Aj. Chamkha, Unsteady laminar hydromagnetic fluid-particle flow and heat transfer in channels and circular pipes, INT J HEA F, 21(6), 2000, pp. 740-746
The problem of unsteady laminar flow and heat transfer of a particulate sus
pension in an electrically conducting fluid through channels and circular p
ipes in the presence of a uniform transverse magnetic held is formulated us
ing a two-phase continuum model. Two different applied pressure gradient (o
scillating and ramp) cases are considered. The general governing equations
of motions which include such effects as particulate phase stresses, magnet
ic ford, and finite particle-phase volume fraction) are non-dimensionalized
and solved in closed form in terms of Fourier cosine and Bessel functions
and the energy equations for both phases are solved numerically since they
are non-linear and are difficult to solve analytically, Numerical solutions
based on the finite-difference methodology are obtained and graphical resu
lts for the fluid-phase volumetric flow rate, the particle-phase volumetric
flow rate the fluid-phase skin-friction coefficient and the particle-phase
skin-friction coefficient as well as the wall heat transfer for plane and
axisymmetric flows are presented and discussed. In addition, these numerica
l results are validated by favorable comparisons with the closed-form solut
ions. A comprehensive parametric study is performed to show the effects of
the Hartmann magnetic number, the particle loading, the viscosity ratio, an
d the temperature inverse Stokes number on the solutions. (C) 2000 Elsevier
Science Inc. All rights reserved.