ORIGINAL PAPER
Unsteady two-layered fluid flow of conducting fluids in a channel between parallel porous plates under transverse magnetic field in a rotating system
More details
Hide details
1
Department of Engineering Mathematics, AUCE(A), Andhra University, VISAKHAPATNAM, Pin code: 530 003, A.P, INDIA
2
Department of Mathematics, Aditya Institute of Technology and Management, TEKKALI, Pin code: 532 201, A.P, INDIA
Online publication date: 2016-05-28
Publication date: 2016-05-01
International Journal of Applied Mechanics and Engineering 2016;21(2):423-446
KEYWORDS
ABSTRACT
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.
REFERENCES (41)
1.
Hide R. and Roberts P.H. (1961): The origin of the mean geomagnetic field. – In: Physics and Chemistry of the Earth. Pergamon Press, New York, vol.4, pp.27–98.
2.
Dieke R.H. (1970): Internal rotation of the sun. – In: L. Goldberg (eds.), Annual Reviews of Astronomy and Astrophysics, vol.8, Annual Reviews Inc., pp.297-328.
3.
Squire H.B. (1956): ‘ Surveys in mechanics’ Edited by Batchelor, G.K. and Davies, R.M. (Camb. Univ. Press, London).
4.
Gilman P.A. and Benton E.R. (1968): Influence of an axial magnetic field on the steady linear Ekman boundary layer. – Phys. Fluid, vol.11, pp.2397-.
5.
Benton E.R. and Loper D.E. (1969): On the spin-up of an electrically conducting fluid part-1. The unsteady hydromagnetic Ekman-Hartmann boundary-layer problem. – J. Fluid Mech., vol.39, pp.561-.
6.
Nanda R.S. and Mohanty H.K. (1971): Hydromagnetic flow in a rotating channel. – Applied Scientific Research, vol.24, pp.65.
7.
Gupta A.S. (1972): Magnetohydrodynamic Ekmann layer. – Acta Mechanica, vol.13, pp.155.
8.
Debnath L. (1972): On unsteady magnetohydrodynamic boundary layers in a rotating system. – ZAMM., vol.52, pp.623.
9.
Seth G.S., Jana R.N. and Maiti M.K. (1982): Unsteady hydromagnetic Couette flow in a rotating system. – International Journal of Engineering Science, vol.20, pp.989.
10.
Seth G.S., Nandkeolyar R., Mahto N. and Singh S.K. (2009): MHD Couette flow in a rotating system in the presence of an inclined magnetic field. – Applied Mathematical Sciences, vol.3, pp.2919.
11.
Mukherjee S. and Debnath L. (1977): On unsteady rotating boundary layer flows between two porous plates. ZAMM, vol.57, pp.188.
12.
Seth G.S. and Jana R.N (1980): Unsteady hydromagnetic flow in a rotating channel with oscillating pressure gradient. – Acta Mechanica, vol.37, p.29.
13.
Singh K.D. (2000): An oscillatory hydromagnetic Couette flow in a rotating system. – ZAMM, vol.80, pp.429.
14.
Ghosh S.K. (1993): Unsteady hydromagnetic flow in a rotating channel with oscillating pressure gradient. – Journal of the Physical Society of Japan, vol.62, pp.3893.
15.
Gupta A.S., Misra J.C., Reza M. and Soundalgekar V.M. (2003): Flow in the Ekman layer on an oscillating porous plate. – Acta Mechanica, vol.165, No.1, pp.1-16.
16.
Ghosh S.K. and Pop I. (2003). Hall effects on unsteady hydromagnetic flow in a rotating system with oscillatory pressure gradient. – Applied Mechanics and Engineering, vol.8, pp.43-.
17.
Hayat T. and Hutter K. (2004): Rotating flow of a second-order fluid on a porous plate. – International Journal of Non-Linear Mechanics, vol.39, pp.767.
18.
Guria M. and Jana R.N. (2007): Hydromagnetic flow in the Ekman layer on an oscillating porous plate. – Magnetohydrodynamics, vol.43, pp.3-11.
19.
Packham B.A. and Shail R. (1971): Stratified laminar flow of two immiscible fluids. – Proceedings of Cambridge Philosophical Society, vol.69, pp.443-448.
20.
Shail R. (1973): On laminar tow-phase flow in magnetohydrodynamics. – International Journal of Engineering Science, vol.11, pp.1103.
21.
