSTRACT FROM AUTHOR]