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

In this paper, we investigate the following cases: (1) the unsteady flow of a mixture consisting of two electrically conducting fluids inside plane an d cylindrical pipes (with porous walls) under constant external magnetic fi eld, (2) the unsteady Row of a mixture consisting of two incompressible flu ids inside plane and cylindrical pipes (with porous walls), (3) the unstead y flow of a conducting viscous incompressible fluid inside plane and cylind rical pipes (with porous walls) under constant external magnetic field. In each case, the time value after which the entire flow becomes steady has be en obtained. This time is used for comparison purposes between the steady a nd unsteady problems. We solved the system of second order partial differen tial equations, describing the flow numerically using an implicit finite di fference method. The dependence of establishment of steady-state time on th e different parameters, affecting the flow, are discussed. It was found tha t the establishment time increases as any of the following parameters incre ase: the magnetic field parameter (E), the ratio of Reynolds numbers (RE), the ratio of the parameters of the porosity (c) and the interaction coeffic ient (K). (C) 2000 Elsevier Science Inc. All rights reserved.