Lielausis O. (1975): Liquid metal magnetohydrodynamics. – Atomic Energy Review, vol.13, pp.527.
22.
Michiyoshi, Funakawa, Kuramoto, C., Akita Y. and Takahashi O. (1977): Instead of the helium-lithium annularmist flow at high temperature, an air-mercury stratified flow in a horizontal rectangular duct in a vertical magnetic field. – International Journal of Multiphase Flow, vol.3, pp.445.
23.
Chao J., Mikic B.B. and Todreas N.E. (1979): Radiation streaming in power reactors. – Proceedings of the Special Session, American Nuclear Society (ANS) Winter Meeting, Washington, D.C. Nuclear Technology, vol.42, pp.22-.
24.
Dunn P.F. (1980): Single-phase and two-phase magnetohydrodynamic pipe flow. – International Journal of Heat Mass Transfer, vol.23, pp.373.
25.
Gherson P. and Lykoudis P.S. (1984): Local measurements in two-phase liquid-metal magneto-fluid mechanic flow. – Journal of Fluid Mechanics, vol.147, pp.81-104.
26.
Lohrasbi J. and Sahai V. (1987): Magnetohydrodynamic heat transfer in two phase flow between parallel plates. – Journal of Applied Sciences Research, vol.45, pp.53-66.
27.
Serizawa A., Ida T., Takahashi O. and Michiyoshi I. (1990): MHD effect on Nak-nitrogen two-phase flow and heat transfer in a vertical round tube. – International Journal Multi-Phase Flow, vol.16, No.5, pp.761.
28.
Malashetty M.S. and Leela V. (1992): Magnetohydrodynamic heat transfer in two phase flow. – International Journal of Engineering Science, vol.30, pp.371-377.
29.
Ramadan H.M. and Chamkha A.J. (1999): Two-phase free convection flow over an infinite permeable inclined plate with non-uniform particle-phase density. – International Journal of Engineering Science, vol.37, pp.1351.
30.
Chamkha A.J. (2000): Flow of two-immiscible fluids in porous and non-porous channels. – ASME Journal of Fluids Engineering, 122, 117-124.
31.
Raju T.L. and Murti P.S.R. (2006): Hydromagnetic two-phase flow and heat transfer through two parallel plates in a rotating system. – J. Indian Academy of Mathematics, Indore, India, vol.28, No.2, pp.343-360.
32.
Healy J.V. and Young H.T. (1970): Oscillating two-phase channel flows. – Z. Angew. Math. Phys., vol.21, pp.454.
33.
Debnath L. and Basu U. (1975): Unsteady slip flow in an electrically conducting two-phase fluid under transverse magnetic fields. – NUOVO Cimento, vol.28B, pp.349-362.
34.
Chamkha A.J. (2004): Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption. – International Journal of Engineering Science, vol.42, pp.217-230.
35.
Umavathi J.C., Abdul Mateen, Chamkha A.J. and Al-Mudhaf A. (2006): Oscillatory Hartmann two-fluid flow and heat transfer in a horizontal channel. – International Journal of Applied Mechanics and Engineering, vol.11, No.1, pp.155-178.
36.
Tsuyoshi I. and Shu-Ichiro I. (2008): Two-fluid magnetohydrodynamic simulation of converging Hi flows in the interstellar medium. – The Astrophysical Journal, vol.687, No.1, pp.303-310.
37.
Raju T.L. and Sreedhar M. (2009): Unsteady two-fluid flow and heat transfer of conducting fluids in channels under transverse magnetic field. – International Journal of Applied Mechanics and Engineering, vol.14, No.4, pp.1093-1114.
38.
Raju T.L. and Nagavalli M. (2013): Unsteady two-layered fluid flow and heat transfer of conducting fluids in a channel between parallel porous plates under transverse magnetic field. – International Journal of Applied Mechanics and Engineering, vol.18, No.3, pp.699-726.
39.
Raju T.L. and Nagavalli M. (2014): MHD two-layered unsteady fluid flow and heat transfer through a horizontal channel between parallel plates in a rotating system. – International Journal of Applied Mechanics and Engineering, vol.19, No.1, pp.97-121.
40.
Holton J.R. (1965). The influence of viscous boundary layers on transient motions in a stratified rotating fluid. – International Journal of Atmospheric Science, vol.22, pp.402.
41.
Siegmann W.L. (1971): The spin-down of rotating stratified fluids. – Journal of Fluid Mechanics, vol.47, pp.689.