0
Research Papers: Forced Convection

Viscous Corrections for the Viscous Potential Flow Analysis of Rayleigh–Taylor Instability With Heat and Mass Transfer

[+] Author and Article Information
Mukesh Kumar Awasthi

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

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

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 15, 2011; final manuscript received January 28, 2013; published online June 6, 2013. Assoc. Editor: Alfonso Ortega.

J. Heat Transfer 135(7), 071701 (Jun 06, 2013) (8 pages) Paper No: HT-11-1352; doi: 10.1115/1.4023580 History: Received July 15, 2011; Revised January 28, 2013

Viscous corrections for the viscous potential flow analysis of Rayleigh–Taylor instability of two viscous fluids when there is heat and mass transfer across the interface have been considered. Both fluids are taken as incompressible and viscous with different kinematic viscosities. In viscous potential flow theory, viscosity enters through a normal stress balance and the effects of shearing stresses are completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface of the two fluids. It has been observed that heat and mass transfer has a stabilizing effect on the stability of the system. It has been shown that the irrotational viscous flow with viscous corrections gives rise to exactly the same dispersion relation as the dissipation method in which no pressure term is required and the viscous effect is accounted for by evaluating viscous dissipation using irrotational flow. It has been observed that the inclusion of irrotational shearing stresses has a stabilizing effect on the stability of the system.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Equilibrium configuration of the system. Here η denotes perturbation from its equilibrium value.

Grahic Jump Location
Fig. 2

Neutral curves for critical wave number, system at ρ∧ = 0.001,vapor fraction ϕ = 0.1 for different values of alternative heat transfer coefficient Λ

Grahic Jump Location
Fig. 3

Neutral curves for critical wave number, system at ρ∧ = 0.001,Λ = 10-5 for the different values of vapor fraction ϕ

Grahic Jump Location
Fig. 4

Neutral curves for critical wave number at ρ∧ = 0.001,Λ = 10-5 for the different values of kinematic viscosity ratio κ

Grahic Jump Location
Fig. 5

Growth rate curves when ρ∧ = 0.001,μ∧ = 0.001,ϕ = 0.1 for the different values of heat transfer coefficient, α∧

Grahic Jump Location
Fig. 6

Comparison between the neutral curves for critical wave number at ρ∧ = 0.001,Λ = 10-4,ϕ = 0.1 for the IPF, VPF, and VCVPF solutions

Grahic Jump Location
Fig. 7

Comparison between the growth rate curves for the water-vapor system at ρ∧ = 0.001,μ∧ = 0.001,ϕ = 0.1,α = 0.0 for the VPF and VCVPF solutions

Grahic Jump Location
Fig. 8

Comparison between the growth rate curves for the water-vapor system at ρ∧ = 0.001,μ∧ = 0.001,ϕ = 0.1,α = 1.0 for the VPF and VCVPF solutions

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In