Establishment of steady-state flow in mixture consisting of two electrically and non-electrically conducting fluids in porous pipes

摘要

In this paper, we investigate the following cases: (1) the unsteady flow of a mixture consisting of two electrically conducting fluids inside plane and cylindrical pipes (with porous walls) under constant external magnetic field, (2) the unsteady flow of a mixture consisting of two incompressible fluids inside plane and cylindrical pipes (with porous walls), (3) the unsteady flow of a conducting viscous incompressible fluid inside plane and cylindrical pipes (with porous walls) under constant external magnetic field. In each case, the time value after which the entire flow becomes steady has been obtained. This time is used for comparison purposes between the steady and unsteady problems. We solved the system of second order partial differential equations, describing the flow numerically using an implicit finite difference method. The dependence of establishment of steady-state time on the different parameters, affecting the flow, are discussed. It was found that the establishment time increases as any of the following parameters increase: the magnetic field parameter (E), the ratio of Reynolds numbers (RE), the ratio of the parameters of the porosity (c) and the interaction coefficient (K).