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Hall and Ion-slip effects on unsteady MHD Bingham fluid flow through non-conducting parallel plates with uniform suction has been studied numerically. The fluid motion is subjected to uniform suction and external uniform magnetic field is applied perpendicular to the plates. The lower plate is stationary while upper plate moves with a constant velocity. Both plates are kept at different but constant temperatures. The governing non-linear coupled partial differential equations have been transformed into partial differential equations by usual transformations. The obtained equations have been solved numerically by the explicit finite difference method under the stability and convergence analysis. The effects of some important parameters on shear stress, Nusselt number as well as Primary Velocity, Secondary Velocity and Temperature distributions have been discussed graphically by MATLAB R2015a and Studio Developer FORTRAN 6.6a both. Finally, qualitative and quantitative comparisons of the present study with published results have been discussed.

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.

The numerical study of EMHD laminar flow of Bingham fluid flowing among two Riga plates with thermal radiation has been established. Both the Riga plates, upper and lower, are taken as stationary. Constant heat transfer is considered for both Riga plates. The governing equations for the problem have been transformed into dimensionless non-linear PDEs by using usual transformations. The obtained non-dimensional PDEs have been solved numerically by applying the explicit FDM. MATLAB has been conducted for the numerical simulation. The stability analysis stated that the governing equations will be converged for 0.09, r P  1.00 , 40, 40 mn = and  = 4.00 respectively.Finally, a comparison with several published results has been discussed.

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The numerical approach has been performed to study the Bingham fluid flow through an oscillatory porous plate with Ion-Slip and Hall current. Initially, at time; c E  , 0.05 Y  and 0.0001   . The steady-state solution has achieved at the dimensionless time 2.00  . At the steady-state time, the effect of several parameters on the flow patterns, local shear stress and the Nusselt number have been shown graphically.

This study presents the numerical solution of velocity and temperature fields based on mass conservation, momentum and energy balances for the time-dependent Couette-Poiseuille flow of Bingham materials through channels. The channel flow of Bingham fluid concerns the flow of cement paste in the building industry and the mudflow in the drilling industry. The specific aim is to introduce the magnetohydrodynamic (MHD) phenomena specified by both Ion-slip and Hall currents into the non-isothermal channel flow in a theoretical approach. The Bingham constitutive equation is formulated by the generalized Newtonian fluid technique and solved by employing the explicit Finite Difference Method (FDM) using the MATLAB R2015a and Compaq Visual FORTRAN 6.6a both. For the exactness of numerical performance estimations, the criteria for stabilization and the convergence factor are analyzed. The velocity and temperature profiles are discussed individually at the moving and stationary walls of the channel. It is observed that magnetohydrodynamic phenomena accelerate the flow, and the temperature distributions reach the steady-state situation earlier than velocity distributions. Furthermore, the dominance of MHD parameters on the velocity distributions, shear stress, temperature distributions, and Nusselt number are discussed.