Effects of Hall Current and Ion-Slip on Unsteady MHD Couette Flow

Affiliation(s)

Department of Applied Mathematics, Vidyasagar University, Midnapore, India.

Department of Mathematics, Narajole Raj College, Narajole, India.

Department of Applied Mathematics, Vidyasagar University, Midnapore, India.

Department of Mathematics, Narajole Raj College, Narajole, India.

ABSTRACT

The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting horizontal porous plates under the boundary layer approximations has been studied with the consideration of both Hall currents and ion-slip. An analytical solution of the governing equations describing the flow is obtained by the Laplace transform method. It is seen that the primary velocity decreases while the magnitude of secondary velocity increases with increase in Hall parameter. It is also seen that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. It is observed that a thin boundary layer is formed near the stationary plate for large values of squared Hartmann number and Reynolds number. The thickness of this boundary layer increases with increase in either Hall parameter or ion-slip parameter.

The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting horizontal porous plates under the boundary layer approximations has been studied with the consideration of both Hall currents and ion-slip. An analytical solution of the governing equations describing the flow is obtained by the Laplace transform method. It is seen that the primary velocity decreases while the magnitude of secondary velocity increases with increase in Hall parameter. It is also seen that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. It is observed that a thin boundary layer is formed near the stationary plate for large values of squared Hartmann number and Reynolds number. The thickness of this boundary layer increases with increase in either Hall parameter or ion-slip parameter.

KEYWORDS

MHD; Couette Flow; Porous Plate; Hall Current; Ion-Slip; Hartmann Number and Reynolds Number

MHD; Couette Flow; Porous Plate; Hall Current; Ion-Slip; Hartmann Number and Reynolds Number

Cite this paper

N. Ghara, S. Maji, S. Das, R. Jana and S. Ghosh, "Effects of Hall Current and Ion-Slip on Unsteady MHD Couette Flow,"*Open Journal of Fluid Dynamics*, Vol. 2 No. 1, 2012, pp. 1-13. doi: 10.4236/ojfd.2012.21001.

N. Ghara, S. Maji, S. Das, R. Jana and S. Ghosh, "Effects of Hall Current and Ion-Slip on Unsteady MHD Couette Flow,"

References

[1] K. R. Crammer and S.-I. Pai, “Magnetofluid Dynamics for Engineers and Applied Physicists,” McGraw-Hill, New York, 1973.

[2] V. M. Soundalgekar, N. V. Vighnesam and H. S. Takhar, “Hall and Ion-Slip Effects in MHD Couette Flow with Heat Transfer,” IEEE Transactions on Plasma Science, Vol. 7, No. 3, 1978, pp. 178-182. doi:10.1109/TPS.1979.4317226

[3] H. A. Attia, “Unsteady Couette Flow with Heat Transfer Considering Ion-Slip,” Turk-ish Journal of Physics, Vol. 29, 2005, pp. 379-388.

[4] H. A. Attia, “Unsteady Couette Flow with Heat Transfer of a Viscoe-lastic Fluid Considering the Ion Slip,” Journal of the Korean Physical Society, Vol. 47, No. 5, 2005, pp. 809-817.

[5] H. A. Attia, “Time Varying Hydromagnetic Flow of Dus- ty Fluid between Parallel Porous Plates Considering the Ion Slip,” Journal of Technical Physics, Vol. 47, No. 3, 2006, pp. 131-147.

[6] H. A. Attia, “Analytical Solution for Flow of a Dusty Fluid in a Circular Pipe with Hall and Ion Slip Effects,” Chemical Engineering Communications (CEC), Vol. 194, No. 10, 2007, pp. 1287-1296.

[7] H. A. Attia, “Transient Hart-mann Flow with Heat Transfer Considering the Ion Slip,” Physica Scripta, Vol. 66, 2002, pp. 470-475. doi:10.1238/Physica.Regular.066a00470

[8] M. A. Seddeek, “The Effects of Hall and Ion-Slip Currents on Mag-neto-Micropolar Fluid and Heat Transfer over a Non-Isothermal Stretching Sheet with Suction and Blowing,” Proceedings of the Royal Soceity: London A, Vol. 457, 2001, pp. 3039-3050. doi:10.1098/rspa.2001.0847

[9] P. C. Ram, “The Effects of Hall and Ion-Slip Currents on Free Convective Heat Generating Flow in a Rotating Fluid,” International Journal of Energy Research, Vol. 19, No. 5, 1995, pp. 371-376. doi:10.1002/er.4440190502

[10] M. L. Mittal and A. N. Bhat, “Forced Convective Heat Transfer in a MHD Channel with Hall and Ion Slip Currents,” Applied Scientific Research, Vol. 35, No. 4, 1979, pp. 251-264. doi:10.1007/BF00418216

[11] R. N. Jana and N. Datta, “Couette Flow and Heat Transfer in a Rotating System,” Acta Meccanica, Vol. 26, No. 1-4, 1977, pp. 301-306. doi:10.1007/BF01177152

[12] A. K. Kanch and R. N. Jana, “ Hall Effect on Unsteady Couette Flow under Boundary Layer Approximations,” Journal of the Physical Sciences, Vol. 7, 2001, pp. 74-86.

