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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 nonconducting 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.

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