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RESEARCH PAPER

The Dynamics of Two-Dimensional Buoyancy Driven Convection in a Horizontal Rotating Cylinder

[+] Author and Article Information
Nadeem Hasan, Sanjeev Sanghi

Dept. of Applied Mechanics, IIT Delhi, New Delhi, India-110016

J. Heat Transfer 126(6), 963-984 (Jan 26, 2005) (22 pages) doi:10.1115/1.1833370 History: Received January 14, 2004; Revised September 16, 2004; Online January 26, 2005
Copyright © 2004 by ASME
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References

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Martini,  W. R., and Churchill,  S. W., 1960, “Natural Convection Inside a Horizontal Cylinder,” AIChE J., 6, pp. 251–257.
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Weinbaum,  S., 1964, “Natural Convection in a Horizontal Cylinder,” J. Fluid Mech., 18, pp. 409–437.
Hellums,  J. D., and Churchill,  S. W., 1962, “Transient and Steady State, Free and Natural Convection, Numerical Solutions: Part II—The Region Inside a Horizontal Cylinder,” AIChE J., 8, pp. 692–695.
Heinrich,  J. C., and Yu,  C. C., 1988, “Finite Element Simulation of Buoyancy Driven Flows With Emphasis on Natural Convection in a Horizontal Circular Cylinder,” Comput. Methods Appl. Mech. Eng., 69, pp. 1–27.
Xin,  S., Le Quere,  P., and Daube,  O., 1997, “Natural Convection in a Differentially Heated Horizontal Cylinder: Effects of Prandtl Number on Flow Structure and Instability,” Phys. Fluids, 4, pp. 1014–1033.
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Amsden, A. A., and Harlow, F. H., 1970, “The SMAC Method: A Numerical Technique for Calculating Incompressible Fluid Flows,” Los Alamos Scientific Report, LA 4370.
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Figures

Grahic Jump Location
Geometry of the problem
Grahic Jump Location
A comparison of circumferential distribution of local wall normal heat flux with that of Xin et al. 7 for (a) Rag=1×104; (b) Rag=5×104; (c) Rag=1×105; (d) Rag=5×105
Grahic Jump Location
(a) Streamline (left) and isotherm (right) patterns at Rag=105,RaΩ=0. (b) Similar variation of nondimensional temperature θ along the horizontal diameter for x<0 for different Rag; (c) similar variation of nondimensional circumferential velocity vθ along the horizontal diameter for x<0 for different Rag.
Grahic Jump Location
Streamline and Isotherm patterns for RaΩ=102,Ta=104 at (a) ϕg=3π/2, (b) ϕg=π, (c) ϕg=π/2, (d) ϕg=0
Grahic Jump Location
Profiles of (a) u velocity across the vertical diameter; (b) v velocity across the horizontal diameter; and (c) θ across the horizontal diameter for different ϕg at RaΩ=102,Ta=104
Grahic Jump Location
Streamline and isotherm patterns for RaΩ=103,Ta=105 at (a) ϕg=3π/2, (b) ϕg=π, (c) ϕg=π/2, (d) ϕg=0
Grahic Jump Location
Profiles of (a) u velocity across the vertical diameter, (b) v velocity across the horizontal diameter, and (c) θ across the horizontal diameter for different ϕg at RaΩ=103,Ta=105
Grahic Jump Location
Streamline and isotherm patterns for RaΩ=104,Ta=106 at (a) ϕg=3π/2, (b) ϕg=π, (c) ϕg=π/2, (d) ϕg=0
Grahic Jump Location
Profiles of (a) u velocity across the vertical diameter, (b) v velocity across the horizontal diameter, and (c) θ across the horizontal diameter for different ϕg at RaΩ=104,Ta=106
Grahic Jump Location
Streamline and isotherm patterns for RaΩ=105,Ta=107 at (a) ϕg=3π/2 (b) ϕg=π, (c) ϕg=π/2, (d) ϕg=0
Grahic Jump Location
Profiles of (a) u velocity across the vertical diameter, (b) v velocity across the horizontal diameter, and (c) θ across the horizontal diameter for different ϕg at RaΩ=105,Ta=107
Grahic Jump Location
Streamline and isotherm patterns for RaΩ=106,Ta=108 at (a) ϕg=3π/2, (b) ϕg=π, (c) ϕg=π/2, (d) ϕg=0
Grahic Jump Location
Profiles of (a) u velocity across the vertical diameter, (b) v velocity across the horizontal diameter, and (c) θ across the horizontal diameter for different ϕg at RaΩ=106,Ta=108
Grahic Jump Location
Streamline and isotherm pattern for RaΩ=107,Ta=109 at ϕg=3π/2
Grahic Jump Location
Time histories of v velocity at point (−0.72,0) for (a) RaΩ=102, (b) RaΩ=103, (c) RaΩ=104, (d) RaΩ=105, (e) RaΩ=106, (f) RaΩ=107
Grahic Jump Location
Power spectral density curves for time series of v velocity at (−0.72,0) for (a) RaΩ=102, (b) RaΩ=103, (c) RaΩ=104, (d) RaΩ=105, (e) RaΩ=106, (f) RaΩ=107
Grahic Jump Location
Profiles of vorticity across the horizontal diameter for different ϕg at (a) RaΩ=102, (b) RaΩ=103, (c) RaΩ=104, (d) RaΩ=105, (e) RaΩ=106, (f) RaΩ=107
Grahic Jump Location
Profiles of kinetic energy across the horizontal diameter for different ϕg at (a) RaΩ=102, (b) RaΩ=103, (c) RaΩ=104, (d) RaΩ=105, (e) RaΩ=106, (f) RaΩ=107
Grahic Jump Location
The time history of Nu over the hot portion of the cylinder wall at (a) RaΩ=102, (b) RaΩ=103, (c) RaΩ=104, (d) RaΩ=105, (e) RaΩ=106, (f) RaΩ=107
Grahic Jump Location
Variation of Nu with RaΩ
Grahic Jump Location
Profiles of vorticity (left) kinetic energy (right) across the horizontal diameter for different ϕg at (a) RaΩ=1.9×103, (b) RaΩ=1.92×103, (c) RaΩ=1.95×103, (d) RaΩ=2×103

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