Open Access Peer-reviewed

Hall Effects on the Unsteady Incompressible MHD Fluid Flow with Slip Conditions and Porous Walls

H. Zaman
Department of Mathematics, Islamia College Chartered University, Peshawar, Pakistan
Applied Mathematics and Physics. 2013, 1(2), 31-38. DOI: 10.12691/amp-1-2-3
Published online: August 25, 2017

Abstract

This work is concerned with the influence of Hall current on unsteady incompressible MHD fluid with slip conditions. The effects of Hall current on uniform suction or injection are also seen. As a special case of this problem for no slip condition, the effects of Hall current on Couette flow are discussed. The resulting unsteady problems for velocity are solved by means of Laplace transform, however, the inversion procedure for obtaining the solution is not a trivial matter. The characteristics of the complex transient velocity, complex overall transient velocity, complex steady state velocity are analyzed and discussed for both the cases. Graphical results for the Hall parameter reveal that it has significant influence on the real and imaginary parts of the velocity profiles.

Keywords:

hall effects, unsteady, Laplace transform, transient velocity, wall slip, porous walls
[1]  Craner, K. P. and Pai, S. I., Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw-Hill, New York, 1973.
 
[2]  Katagiri, M., The effect of Hall currents on the magnetohydrodynamic boundarylayer flow past a semi-infinite flate plate. J. Phys. Soc. Japan 27 1051-1059 1969.View Article
 
[3]  Gupta, A. S., Hydromagnetic flow past a porous flate plate with Hall effects. Acta Mech. 22 281-287 1975.View Article
 
[4]  Pop, I. and Soundalgekar, V. M., Effects of Hall current on hydromagnetic flow near a porous plate. Acta Mech. 20 315-318 1974.View Article
 
[5]  Debnath, L., Ray, S. C. and Chatterjee, A. K., Effects of Hall current on unsteady hydromagnetic flow past a porous plate in a rotating fluid system. Z. Angew. Math. Mech. 59 469-471 1979.View Article
 
[6]  Hayat, T., Naz, R. and Asghar, S., Hall effects on unsteady duct flow of a non-Newtonian fluid in a porous medium. Appl. Math. Computation 157 103-114 2004.View Article
 
[7]  Sato, H., The Hall effects in the viscous flow of ionized gas between parallel plates under transverse magnetic field. J. Phys. Soc. Japan 16 1427-1433 1961.View Article
 
[8]  M. A. Hossain, Effect of Hall current on unsteady hydromagnetic free convection flow near an infinite vertical porous plate. J. Phys. Soc. Japan 55 2183-2190 1986.View Article
 
[9]  M. A. Hossain, K. Mohammad, Effect of Hall current on hydromagnetic free convection flow near an accelerated porous plate. J. Phys. Soc. Japan 27 1531-1535 1988.View Article
 
[10]  Hossain, M. A., Rashid, R. I. M. A., The effect of Hall currents on hydromagnetic free convection flow near an accelerated porous plate. J. Phys. Soc. Japan 56 97-104 1987.View Article
 
[11]  Raptis, A., Ram, P. C., Effects of Hall current and rotation. Astrophys. Space Sci. 106 257-264 1984.View Article
 
[12]  Ram, P. C., Hall effects on free convection flow and mass transfer through a porous medium. Warme Stoffubertrag 22 223-225 1988View Article
 
[13]  Asghar, S., Mohyuddin, M. R. and Hayat, T., Effects of Hall current and heat transfer on flow due to a pull of ecentric rotating disks. Int. J. Heat and Mass Transfer 48 599-607 2005.View Article
 
[14]  Abo-Eldahab, E. M. and Elbarbary, M. E., Hall current effect on magnetohydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer. Int. J. Eng. Sci. 39 1641-1652 2001.View Article
 
[15]  Abo-Eldahab, E. M. and Abd El Aziz, M., Hall current and Ohmic heating effects on mixed convection boundary layer flow of a micropolar fluid from a rotating cone with power law variation in surface temperature. Int. Comm. Heat Mass Transfer 31 751-762 2004.View Article
 
