Abstract
The problem of two-phase unsteady MHD flow between two concentric cylinders of infinite length has been analysed when the outer cylinder is impulsively started. The system of partial differential equations describing the flow problem is formulated taking the viscosity of the particle phase into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving outer cylinder. The problem is solved using a combination of the Laplace transform technique, D’Alemberts and the Riemann-sum approximation methods. The solution obtained is validated by comparisons with the closed form solutions obtained for the steady states which has been derived separately. The governing equations are also solved using the implicit finite difference method to verify the present proposed method. The variation of the velocity and the skin friction with the dimensionless parameters occuring in the problem are illustrated graphically and discussed for both phases.
Highlights
The study of fluid/particle mixture is important in petroleum transport, powder technology, fluidization transport of solid particles by a liquid and liquid slurries in chemical and nuclear processing and metalized liquid fuel slurries for rocketry
The flow of an electrically conducting fluid through a channel or a circular pipe in the presence of a transverse magnetic field is encountered in a variety of applications such as magnetohydrodynamic (MHD) generators, pumps, accelerators, and flow meters
Makinde et al.[2] studied the steady, axisymmetric, MHD flow of a viscous, Newtonian, incompressible, electricallyconducting fluid through an isotropic, homogenous porous medium located in the annular zone between two concentric rotating cylinders in the presence of a radial magnetic field
Summary
The study of fluid/particle mixture is important in petroleum transport, powder technology, fluidization transport of solid particles by a liquid and liquid slurries in chemical and nuclear processing and metalized liquid fuel slurries for rocketry. Gidaspow,[17] Gadiraju et al.[18] and Chamkha and Ramadan.[19] Chamkha[20] studied the unsteady laminar flow and heat transfer of a particulate suspension in an electrically conducting fluid through channels and circular pipes in the presence of uniform transverse magnetic field which is formulated using a two-phase continuum model. He assumed the particle-phase viscosity to be constant in order to obtain a closed form solutions. The effect of the various dimensionless parameters entering into the problem are discussed with the aid of both line and contour graphs
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