Criteria for Instability of Viscous Fluid

Jagjit Singh

Department of Mathematics, Govt. College Bhoranj (Tarkwari) District Hamirpur (H.P.)-176302, India

*Corresponding Author E-mail: jagjitsinghpatial@gmail.com

ABSTRACT:

Results relating to the stability of viscous fluid flow governed by the orr-somerfield equation will be presented in this paper, when velocity function is uniform continuous between the two boundaries.. Also bounds for c_r and c_i will be obtained by extending the existing previous results.. Further some results based on particular values of uniform continuous function U of velocity of the flow of the fluid will be discussed.

KEYWORDS: Viscous, bound, eigenvalue, boundary.

1. INTRODUCTION:

Joseph (1968, 1969) derived the bounds for c_r and c_icalculated from the Orr-Somerfield equation governing flow of viscous fluid with uniform velocity distribution given by U. The results given by Joseph will be extended here with the methods of integration and complex numbers. Adequate study has been done about results of governing equation of viscous fluid flow formed by Orr-Somerfield in Drazin and Reid (1981). These results have been used in this paper for further extension.

REFERENCES:

1. Drazin, P. G. and W. H. Reid(1981). “Hydrodynamic Stability” Cambridge University Press.

2. Joseph, D. D. (1968). Eigenvalue bounds for the Orr-Sommerfeld equation. J. Fluid Mech. 33, 617-21. [pp. 161-163.]

3. Joseph, D. D. (1969). Eigenvalue bounds for the Orr-Sommerfeld equation. Part 2 J. Fluid Mech. 36, 721-34. [pp. 161-164.]

Received on 07.11.2016 Modified on 18.11.2016

Research J. Science and Tech. 2017; 9(1):09-16.