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TECHNICAL PAPERS: Natural and Mixed Convection

Linear Stability of Mixed Convection Flow of Two Immiscible Fluids in a Vertical Annulus

[+] Author and Article Information
Kai-Ti R. Chang

M. I. Systems, 1826 W. Broadway Rd. #B43, Mesa, AZ 85202

Kang Ping Chen

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106

J. Heat Transfer 123(3), 434-440 (Jan 20, 2001) (7 pages) doi:10.1115/1.1370511 History: Received September 05, 2000; Revised January 20, 2001
Copyright © 2001 by ASME
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References

Preziosi,  L., Chen,  K., and Joseph,  D. D., 1989, “Lubricated Pipelining: Stability of Core-Annular Flow,” J. Fluid Mech., 201, pp. 323–356.
Charles,  M. E., Govier,  G. W., and Hodgson,  G. W., 1961, “The Horizontal Pipeline Flow of Equal Density Oil-Water Mixtures,” Can. J. Chem. Eng., 39, pp. 27–36.
Chen,  K., Bai,  R., and Joseph,  D. D., 1990, “Lubricated Pipelining. Part 3 Stability of Core-Annular Flow in Vertical Pipes,” J. Fluid Mech., 214, pp. 251–286.
Chen,  K., and Zhang,  Y., 1993, “Stability of the Interface in Co-Extrusion Flow of Two Viscoelastic Fluids through a Pipe,” J. Fluid Mech., 247, pp. 489–502.
Joseph, D. D., and Renardy, Y., 1992, Fundamentals of Two-Fluid Dynamics I, II, Springer-Verlag, New York.
Chen,  K., 1995, “Interfacial Instabilities in Stratified Shear Flows Involving Multiple Viscous and Viscoelastic Fluids,” Appl. Mech. Rev., 48, pp. 763–776.
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Pinarbasi,  A., and Liakopoulos,  A., 1995, “The Effect of Variable Viscosity on the Interfacial Stability of Two-Layer Poiseuille Flow,” Phys. Fluids, 7, pp. 1318–1324.
Chang, K.-T., 1998, “Linear Stability Theory of Mixed Convection Flow for Two Immiscible Fluids in a Vertical Annulus,” Ph.D. dissertation, Arizona State University, Tempe, AZ.
Arnoldi,  W. E., 1951, “The Principle of Minimized Iterations in the Solution of the Matrix Eigenvalue Problem,” Quarterly Appl. Math., 214, pp. 17–29.
Huang, A., 1993, private communication.
Yao,  L. S., and Rogers,  B. B., 1989, “The Linear Stability of Mixed Convection in a Vertical Annulus,” J. Fluid Mech., 201, pp. 279–298.
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Vargaftik, N. B., 1975, Tables on the Thermophysical Physical Properties of Liquids and Gases, 2nd ed., Hemisphere, Washington, D.C.

Figures

Grahic Jump Location
Critical Re of capillary, thermal and shear modes. (a=0.01,b=1.1, transformer oil-water system with density matched, J=1669.6,ΔT̃=20 K) s: stable; u: unstable.
Grahic Jump Location
Effect of temperature-dependent viscosity on the capillary, shear and thermal modes. (solid line: variable viscosity, dotted line: constant viscosity): (a) ΔT̃>0, inner cylinder is hotter than the outer cylinder; and (b) ΔT̃<0, inner cylinder is cooler than the outer cylinder.
Grahic Jump Location
Neutral curves of capillary, shear, and thermal modes with μ(T) at (a) ΔT̃=10 K, (b) ΔT̃=20 K, (c) ΔT̃=40 K, and (d) ΔT̃=80 K. (solid line: thermal mode, dotted line: shear mode, dash-dot-dot line: capillary mode; s: stable; u: unstable)
Grahic Jump Location
Neutral curves of shear and thermal modes with μ(T) at (a) ΔT̃=−10 K, (b) ΔT̃=−20 K, (c) ΔT̃=−40 K, and (d) ΔT̃=−80 K. (solid line: thermal mode, dotted line: shear mode, s: stable, u: unstable)

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