DRBEM solution to MHD flow in ducts with thin slipping side walls and separated by conducting thick Hartmann walls

摘要

In this study, the dual reciprocity boundary element method (DRBEM) solution to magnetohydrodynamic (MHD) flow is given in a single and two ducts stacked in the direction of external magnetic field. The duct walls perpendicular to the applied magnetic field (Hartmann walls) are conducting, thick and no-slip whereas the horizontal walls (side walls) are insulated, thin and allow the velocity slip. The DRBEM transforms the convection diffusion type MHD equations in the duct and Laplace equation in the thick walls to boundary integral equations which are discretized by using constant elements. The resultant matrix-vector equations are solved as a whole with the coupled boundary conditions on the common boundaries between the fluid and the thick walls. The effects of the slip length, thickness of conducting walls and the applied magnetic field strength are shown in the flow and the induced magnetic field. It is found that, in the absence of the slip, as Hartmann number (Ha) increases, the flow is concentrated in front of the side walls in terms of two side layers, and this separation is happened for much smaller value of Ha when the thickness of the conducting walls is increased. The continuation of induced magnetic fields to the thick walls is well observed in both co-flow and counter flow cases. When the side walls admit slip, opposite to the no-slip case, an increase in the conductivity of the fluid enlarges the core region where the fluid is stagnant. The proposed numerical scheme DRBEM is capable of capturing the well known MHD flow characteristics in ducts with thick walls as well as perturbations in the behaviors of the flow and the induced magnetic field due to the thin slip walls. (C) 2019 Elsevier Ltd. All rights reserved.