[13] H. A. Attia, “Ion Slip Effect on Un-steady Couette Flow with Heat Transfer under Exponential Decaying Pressure Gradient,” Tamkang Journal of Science and Engineering, Vol. 12, No. 2, 2009, pp. 209-214.

[14] B.K. Jha and C. A. Apere, “Combined Effect of Hall and Ion-Slip Cur-rents on Unsteady MHD Couette Flows in a Rotating System,” Journal of the Physical Society of Japan, Vol. 79, No. 10, 2010, pp. 104401-104401-9. doi:10.1143/JPSJ.79.104401

[15] H. S. Carslaw and J. C. Jae-ger, “Conduction of Heat in Solids,” Oxford University Press, Oxford, 1959.

[16] A. S. Gupta, “Hydromagnetic Flow Past a Porous Flat Plate with Hall Effects,” Acta Mechanica, Vol. 22, No. 3-4, 1975, pp. 281-287. doi:10.1007/BF01170681

[1] K. R. Crammer and S.-I. Pai, “Magnetofluid Dynamics for Engineers and Applied Physicists,” McGraw-Hill, New York, 1973.

[2] V. M. Soundalgekar, N. V. Vighnesam and H. S. Takhar, “Hall and Ion-Slip Effects in MHD Couette Flow with Heat Transfer,” IEEE Transactions on Plasma Science, Vol. 7, No. 3, 1978, pp. 178-182. doi:10.1109/TPS.1979.4317226

[3] H. A. Attia, “Unsteady Couette Flow with Heat Transfer Considering Ion-Slip,” Turk-ish Journal of Physics, Vol. 29, 2005, pp. 379-388.

[4] H. A. Attia, “Unsteady Couette Flow with Heat Transfer of a Viscoe-lastic Fluid Considering the Ion Slip,” Journal of the Korean Physical Society, Vol. 47, No. 5, 2005, pp. 809-817.

[5] H. A. Attia, “Time Varying Hydromagnetic Flow of Dus- ty Fluid between Parallel Porous Plates Considering the Ion Slip,” Journal of Technical Physics, Vol. 47, No. 3, 2006, pp. 131-147.

[6] H. A. Attia, “Analytical Solution for Flow of a Dusty Fluid in a Circular Pipe with Hall and Ion Slip Effects,” Chemical Engineering Communications (CEC), Vol. 194, No. 10, 2007, pp. 1287-1296.

[7] H. A. Attia, “Transient Hart-mann Flow with Heat Transfer Considering the Ion Slip,” Physica Scripta, Vol. 66, 2002, pp. 470-475. doi:10.1238/Physica.Regular.066a00470

[8] M. A. Seddeek, “The Effects of Hall and Ion-Slip Currents on Mag-neto-Micropolar Fluid and Heat Transfer over a Non-Isothermal Stretching Sheet with Suction and Blowing,” Proceedings of the Royal Soceity: London A, Vol. 457, 2001, pp. 3039-3050. doi:10.1098/rspa.2001.0847

[9] P. C. Ram, “The Effects of Hall and Ion-Slip Currents on Free Convective Heat Generating Flow in a Rotating Fluid,” International Journal of Energy Research, Vol. 19, No. 5, 1995, pp. 371-376. doi:10.1002/er.4440190502

[10] M. L. Mittal and A. N. Bhat, “Forced Convective Heat Transfer in a MHD Channel with Hall and Ion Slip Currents,” Applied Scientific Research, Vol. 35, No. 4, 1979, pp. 251-264. doi:10.1007/BF00418216

[11] R. N. Jana and N. Datta, “Couette Flow and Heat Transfer in a Rotating System,” Acta Meccanica, Vol. 26, No. 1-4, 1977, pp. 301-306. doi:10.1007/BF01177152

[12] A. K. Kanch and R. N. Jana, “ Hall Effect on Unsteady Couette Flow under Boundary Layer Approximations,” Journal of the Physical Sciences, Vol. 7, 2001, pp. 74-86.

[13] H. A. Attia, “Ion Slip Effect on Un-steady Couette Flow with Heat Transfer under Exponential Decaying Pressure Gradient,” Tamkang Journal of Science and Engineering, Vol. 12, No. 2, 2009, pp. 209-214.

[14] B.K. Jha and C. A. Apere, “Combined Effect of Hall and Ion-Slip Cur-rents on Unsteady MHD Couette Flows in a Rotating System,” Journal of the Physical Society of Japan, Vol. 79, No. 10, 2010, pp. 104401-104401-9. doi:10.1143/JPSJ.79.104401

[15] H. S. Carslaw and J. C. Jae-ger, “Conduction of Heat in Solids,” Oxford University Press, Oxford, 1959.

[16] A. S. Gupta, “Hydromagnetic Flow Past a Porous Flat Plate with Hall Effects,” Acta Mechanica, Vol. 22, No. 3-4, 1975, pp. 281-287. doi:10.1007/BF01170681