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An unsteady Hartmann flow of a viscous incompressible electrically conducting fluid in a rotating channel with perfectly conducting walls under the action of a periodic pressure gradient is studied. An exact solution of the governing equations for the fully developed flow is obtained in a closed form. The expression for the shear stress at the upper plate is also derived. The solutions valid for vanishing and small finite magnetic Prandtl number are derived from the general solution. The asymptotic behavior of these solutions is analyzed, for large values of the frequency parameter […], to gain some physical insight into the flow pattern. It is found that a magnetic field tends to retard the fluid flow in both the primary and secondary flow directions whereas oscillations and rotation tend to accelerate it in both the directions. The magnetic field reduces primary and secondary induced magnetic fields whereas oscillations and rotation have reverse effect on it. The magnetic field reduces the primary as well as secondary shear stress at the upper plate […] whereas oscillations and rotation tend to increase it.
Rocznik
Tom
Strony
1129--1146
Opis fizyczny
Bibliogr. 24 poz., tab., wykr.
Twórcy
autor
autor
autor
- Department of Applied Mathematics Indian School of Mines, Dhanbad-826004, INDIA, gsseth_ism@yahoo.com
Bibliografia
- Acheson D.J. (1975): Forced hydromagnetic oscillations of a rapidly rotating fluid. - Phys. Fluids, vol.18, pp.961-968.
- 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.561-586.
- Cramer K.R. and Pai S.I. (1973): Magnetofluid dynamics for Engineers and Applied physicists. - New York: McGraw Hill Book Company.
- Das S., Maji S.L., Guria M. and Jana R.N. (2009): Unsteady MHD Couette flow in a rotating system. - Math. Comp. Modelling, vol.50, pp.1211-1217.
- Debnath L. (1974): On Ekman and Hartmann boundary layers in a rotating fluid. - Acta Mech., vol.18, pp.333-341.
- Debnath L. (1975): Resonant oscillations of a porous plate in an electrically conducting rotating viscous fluid. - Phys. Fluids, vol.17, pp.1704-1706.
- Ghosh S.K. (1993): Unsteady hydromagnetic flow in a rotating channel with oscillating pressure gradient. - J. Phy. Soc. Japan, vol.62, No.11, pp.3893-3903.
- Ghosh S.K. and Pop I. (2004): Hall effects on MHD Couette flow in a rotating environment. - Int. J. Appl. Mech. Eng., vol.9, pp.293-305.
- Ghosh S.K. and Pop I. (2006): An analytical approach on MHD plasma behaviour of rotating environment in the presence of an inclined magnetic field as compared to excitation frequency. - Int. J. Appl. Mech. Eng., vol.11, pp.845-856.
- Ghosh S.K., Beg O.A. and Narahari M. (2009): Hall effects on MHD flow in a rotating system with heat transfer characteristics. - Mecannica, vol.44, pp.741-765.
- Gupta A.S. (1972): Magnetohydrodynamic Ekman layer. - Acta Mech., vol.13, pp.155-160.
- Guria M., Das S., Jana R.N. and Ghosh S.K. (2009): Oscillatory Couette flow in the presence of an inclined magnetic field. - Mecannica, vol.44, pp.555-564.
- Hayat T., Hutter K., Nadeem S. and Asghar S. (2004a): Unsteady hydromagnetic rotating flow of a conducting second grade fluid. - Z. Angew. Math. Phys., vol.55, pp.626-641.
- Hayat T., Nadeem S. and Asghar S. (2004b): Hydromagnetic Couette flow of an Oldroyd-B fluid in a rotating system. - Int. J. Engng. Sci., vol.42, pp.65-78.
- Hayat T., Khan S.B. and Khan M. (2008): Exact solution for rotating flows of a generalized Burgers' fluid in a porous space. - Appl. Math. Modelling, vol.32, pp.749-760.
- Hide R. and Roberts P.H. (1960): Hydromagnetic flow due to an oscillating plane. - Rev. Mod. Phys., vol.32, pp.799-806.
- Nagy T. and Demendy Z. (1995): Effects of Hall currents and Coriolis force on Hartmann flow under general wall conditions. - Acta Mech., vol.113, pp.77-91.
- Nanda R.S. and Mohanty H.K. (1971): Hydromagnetic flow in a rotating channel. - Appl. Sci. Res., vol.24, pp.65-78.
- Nanousis N. (1992): Thermal-diffusion effects on MHD free-convection and mass transfer flow past a moving infinite vertical plate in a rotating fluid. - Astrophys. Space Sci., vol.191, pp.313-322.
- Raptis A. and Singh A.K. (1986): Hydromagnetic Rayleigh problem in a rotating fluid. - Acta Physica Hungarica, vol.60, pp.221-226.
- Seth G.S., Ansari Md. S. and Nandkeolyar R. (2010): Unsteady hydromagnetic Couette flow within porous plates in a rotating system. - Adv. Appl. Math. Mech., vol.2, pp.286-302.
- Seth G.S. and Ghosh S.K. (1986): Unsteady hydromagnetic flow in a rotating channel in the presence of oblique magnetic field. - Int. J. Engng. Sci., vol.24, pp.1183-1193.
- Seth G.S. and Jana R.N. (1980): Unsteady hydromagnetic flow in a rotating channel with oscillating pressure gradient. - Acta Mech., vol.37, pp.29-41.
- Seth G.S., Jana R.N. and Maiti M.K. (1982): Unsteady hydromagnetic Couette flow in a rotating system. - Int. J. Engng. Sci., vol.20, pp.989-999.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0018-0014