This study is performed on the numerical investigation of electro-magnetohydrodynamic (EMHD) radiating fluid flow nature along an infinitely long vertical Riga plate with suction in a rotating system. The prevailing equations are generated from the Navier–Stokes’ and energy equations. A uniform suction velocity is introduced to control the flow. The prevailing boundary layer (BL) equations are the stuff to delineate the mechanical features of the flowing nature along with the electromagnetic device (Riga plate). Accordingly, the use of usual transformations on the equations transformed those into a coupled dimensionless system of non-linear partial differential equations (PDEs). After conversion, the elucidation of the set of equations is conducted numerically by an explicit finite difference method (FDM). The criteria for stable and converging solutions are constructed to find restrictions on various non-dimensional parameters. The retrieved restrictions are $$P_{r} \ge 0.19,\,$$ P r ≥ 0.19 , $$R_{d} \ge 0.1,\,\,$$ R d ≥ 0.1 , $$S \ge 1,$$ S ≥ 1 , $$E_{c} = 0.01\,\,$$ E c = 0.01 and $$0 < R \le 0.1$$ 0 < R ≤ 0.1 . Furthermore, sensitivity tests on mesh and time as well as comparison within the literature have been demonstrated in graphical and tabular form. Finally, the important findings of the non-dimensional parameters influences have been portrayed in graphical manner by using the MATLAB R2015a tool. A substantial uprise is noted for both the velocities (secondary and primary) under the rising actions of the modified Hartmann number, whereas the suction parameter suppresses both the velocities.

The fluid flow along the Riga plate with the influence of magnetic force in a rotating system has been investigated numerically. The governing equations have been derived from Navier-Stokes' equations. Applying the boundary layer approximation, the appropriate boundary layer equations have been obtained. By using a usual transformation, the obtained governing equations have been transformed into a coupled dimensionless non-linear partial differential equation. The obtained dimensionless equations have been solved numerically by an explicit finite difference scheme. The simulated results have been obtained by using MATLAB R2015a. Also, the stability and convergence criteria have been analyzed. The effect of several parameters on the primary velocity, secondary velocity, temperature distributions as well as the local shear stress and the Nusselt number have been shown graphically.

Bingham fluid through porous parallel plates with Ion-slip and Hall currents has been studied numerically. The non-linear PDEs, governing the problem under assumptions, have been transformed into dimensionless non-linear PDEs by using usual transformations. The obtained dimensionless governing equations have been solved numerically by applying the explicit finite difference method (FDM) with the help of MATLAB R2015a tool. The time sensitivity test is performed for the steady-state solution and is obtained at dimensionless time τ=4.00. It is also observed that the secondary velocity reaches the steady-state more gradually than the primary velocity and temperature profiles. The appropriate mesh space (m=40 and n=40) is obtained by the mesh sensitivity test. The impact of various interesting parameters on the primary velocity, secondary velocity and temperature profiles, also on the local Nusselt number and shear stress have been analyzed and discussed through the graph in details. Finally, a qualitative and quantitative comparison with the published results has been discussed.

Numerical investigation for unsteady, viscous, incompressible Bingham fluid flow through parallel plates is studied. The upper plate drifts with a constant uniform velocity and the lower plate is stationary. Both plates are studied at different fixed temperatures. To obtain the dimensionless equations, the governing equations for this study have been transformed by usual transformations. The obtained dimensionless equations are solved numerically using the explicit finite difference method (FDM). The studio developer Fortran (SDF) 6.6a and MATLAB R2015a are both used for numerical simulations. The stability criteria have been established and the system is converged for Prandtl number Pr≥0.08 with ΔY=0.05 and Δτ=0.0001 as constants. As a key outcome, the steady-state solutions have been occurred for the dimensionless time τ = 4.00. The influence of parameters on the flow phenomena and on shear stress, including Nusselt number, are explained graphically. Finally, qualitative and quantitative comparison are shown.

The Numerical study for the unsteady electro magneto-hydrodynamic (EMHD) Couette flow of Bingham fluid through a porous parallel Riga plates with the consideration of thermal radiation has been carried out. The Couette flow is considered where the upper Riga plate moves with a uniform velocity U0 and the lower Riga plate is stationary. An external uniform magnetic field is applied perpendicular to the plates. Both the upper and lower Riga plates are kept at different but constant temperatures T1 and T2. respectively, where T2>T1. The governing equations have been transformed into dimensionless nonlinear partial differential equations by using usual transformations. The obtained equations have been solved numerically by the explicit finite difference method (FDM) under the stability and convergence analysis. The effects of some important parameters on shear stress, Nusselt number including velocity and temperature distributions have been discussed graphically by MATLAB R2015a.