MHD flow in a circular pipe with arbitrarily conducting slipping walls

Abstract

In this study, the magnetohydrodynamic (MHD) flow is simulated in a circular pipe with slipping and arbitrarily conducting boundary. The 2D governing coupled equations in terms of the velocity and the induced magnetic field are solved by the Dual Reciprocity Boundary Element Method (DRBEM). The discretized system of equations is solved in one stroke without introducing an iteration which reduces the computational cost. It is shown that, the flow decelerates, Hartmann layers enlarge through the top and the bottom of the pipe and induced current lines align as the wall conductivity or Hartmann number increases. An increase in the slip length accelerates the flow, shrinks the stagnant region, diminishes the boundary layers and retards the effect of the wall conductivity increase. The DRBEM is an advantageous method in solving MHD flow especially with slipping and arbitrarily conducting boundary conditions, since it enables to insert both the unknowns and their normal derivatives in slip and conductivity wall conditions.