Bingham Fluid Flow through Oscillatory Porous Plate with Ion-Slip and Hall Current

TL;DR

This paper numerically investigates Bingham fluid flow between oscillating and stationary plates under magnetic effects, analyzing flow behavior, shear stress, and heat transfer with various parameters.

Contribution

It introduces a numerical method to analyze Bingham fluid flow with ion-slip and Hall current effects in an oscillatory porous plate setup.

Findings

Flow patterns depend on magnetic and slip parameters.

Shear stress and Nusselt number vary with system parameters.

Steady-state achieved at dimensionless time 2.00.

Abstract

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; t = 0 both the fluid and the upper plate are at rest. At time; t > 0 the upper plate begins to oscillate in its own plane while the lower plate is stationary. The lower plate temperature is constant while the upper plate temperature has oscillated. A uniform magnetic field is applied perpendicular to the plates. To obtain the dimensionless equations from the governing non-linear partial differential equations, the usual transformations have been used. The explicit finite difference technique has been applied to solve the obtained dimensionless equations. The MATLAB R2015a has been used for numerical simulation. For the accuracy of the numerical technique, the stability and convergence criteria have been discussed and the system has found to be converged for P_r>=0.08, Beta_i>=2, H_a<=20, K_o<=8 (k~=2) and R_e>=0.011 with Beta_e=0.10, E_c=0.10, Delta(Y)=0.05 and Delta(Tau)=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.