Combined Effects of Hall Current and Rotation on Unsteady Couette Flow in a Porous Channel

ABSTRACT

The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating system in the presence of a uniform transverse magnetic field have been carried out. The solutions for the velocity field as well as shear stresses have been obtained for small time as well as for large times by Laplace transform technique. It is found that for large times the Hall currents accelerates primary flow whereas it retards secondary flow while the rotation retards the primary flow whereas it accelerates the secondary flow. It is also found that the velocity components converge more rapidly for small time solution than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of magnetic parameter*M*^{2}, rotation parameter *K*^{2} and Reynolds number *R*_{e}. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the layer increases with increase in either Hall parameter *m* or Reynolds number *R*_{e} while it decreases with increase in Hartmann number *M*. It is interesting to note that for large values of *M*^{2} , the boundary layer thickness is independent of the rotation parameter.

The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating system in the presence of a uniform transverse magnetic field have been carried out. The solutions for the velocity field as well as shear stresses have been obtained for small time as well as for large times by Laplace transform technique. It is found that for large times the Hall currents accelerates primary flow whereas it retards secondary flow while the rotation retards the primary flow whereas it accelerates the secondary flow. It is also found that the velocity components converge more rapidly for small time solution than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of magnetic parameter

KEYWORDS

MHD Couette Flow, Hall Current, Hartmann Number, Rotation Parameter, Reynolds Number And Boundary Layer

MHD Couette Flow, Hall Current, Hartmann Number, Rotation Parameter, Reynolds Number And Boundary Layer

Cite this paper

nullS. Guchhait, S. Das, R. Jana and S. Ghosh, "Combined Effects of Hall Current and Rotation on Unsteady Couette Flow in a Porous Channel,"*World Journal of Mechanics*, Vol. 1 No. 3, 2011, pp. 87-99. doi: 10.4236/wjm.2011.13013.

nullS. Guchhait, S. Das, R. Jana and S. Ghosh, "Combined Effects of Hall Current and Rotation on Unsteady Couette Flow in a Porous Channel,"

References

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[4] S. K. Ghosh and I. Pop, “Hall Effects on MHD Plasma Couette Flow in a Rotating Environmen,” Interantional Journal of Applied Mechanics and Engineering, Vol. 9, No. 2, 2004, pp. 293-305.

[5] S. K. Ghosh, “Effects of Hall Current on MHD Couette Flow in a Rotating System with Arbitrary Magnetic Field,” Czechoslovak Journal of Physics, Vol. 52, No. 1, 2002, pp. 51-63. doi:10.1023/A:1013913730086

[6] A. I Gubanov and P. T. Lunkin, “Couette Flow of an Electrically Conducting Fluid between Two Parallel Plates with Hall Effects,” Soviet Physics-Technical Physics, Vol. 5, 1961, p. 984.

[7] R. N. Jana and N. Datta, “Hall Effects on MHD Couette Flow in a Rotating System,” Czechoslovak Journal of Physics, Vol. B30, 1980, p. 659.

[8] N. B. Reddy and D. Bathaiah, “Hall Effects on MHD Couette Flow through a Porous Straight Channe,” Defense Science Journal, Vol. 32, 1982, pp. 313-326.

[9] S. Das, S. L. Maji, M. Guria and R. N. Jana, “Unsteady MHD Couette Flow in a Rotating System,” Mathematical and Computer Modelling, Vol. 50, 2009, pp. 1211-1217. doi:10.1016/j.mcm.2009.05.036

[10] D. R. V. Prasad Rao, D. V. Krishna and L. Debnath, “Combined Effect of Free and Forced Convection on MHD Flow in a Rotating Porous Channe,” International Journal of Mathematics and Mathematical Sciences, Vol. 5, 1982, pp. 165-182. doi:10.1155/S0161171282000167

[11] G. Mandal and K. K. Mandal, “Effect of Hall Current on MHD Couette Flow between Thick Arbitrarily Con- ducting Plates in a Rotating System”, Journal of the Physical Society of Japan, Vol. 52, 1983, pp. 470-477. doi:10.1143/JPSJ.52.470

[12] R. Sivaprasad, D. R. V. P. Rao and D. V. Krishna, “Hall Effects on Unsteady MHD Free and Forced Convection Flow in a Porous Channel,” Indian Journal of Pure and Applied Mathematics, Vol. 19, No. 7, 1988, pp. 688-696.

