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Unsteady two-layered fluid flow and heat transfer of conducting fluids in a channel between parallel porous plates under transverse magnetic field

Linga Raju T., Nagavalli M.

International Journal of Applied Mechanics and Engineering

2013

Vol. 18, no. 3

699--726

The unsteady magnetohydrodynamic flow of two immiscible fluids in a horizontal channel bounded by two parallel porous isothermal plates in the presence of an applied magnetic and electric field is investigated. The flow is driven by a constant uniform pressure gradient in the channel bounded by two parallel insulating plates, one being stationary and the other oscillating, when both fluids are considered as electrically conducting. Also, both fluids are assumed to be incompressible with variable properties, viz. different viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperatures. The governing equations are partial in nature, which are then reduced to the ordinary linear differential equations using two-term series. Closed form solutions for velocity and temperature distributions are obtained in both fluid regions of the channel. Profiles of these solutions are plotted to discuss the effect on the flow and heat transfer characteristics, and their dependence on the governing parameters involved, such as the Hartmann number, porous parameter, ratios of the viscosities, heights, electrical and thermal conductivities.

Unsteady two-fluid flow and heat transfer of conducting fluids in channels under transverse magnetic field

Linga Raju T., Sreedhar S.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 4

1093-1114

An attempt has been made to investigate the behaviour of flow formation and heat transfer aspects on an unsteady MHD two-fluid flow of electrically conducting fluids under the influence of a transversely applied uniform magnetic field in a horizontal channel. The flow is driven by a constant uniform pressure gradient in a channel bounded by two parallel walls, one being stationary and the other oscillating. The two fluids are assumed to be incompressible and electrically conducting possessing different viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding walls are maintained at constant and equal temperature. The governing partial differential equations are reduced to the ordinary linear differential equations using two-term series, and which in turn are solved analytically to obtain exact solutions for the velocity distributions and the corresponding temperature distributions in the two-fluid regions respectively. Profiles of these solutions are plotted to illustrate the details of the flow and heat transfer characteristics and their dependence on some of the physical parameters, such as the Hartmann number, ratios of the viscosities, heights, electrical and thermal conductivities. And, it is shown how the velocity and temperature distributions vary with hydromagnetic interaction in the case of steady flow and unsteady flow motions. Also, as expected, it is observed that these distributions are pronounced more in the unsteady state when compared to the steady state problem.