Run-Up Flow of a Maxwell Fluid through a Parallel Plate Channel

Syed Yedulla Qadri, M. Veera Krishna

Department of Mathematics, Rayalaseema University, Kurnool, India.
Department of Mathematics, St. Josephs PG College, Kurnool, India.

DOI: 10.4236/ajcm.2013.34039                

Abstract

We consider the flow of an incompressible viscous Maxwell fluid between two parallel plates, initially induced by a constant pressure gradient. The pressure gradient is withdrawn and the upper plate moves with a uniform velocity while the lower plate continues to be at rest. The arising flow is referred to as run-up flow. The unsteady governing equations are solved as initial value problem using Laplace transform technique. The expression for velocity, shear stresses on both plates and discharge are obtained. The behavior of the velocity, shear stresses and mass flux has been discussed in detail with respect to variations in different governing flow parameters and is presented through graphs.

Keywords

Run-Up Flow; Maxwell’s Fluid; Laplace Transforms; Reynolds Number and Parallel Plate Channels

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	N. B. Naduvinamani, P. S. Hiremath and G. Gurubasavaraj, “Squeeze Film Lubrication of a Short Porous Journal Bearing with Couple Stress Fluids,” Tribology International, Vol. 34, No. 11, 2001, pp. 739-747.
[2]	N. B. Naduvinamani, P. S. Hiremath and G. Gurubasavaraj, “Surface Roughness Effects in A Short Porous Journal Bearing with a Couple Stress Fluid,” Fluid Dynamics Residuals, Vol. 31, No. 5-6, 2002, pp. 333-354.
[3]	N. B. Naduvinamani, P. S. Hiremath and G. Gurubasavaraj, “Effects of Surface Roughness on the Couple Stress Squeeze Film between a Sphere and a Flat Plate,” Tribology International, Vol. 38, No. 5, 2005, pp. 451-458.
[4]	N. B. Naduvinamani, S. T. Fathima and P. S. Hiremath, “Hydro Dynamic Lubrication of Rough Slider Bearings with Couple Stress Fluids,” Tribology International, Vol. 36, No. 12, 2003, pp. 949-959.
[5]	N. B. Naduvinamani, S. T. Fathima and P. S. Hiremath, “Effect of Surface Roughness on Characteristics of Couple Stress Squeeze Film between Anisotropic Porous Rectangular Plates,” Fluid Dynamics Residuals, Vol. 32, No. 5, 2003, pp. 217-231.
[6]	J. R. Lin and C. R. Hung, “Combined Effects of Non-Newtonian Couple Stresses and Fluid Inertia on the Squeeze Film Characteristics between a Long Cylinder and an Infinite Plate,” Fluid Dynamics Residuals, Vol. 39, No. 8, 2007, pp. 616-639.
[7]	J. Y. Kazakia and R. S. Rivlin, “Run-Up and Spin-Up in a Visco-Elastic Fluid I,” Rheologica Acta, Vol. 20, No. 2, 1981, pp. 111-127.
[8]	R. S. Rivlin, “Run-Up and Spin-Up in a Visco-Elastic Fluid II,” Rheologica Acta, Vol. 21, No. 2, 1982, pp. 107-111.
[9]	R. S. Rivlin, “Run-Up and Spin-Up in a Visco-Elastic Fluid III,” Rheologica Acta, Vol. 21, No. 3, 1982, pp. 213-222.
[10]	R. S. Rivlin, “Run-Up and Spin-Up in a Visco-Elastic Fluid IV,” Rheologica Acta, Vol. 22, No. 3, 1983, pp. 275-283.
[11]	N. Ch. Pattabhi Ramacharyulu and K. A. Raju, “Run-Up in a Generalized Porous Medium,” Indian Journal of Pure Applied Mathematics, Vol. 15, No. 6, 1984, pp. 665-670.
[12]	D. Ramakrishna, “Some Problems in the Dynamics of Fluids with Particle Suspensions,” Ph.D. Thesis, Kakatiya University, Warangal, 1986.
[13]	G. Honig and U. Hirdes, “A Method for the Numerical In-version of Laplace Transforms,” Journal of Computational Applied Mathematics, Vol. 10, No. 1, 1984, pp. 113-132.
[14]	M. Diwakar and T. K. V. Iyengar, “Run-Up Flow of a Couple Stress Fluid between Parallel Plates,” Nonlinear Analysis: Modelling and Control, Vol. 15, No. 1, 2010, pp. 29-37.
[15]	V. Sugunamma, M. S. Latha and N. Sandeep, “Run-Up Flow of a Rivlin-Ericksen Fluid through a Porous Medium in a Channel,” International Journal of Mathematical Archive, Vol. 2, No. 12, 2011, pp. 2625-2639.
[16]	M. Veera Krishna, S. V. Suneetha and R. Siva Prasad, “Hall Current Effects on Unsteady MHD Flow of Rotating Maxwell Fluid through a Porous Medium,” Journal of Ultra Scientist of Physical Sciences, Vol. 22, No. 1, 2010, pp. 133-144.
[17]	R. Reddy Sheelam, “Computational Techniques in Transient Magneto Hydro Dynamics Dusty Viscous and Run-Up Flows,” Ph.D. Thesis, Osmania University, Hyderabad, 1992, pp. 47-65.
[18]	M. Basha, “Visco-Elastic Fluid Flow and the Heat Transfer through Porous Medium,” Ph.D. Thesis, SriKrishnadevaraya University, Anantapur, 1994.
[19]	D. Malleswari, “Unsteady Flow of a Rivlin-Ericksen Fluid through Plannar Channels with Porous Lining,” Ph.D. Thesis, Sri Padmavathi Mahila Viswavidyalayam, Tirupati, 2010.