[16]  Abo-Eldahab, E. M. and Salem, A. M., Hall effects on MHD free convection flow of a non-Newtonian power law fluid at a stretching surface. Int. Comm. Heat Mass Transfer 31 343-354 2004.View Article
 
[17]  Abo-Eldahab, E. M. and Abd El Aziz, M., Flow and heat transfer in a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream. Appl. Math. Comput. 162 881-899 2005.View Article
 
[18]  Ahmad, M., Zaman, H. and Rehman, N., Effects of Hall current on unsteady MHD flows of a second grade fluid. Cent. Eur. J. Phys. 8(3) 422-431 2010.View Article
 
[19]  Ayub, M., Zaman, H. and Ahmad, M., Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet. Cent. Eur. J. Phys. 8(1) 135-149 2010.View Article
 
[20]  Khan, M., Asghar, S. and Hayat, T., Hall effect on the pipe flow of a Burgers' fluid: An exact solution. Nonlinear Analysis: Real World Applications. 10 974-979 2009.View Article
 
[21]  Fang, T., A note on the incompressible Couette flow with porous walls. Int. Comm. Heat Mass Transfer. 31 (1)31-41 2004.View Article
 
[22]  Schlichting, H. and Gersten, K., Boundary layer theory, 8th Edition, Springer-Verlag, Berlin Heidelberg, 2000. PubMed
 
[23]  Khaled, A. R. A. and Vafai, K., The effect of the slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions. Int. J. Non-Linear Mech.39 795-809 2004.View Article
 
[24]  Hayat, T., Khan, M., Siddiqui, A. M. and Asghar, S., Transient flows of a second grade fluid. Int. J. Non-Linear Mech. 39 1621-1633 2004.View Article
 
[25]  Erdogan, M. E., A note on an unsteady flow of a viscous fluid due to an oscillating plane wall. Int. J. Non-Linear Mech. 35 1-6 2000.View Article
 
[26]  Hayat, T., Javed, T. and Abbas, Z., MHD flow of a micropolar fluid near a stagnation point towards a non-linear stretching surface. Nonlinear Analysis: Real World Applications. 10 1514-1526 2009.View Article
 
[27]  Hayat, T., Abbas, Z. and Javed, T., MHD stagnation point flow and heat transfer over a permeable surface through a porous space. Journal of Porous media. 12 183-195 2009.View Article
 
[28]  Asghar, S., Khan, M. and Hayat, T., Magnetohydrodynamic transient flows of a non-Newtonian fluid. Int. J. Non-Linear Mech. 40 589-601 2005.View Article
 
[29]  Khan, M., Hyder Ali, S., Hayat, T. and Fetecau, C., MHD flows of a second grade fluid between two side walls perpendicular to a plate through a porous medium. Int. J. Non-Linear Mech. 43 302-319 2008.View Article
 
[30]  Cortell, R., MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive pecies. Chem. Eng and Processing. 46 721-728 2007.View Article
 
[31]  Hayat, T., Zaman, H. and Ayub, M., Analytic solution of hydromagnetic flow with Hall effect over a surface stretching with a power law velocity. Numerical Methods for Partial Differential Equations. 27(4) 937-959 2010.View Article
 
[32]  Soltani, F. and Yilmazer, U., Slip velocity and slip layer thickness in flow of concentrated suspensions. J. Appl. Polym. Sin. 70 515-52 1998.View Article
 
[33]  Derek, C., Tretheway, D. C. and Meinhart, C. D., Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids. 14 9-12 2002.View Article
 
[34]  Yu, S. and Ameel, T. A., Slip-flow Heat Transfer in Rectangular Micro channels. Int. J. Heat and Mass Transfer. 44 4225-4234 2002.View Article
 
[35]  Roberts, G. E. and Kaufman, H., Tables of Laplace Transforms, p. 284, W. B. Saunders Company, Philadelphia 1966.