[13] T. G. Cowling, “Magnetohydrodynamics,” Interscience, New York, 1957.

[14] S. I. Pai, “Magnetogasdynamics and Plasma Dynamics,” Springer-Verlag, Viena; Prentice Hall, Englewood cliffs, 1962.

[15] G. K. Batchelor, An Introduction to Fluid Dynamics, Ist ed., Cambridge Press, Cambridge, U. K., 1967, p. 200.

[16] H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, Oxford, 1959.

[1] G. W. Sutton and A. Sherman, “Engineering Magnetohy- drodynamics,” McGraw-Hill, New York, 1965.

[2] P. Chandran, N. C. Sacheti and A. K. Singh, “Effect of Rotation on Unsteady Hydromagnetic Couette Flow,” Astrophysics and Space Science, Vol. 202, No. 1, 1993, pp. 1-10. doi:10.1007/BF00626910

[3] G. S. Seth and Md. S. Ansari, “Magnetohydrodynamic Convective Flow in a Rotating Channel with Hall Effects,” International Journal of Theoretical and Applied Mechanics, Vol. 4, No. 2, 2009, pp. 205-222.

[4] S. K. Ghosh and I. Pop, “Hall Effects on MHD Plasma Couette Flow in a Rotating Environmen,” Interantional Journal of Applied Mechanics and Engineering, Vol. 9, No. 2, 2004, pp. 293-305.

[5] S. K. Ghosh, “Effects of Hall Current on MHD Couette Flow in a Rotating System with Arbitrary Magnetic Field,” Czechoslovak Journal of Physics, Vol. 52, No. 1, 2002, pp. 51-63. doi:10.1023/A:1013913730086

[6] A. I Gubanov and P. T. Lunkin, “Couette Flow of an Electrically Conducting Fluid between Two Parallel Plates with Hall Effects,” Soviet Physics-Technical Physics, Vol. 5, 1961, p. 984.

[7] R. N. Jana and N. Datta, “Hall Effects on MHD Couette Flow in a Rotating System,” Czechoslovak Journal of Physics, Vol. B30, 1980, p. 659.

[8] N. B. Reddy and D. Bathaiah, “Hall Effects on MHD Couette Flow through a Porous Straight Channe,” Defense Science Journal, Vol. 32, 1982, pp. 313-326.

[9] S. Das, S. L. Maji, M. Guria and R. N. Jana, “Unsteady MHD Couette Flow in a Rotating System,” Mathematical and Computer Modelling, Vol. 50, 2009, pp. 1211-1217. doi:10.1016/j.mcm.2009.05.036

[10] D. R. V. Prasad Rao, D. V. Krishna and L. Debnath, “Combined Effect of Free and Forced Convection on MHD Flow in a Rotating Porous Channe,” International Journal of Mathematics and Mathematical Sciences, Vol. 5, 1982, pp. 165-182. doi:10.1155/S0161171282000167

[11] G. Mandal and K. K. Mandal, “Effect of Hall Current on MHD Couette Flow between Thick Arbitrarily Con- ducting Plates in a Rotating System”, Journal of the Physical Society of Japan, Vol. 52, 1983, pp. 470-477. doi:10.1143/JPSJ.52.470

[12] R. Sivaprasad, D. R. V. P. Rao and D. V. Krishna, “Hall Effects on Unsteady MHD Free and Forced Convection Flow in a Porous Channel,” Indian Journal of Pure and Applied Mathematics, Vol. 19, No. 7, 1988, pp. 688-696.

[13] T. G. Cowling, “Magnetohydrodynamics,” Interscience, New York, 1957.

[14] S. I. Pai, “Magnetogasdynamics and Plasma Dynamics,” Springer-Verlag, Viena; Prentice Hall, Englewood cliffs, 1962.

[15] G. K. Batchelor, An Introduction to Fluid Dynamics, Ist ed., Cambridge Press, Cambridge, U. K., 1967, p. 200.

[16] H. S. Carslaw and J. C. Jaeger, “Conduction of Heat in Solids,” Oxford University Press, Oxford, 1959.