MHD Transient Flow with Hall Current Past an Accelerated Horizontal Porous Plate in a Rotating System

Affiliation(s)

Department of Mathematics, Gauhati University, Guwahati, India.

Department of Mathematics, ADP College, Nagaon, India.

Department of Mathematics, Gauhati University, Guwahati, India.

Department of Mathematics, ADP College, Nagaon, India.

ABSTRACT

An exact solution to the problem of an MHD transient flow with Hall current past a uniformly accelerated horizontal porous plate in a rotating system has been presented. The dimensionless governing equations of the flow problem are solved by Laplacetransform technique in closed form. A uniform magnetic field is assumed to be applied transversely to the direction of the flow. The expressions for velocity fields and skin-frictions are obtained in non-dimensional form. The primary and secondary velocity distributions and skin-frictions at the plate due to primary and secondary velocity field are demonstrated graphically and the effects of the different parameters namely, rotational parameter, Hartmann number, Hall parameter and acceleration parameter are discussed and the results are physically interpreted.

An exact solution to the problem of an MHD transient flow with Hall current past a uniformly accelerated horizontal porous plate in a rotating system has been presented. The dimensionless governing equations of the flow problem are solved by Laplacetransform technique in closed form. A uniform magnetic field is assumed to be applied transversely to the direction of the flow. The expressions for velocity fields and skin-frictions are obtained in non-dimensional form. The primary and secondary velocity distributions and skin-frictions at the plate due to primary and secondary velocity field are demonstrated graphically and the effects of the different parameters namely, rotational parameter, Hartmann number, Hall parameter and acceleration parameter are discussed and the results are physically interpreted.

Cite this paper

N. Ahmed, J. Goswami and D. Barua, "MHD Transient Flow with Hall Current Past an Accelerated Horizontal Porous Plate in a Rotating System,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 4, 2013, pp. 278-285. doi: 10.4236/ojfd.2013.34035.

N. Ahmed, J. Goswami and D. Barua, "MHD Transient Flow with Hall Current Past an Accelerated Horizontal Porous Plate in a Rotating System,"

References

[1] A. Raptis, “Mass Transfer and Free Convection through a Porous Medium by the Presence of a Rotating Fluid,” International Communications in Heat and Mass Transfer, Vol. 10, No. 2, 1983, pp. 141-146. http://dx.doi.org/10.1016/0735-1933(83)90040-4

[2] A. K. Singh, “Hydromagnetic Free-Convection Flow Past an Impulsively Started Vertical Plate in a Rotating Fluid,” International Communications in Heat and Mass Transfer, Vol. 11, No. 4, 1984, pp. 339-406.

[3] A. K. Singh, “MHD Free Convection Flow in the Stokes Problems for a Vertical Porous Plate in a Rotating System,” Astrophysics and Space Science, Vol. 95, No. 2, 1983, pp. 283-289.

[4] M. Alam, M. A. Sattar and M. Mansur, “Similarity Solution of Steady MHD Free Convection and Mass Transfer Flow with Thermal Diffusion in a Rotating System,” Dhaka University Journal of Science, Vol. 49, No. 2, 2001, p. 147.

[5] L. Debnath, “Exact Solutions of the Unsteady Hydrodynamic and Hydro Magnetic Boundary Layer Equations in a Rotating Fluid System,” ZAMM, Vol. 55, No. 7-8, 1975, pp. 431-438.

[6] H. Alfven, “Existence of Electromagnetic-Hydrodynamic Waves,” Nature, Vol. 150, No. 3805, 1942, pp. 405-406.

[7] T. G. Cowling, “Magneto Hydrodynamics,” Wiley Inter Science, New York, 1957.

[8] V. C. A. Ferraro and C. Pulmpton, “An Introduction to Magneto Fluid Mechanics,” Clarandon Press, Oxford, 1966.

[9] I. Pop, “The Effect of Hall Currents on Hydro Magnetic Flow near an Accelerated Plate,” Journal of Mathematical and Physical Sciences, Vol. 5, 1971, pp. 375-379.

[10] M. Kinyanjui, J. K. Kwanza and S. M. Uppal, “Magneto Hydrodynamic Free Convection Heat and Mass Transfer of a Heat Generating Fluid Past an Impulsively, Started Infinite Vertical Porous Plate with Hall Current and Radiation Absorption,” Energy Conversion and Management, Vol. 42, No. 8, 2001, pp. 917-931. http://dx.doi.org/10.1016/S0196-8904(00)00115-1

[11] M. Acharya, G. C. Das and L. P. Singh, “Hall Effect with Simultaneous Thermal and Mass Diffusion on Unsteady Hydro Magnetic Flow near an Accelerated Vertical Plate,” Indian Journal of Physics B, Vol. 75, No. 1, 2001, pp. 68-70.

