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

Linga Raju T., Neela Rao B.

International Journal of Applied Mechanics and Engineering

2016

Vol. 21, no. 2

423--446

An unsteady MHD two-layered fluid flow of electrically conducting fluids in a horizontal channel bounded by two parallel porous plates under the influence of a transversely applied uniform strong magnetic field in a rotating system is analyzed. The flow is driven by a common constant pressure gradient in a channel bounded by two parallel porous plates, one being stationary and the other oscillatory. The two fluids are assumed to be incompressible, electrically conducting with different viscosities and electrical conductivities. The governing partial differential equations are reduced to the linear ordinary differential equations using two-term series. The resulting equations are solved analytically to obtain exact solutions for the velocity distributions (primary and secondary) in the two regions respectively, by assuming their solutions as a combination of both the steady state and time dependent components of the solutions. Numerical values of the velocity distributions are computed for different sets of values of the governing parameters involved in the study and their corresponding profiles are also plotted. The details of the flow characteristics and their dependence on the governing parameters involved, such as the Hartmann number, Taylor number, porous parameter, ratio of the viscosities, electrical conductivities and heights are discussed. Also an observation is made how the velocity distributions vary with the rotating hydromagnetic interaction in the case of steady and unsteady flow motions. The primary velocity distributions in the two regions are seen to decrease with an increase in the Taylor number, but an increase in the Taylor number causes a rise in secondary velocity distributions. It is found that an increase in the porous parameter decreases both the primary and secondary velocity distributions in the two regions.

Non-Newtonian flows over an oscillating plate with variable suction

Hayat T., Abbas Q., Khan M., Siddiqui A. M.

Archives of Mechanics

2003

Vol. 55, nr 4

327-344

The flow of second order fluid due to an oscillating infinite plate in the presence of a transverse magnetic field for two forms of time-depend suction are considered. The analytical solution of the governing boundary value problems are obtained. It is found that an external magnetic field and normal stress coefficient on the flow has opposite effects.