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The study of electromagnetohydrodynamics (EMHD) of non-Newtonian fluid plays a significant role for optical design, thermal management of electronic components, and various operations of microfluidic devices. The use of parallel geometry is seen in the circulatory system, extrusion process, and respiratory system. By considering various practical applications, in the current study, the Poiseuille flow of an incompressible Casson liquid between the plates is investigated. The effects of MHD, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been taken into account. The dimensional governing equations have been converted into dimensionless equations with pertinent nondimensional quantities. The resulting system of nondimensional system of equations has been analytically solved with nondimensional slip boundary conditions. The graphical results have been displayed with various fluid flow parameters. From the current study, it is concluded that the influence of Darcy number and Casson fluid parameter enhances the velocity profile, but the concentration declines with the enhancement of Casson fluid parameter.The radiation parameter and Prandtl number suppress the temperature profile.

The study of an immiscible fluid plays a significant role in the field of petroleum extraction, blood flow in arteries, hydrology, manufacturing process, and reservoir mechanics. These phenomena include immiscible