Abstract:
The flow of electrically conducting fluids in the presence of a magnetic field has wide
applications in science, engineering and technology. Examples of the applications
include industrial processes such as the cooling of reactors, extrusion of plastics,
purification of crude oil, medical applications, aerodynamics and many more. The
induced magnetic field usually act as a flow control mechanism, especially under
intense heat. In this study a couple stress fluid in a channel will be used as the working
fluid. Channel flow and heat transfer characteristics of couple stress fluids find
applications in processes such as the extrusion of polymer fluids, solidification of liquid
crystals, cooling of metallic plates in a bath, tribology of thrust bearings and lubrication
of engine rod bearings. One major characteristic that distinguishes the couple stress
fluid from other non-Newtonian fluids is the inclusion of size-dependent microstructure
that is of mechanical significance. As such, the couple stress constitutive model is
capable of describing the couple stresses, the effect of body couples and the nonsymmetric
tensors manifested in several real fluids of technological importance.
A fully developed laminar magnetohydrodynamic (MHD) flow of an incompressible
couple stress fluid through a vertical channel due to a steady-periodic temperature on
the channel plates is investigated. Specifically, the effects of couple stresses and
internal heat generation on MHD natural convection flow with steady-periodic heat
input, the impact of magnetic field induction on the buoyancy-induced oscillatory flow
of couple stress fluid with varying heating and a mixed convective two dimensional
flow of unsteady MHD couple stress fluid through a channel field with porous medium
are studied. Analytical methods and the semi-analytic Adomian decomposition method
will be used to solve the resulting non-linear differential equations governing the flow
systems. Useful results for velocity, temperature, skin friction and Nusselt number are
obtained and discussed quantitatively. The effects of the various flow governing
parameters on the flow field are investigated.
