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Research Papers: Fundamental Issues and Canonical Flows

Study on Capillary Instability With Heat and Mass Transfer Through Porous Media: Effect of Irrotational Viscous Pressure

[+] Author and Article Information
Mukesh Kumar Awasthi

Department of Mathematics,
University of Petroleum and Energy Studies,
Dehradun-248007
e-mail: mukeshiitr.kumar@gmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 26, 2013; final manuscript received April 24, 2014; published online July 24, 2014. Editor: Malcolm J. Andrews.

J. Fluids Eng 136(10), 101204 (Jul 24, 2014) (7 pages) Paper No: FE-13-1265; doi: 10.1115/1.4027546 History: Received April 26, 2013; Revised April 24, 2014

In this paper, we investigate the effect of irrotational, viscous pressure on capillary instability of the interface between two viscous, incompressible, and thermally conducting fluids in a fully saturated porous medium 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 analysis extends our earlier work in which the capillary instability of two viscous and thermally conducting fluids in a fully saturated porous medium was studied assuming that the motion and pressure are irrotational and the viscosity enters through the jump in the viscous normal stress in the normal stress balance at the interface. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. We use the Darcy's model, and a quadratic dispersion relation is obtained. It is observed that heat and mass transfer has a stabilizing effect on the stability of the system and this effect enhances in the presence of irrotational viscous pressure.

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References

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Awasthi, M. K., and Agrawal, G. S., 2012, “Nonlinear Analysis of Capillary Instability With Heat and Mass Transfer,” Commun. Nonlinear Sci. Numer. Simulat., 17, pp. 2463–2475. [CrossRef]
Awasthi, M. K., Asthana, R., and Agrawal, G. S., 2012, “Pressure Corrections for the Potential Flow Analysis of Kelvin–Helmholtz Instability With Heat and Mass Transfer,” Int. J. Heat Mass Transfer, 55, pp. 2345–2352. [CrossRef]
Awasthi, M. K., Asthana, R., and Agrawal, G. S., 2013, “Viscous Correction for the Viscous Potential Flow Analysis of Capillary Instability With Heat and Mass Transfer,” J. Eng. Math., 80, pp. 75–89. [CrossRef]
Awasthi, M. K., 2013, “Viscous Corrections for the Viscous Potential Flow Analysis of Rayleigh–Taylor Instability With and Heat and Mass Transfer,” ASME J. Heat Transfer, 135(7), p. 071701. [CrossRef]
Asthana, R., Awasthi, M. K., and Agrawal, G. S., 2012, “Kelvin–Helmholtz Instability of Two Viscous Fluids in Porous Media” Int. J. App. Math. Mech., 8(14), pp. 1–10.
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Figures

Grahic Jump Location
Fig. 1

The equilibrium configuration of the fluid system

Grahic Jump Location
Fig. 2

Comparison between the neutral curves kc versus Λ obtained from the VCVPF as well as the VPF solution when ɛ = 0.5,p∧1 = 1/0.004, and φ = 0.05

Grahic Jump Location
Fig. 3

Maximum growth rate curves (ωI) m versus ε obtained from VCVPF as well as VPF solution when α = 10-5,p∧1 = 1/0.004, and φ = 0.05

Grahic Jump Location
Fig. 4

Neutral curves kc versus p∧1 obtained from VCVPF as well as VPF solution when α = 10-5,ɛ = 0.4, and φ = 0.05

Grahic Jump Location
Fig. 5

Neutral curves kc versus φ obtained from VCVPF as well as VPF solution when α = 10-5,ɛ = 0.4, and p∧1 = 1/0.004

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