[12] N. Ahmed and D. Kalita, “Transient MHD Free Convection from an Infinite Vertical Porous Plate in a Rotating Fluid with Mass Transfer and Hall Current,” Journal of Energy, Heat and Mass Transfer, Vol. 33, No. 1, 2011, pp. 271-292.

[13] N. Ahmed, H. Kalita and D. P. Barua, “Unsteady MHD Free Convective Flow Past a Vertical Porous Plate Immersed in a Porous Medium with Hall Current, Thermal Diffusion and Heat Transfer,” International Journal of Engineering, Science and Technology, Vol. 2, No. 6, 2010, pp. 59-74.

[14] N. Ahmed and H. K. Sarmah, “MHD Transient Flow Past an Impulsively Started Horizontal Porous Plate in a Rotating System with Hall Current,” International Journal of Applied Mathematics and Mechanics, Vol. 7, No. 2, 2011, pp. 1-15.

[1] A. Raptis, “Mass Transfer and Free Convection through a Porous Medium by the Presence of a Rotating Fluid,” International Communications in Heat and Mass Transfer, Vol. 10, No. 2, 1983, pp. 141-146. http://dx.doi.org/10.1016/0735-1933(83)90040-4

[2] A. K. Singh, “Hydromagnetic Free-Convection Flow Past an Impulsively Started Vertical Plate in a Rotating Fluid,” International Communications in Heat and Mass Transfer, Vol. 11, No. 4, 1984, pp. 339-406.

[3] A. K. Singh, “MHD Free Convection Flow in the Stokes Problems for a Vertical Porous Plate in a Rotating System,” Astrophysics and Space Science, Vol. 95, No. 2, 1983, pp. 283-289.

[4] M. Alam, M. A. Sattar and M. Mansur, “Similarity Solution of Steady MHD Free Convection and Mass Transfer Flow with Thermal Diffusion in a Rotating System,” Dhaka University Journal of Science, Vol. 49, No. 2, 2001, p. 147.

[5] L. Debnath, “Exact Solutions of the Unsteady Hydrodynamic and Hydro Magnetic Boundary Layer Equations in a Rotating Fluid System,” ZAMM, Vol. 55, No. 7-8, 1975, pp. 431-438.

[6] H. Alfven, “Existence of Electromagnetic-Hydrodynamic Waves,” Nature, Vol. 150, No. 3805, 1942, pp. 405-406.

[7] T. G. Cowling, “Magneto Hydrodynamics,” Wiley Inter Science, New York, 1957.

[8] V. C. A. Ferraro and C. Pulmpton, “An Introduction to Magneto Fluid Mechanics,” Clarandon Press, Oxford, 1966.

[9] I. Pop, “The Effect of Hall Currents on Hydro Magnetic Flow near an Accelerated Plate,” Journal of Mathematical and Physical Sciences, Vol. 5, 1971, pp. 375-379.

[10] M. Kinyanjui, J. K. Kwanza and S. M. Uppal, “Magneto Hydrodynamic Free Convection Heat and Mass Transfer of a Heat Generating Fluid Past an Impulsively, Started Infinite Vertical Porous Plate with Hall Current and Radiation Absorption,” Energy Conversion and Management, Vol. 42, No. 8, 2001, pp. 917-931. http://dx.doi.org/10.1016/S0196-8904(00)00115-1

[11] M. Acharya, G. C. Das and L. P. Singh, “Hall Effect with Simultaneous Thermal and Mass Diffusion on Unsteady Hydro Magnetic Flow near an Accelerated Vertical Plate,” Indian Journal of Physics B, Vol. 75, No. 1, 2001, pp. 68-70.

[12] N. Ahmed and D. Kalita, “Transient MHD Free Convection from an Infinite Vertical Porous Plate in a Rotating Fluid with Mass Transfer and Hall Current,” Journal of Energy, Heat and Mass Transfer, Vol. 33, No. 1, 2011, pp. 271-292.

[13] N. Ahmed, H. Kalita and D. P. Barua, “Unsteady MHD Free Convective Flow Past a Vertical Porous Plate Immersed in a Porous Medium with Hall Current, Thermal Diffusion and Heat Transfer,” International Journal of Engineering, Science and Technology, Vol. 2, No. 6, 2010, pp. 59-74.

[14] N. Ahmed and H. K. Sarmah, “MHD Transient Flow Past an Impulsively Started Horizontal Porous Plate in a Rotating System with Hall Current,” International Journal of Applied Mathematics and Mechanics, Vol. 7, No. 2, 2011, pp. 1-15.