A Note on Hydromagnetic Flow of an Oldroyd-B Fluid near an Infinite Plate Induced by Half Rectified Sine Pulses

Arun Kumar Ghosh, Sanjib Kumar Datta, Pulakesh Sen

Department of Mathematics, D. N. C. College, Aurangabad, India.
Department of Mathematics, University of Kalyani, Kalyani, India.
Jadavpur University, Kolkata, India.

DOI: 10.4236/ojfd.2014.42017                

Abstract

An initial value problem concerning the motion of an incompressible, electrically conducting, viscoelastic Oldroyd-B fluid bounded by an infinite rigid non-conducting plate is solved. The unsteady motion is generated impulsively from rest in the fluid due to half rectified sine pulses subjected on the plate in its own plane in presence of an external magnetic field. It is assumed that no external electric field is acting on the system and the magnetic Reynolds number is very small. The operational method is used to obtain exact solutions for the fluid velocity and the shear stress on the wall. Quantitative analysis of the results is presented with a view to disclose the simultaneous effects of the external magnetic field and the fluid elasticity on the flow and the wall shear stress for different periods of pulsation of the plate. It is also shown that the classical and hydromagnetic Rayleigh solutions appear as the limiting cases of the present analysis.

Keywords

Hydromagnetic, Pulsatile Flow, Oldroyd-B Fluid, Contour Integral

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Ghosh, A.K. (1965) Flow of Viscous Liquid Set up between Two Co-Axial Cylinders Due to Pulses of Longitudinal Impulses Applied on the Inner Cylinder. Journal of Science and Engineering Research, 9, 222.
[2]	Chakraborty, A. and Ray, J. (1980) Unsteady Magnetohydrodynamic Couetteflow between Two Plates When One of the Plates Is Subjected to Random Pulses. Journal of the Physical Society of Japan, 48, 1361-1364. http://dx.doi.org/10.1143/JPSJ.48.1361
[3]	Makar, M.N. (1987) Magnetohydrodynamic Flow between Two Plates When One of the Platesis Subjected to Tooth Pulses. Acta Physica Polonica, A71, 995.
[4]	Bestman, A.R. and Njoku, F.I. (1988) On Hydromagnetic Channel Flow Induced by Toothpulses. Miramare-Trieste.
[5]	Ghosh, A.K. and Sarkar, K. (1995) On Hydromagnetic Channel Flow of a Dusty Fluid Induced by Tooth Pulses. Journal of the Physical Society of Japan, 64, 1489-1500. http://dx.doi.org/10.1143/JPSJ.64.1489
[6]	Ghosh, S. and Ghosh, A.K. (2004) On Hydromagnetic Channel Flow of a Particulate Suspension Induced by Rectified Sine Pulses. Journal of the Physical Society of Japan, 73, 1506-1513. http://dx.doi.org/10.1143/JPSJ.73.1506
[7]	Ghosh, S. and Ghosh, A.K. (2004) On Hydromagnetic Flow of a Two-Phase Fluid near a Pulsating Plate. Indian Journal of Pure and Applied Mathematics, 36, 529.
[8]	Datta, N., Dalal, D.C. and Mishra, S.K. (1993) Unsteady Heat Transfer to Pulsatile Flow of a Dustyviscous Incompressible Fluid in a Channel. International Journal of Heat and Mass Transfer, 36, 1783-1788. http://dx.doi.org/10.1016/S0017-9310(05)80164-4
[9]	Datta, N. and Dalal, D.C. (1995) Pulsatile Flow and Heat Transfer of a Dusty Fluid through an Infinitely Long Annular Pipe. International Journal of Multiphase Flow, 21, 515-528. http://dx.doi.org/10.1016/0301-9322(94)00064-Q
[10]	Tanner, R.I. (1962) Note on the Rayleigh Problem for a Viscoelastic Fluid. Zeitschrift fur Angewandte Mathematik und Physik, 8, 573.
[11]	Ghosh, A.K. and Mitra, S. (1977) On Stokes’ Problems for Linear Viscoelastic Fluids. Bulletinde L’Academie Polonaise des Sciences, 25, 55.
[12]	Ghosh, A.K. and Debnath, L. (1992) On Heat Transfer to Pulsatile Flow of a Viscoelastic Fluid. Acta Mechanica, 93, 169-177. http://dx.doi.org/10.1007/BF01182582
[13]	Rajagopal, K.R. and Bhatnagar, R.K. (1995) Exact Solutions for Some Simple Flows of an Oldroyd-B Fluid. Acta Mechanica, 113, 233-239. http://dx.doi.org/10.1007/BF01212645
[14]	Hayat, T., Siddiqui, A.M. and Asghar, S. (2001) Some Simple Flows of an Oldroyd-B Fluid. International Journal of Engineering Science, 39, 135-147. http://dx.doi.org/10.1016/S0020-7225(00)00026-4
[15]	Hayat, T., Hutter, K., Asghar, S. and Siddiqui, A.M. (2002) MHD Flows of an Oldroyd-B Fluid. Mathematical and Computer Modelling, 36, 987-995. http://dx.doi.org/10.1016/S0895-7177(02)00252-2
[16]	Tan, W.C. and Masuoka, T. (2005) Stokes’ First Problem for an Oldroyd-B Fluid in a Porous Half Space. Physics of Fluids, 17, Article ID: 023101. http://dx.doi.org/10.1063/1.1850409
[17]	Javadjzadegan, A., Esmaeili, M., Majidi, S. and Fakhimghanbarzadeh, B. (2009) Pulsatile Flow of Viscous and Vis- coelastic Fluids in Constricted Tubes. Journal of Mechanical Science and Technology, 23, 2456-2467. http://dx.doi.org/10.1007/s12206-009-0713-9
[18]	Ghosh, A.K. and Sana, P. (2009) On Hydromagnetic Rotating Flow of an Oldroyd-B Fluid near an Oscillating Plate. Zeitschrift für angewandte Mathematik und Physik, 60, 1135-1155. http://dx.doi.org/10.1007/s00033-009-8060-3
[19]	Yang, H.T. and Healy, J.V. (1973) The Stokes Problem for a Conducting Fluid with Suspension of Particles. Applied Scientific Research, 21, 378.