Research Papers: Fundamental Issues and Canonical Flows

Nonlinear Analysis of Rayleigh–Taylor Instability of Cylindrical Flow With Heat and Mass Transfer

[+] Author and Article Information
Mukesh Kumar Awasthi

Department of Mathematics,
Indian Institute of Technology Roorkee,
Roorkee, Uttarakhand 247667, India
e-mail: mukeshiitr.kumar@gmail.com

1Present address: Department of Mathematics, Graphic Era University, Dehradun 248002, India.

Manuscript received October 3, 2012; final manuscript received March 4, 2013; published online April 12, 2013. Assoc. Editor: Ye Zhou.

J. Fluids Eng 135(6), 061205 (Apr 12, 2013) (7 pages) Paper No: FE-12-1492; doi: 10.1115/1.4024001 History: Received October 03, 2012; Revised March 04, 2013

We study the nonlinear Rayleigh–Taylor instability of the interface between two viscous fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. The method of multiple expansions has been used for the investigation. In the nonlinear theory, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. The various stability criteria are discussed both analytically and numerically and stability diagrams are obtained. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis.

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Fig. 1

Equilibrium configuration of the system

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Fig. 5

The neutral curves of wave number versus heat transfer coefficient α for the different values of vapor thickness h1

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Fig. 6

Comparison between the linear and nonlinear stability analysis for vapor-water system

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Fig. 7

The neutral curves of wave number versus viscosity ratio of two fluids μ(μ(1)/μ(2))

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Fig. 2

Comparison between the neutral stability curves obtained for the IPF analysis as well as VPF analysis for r1 = 1 cm and r2 = 2 cm

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Fig. 3

Comparison between the neutral stability curves obtained for the IPF analysis as well as VPF analysis for r1 = 1 cm and r2 = 5 cm

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Fig. 4

The neutral curves of wave number versus vapor thickness h1 for the different values of heat transfer coefficient α




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