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TECHNICAL PAPERS

The Spatial Stability of Natural Convection Flow on Inclined Plates

[+] Author and Article Information
Anatoli Tumin

Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721e-mail: tumin@engr.Arizona.edu

J. Fluids Eng 125(3), 428-437 (Jun 09, 2003) (10 pages) doi:10.1115/1.1566047 History: Received November 02, 2001; Revised November 26, 2002; Online June 09, 2003
Copyright © 2003 by ASME
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References

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Saric,  W. S., and Nayfeh,  A. H., 1975, “Non-Parallel Stability of Boundary-Layer Flows,” Phys. Fluids, 18, pp. 945–950.
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Figures

Grahic Jump Location
Schematic of the flow and the coordinate system
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Eigenvalue map (Rx=100, θ=5°, ω=0.1, γδx=0): ×, ▵ – collocation method; ○ – Runge-Kutta method. Pr=5.5.
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Profiles of streamwise velocity and temperature disturbances (parameters are the same as in Fig. 2
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Eigenvalue map (Rx tan θ=24.26, ω=0, γδx=1.292) showing the quasi-parallel approximation (×). Pr=5.5.
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Eigenvalue map (Rx tan θ=24.26, ω=0, γδx=1.292): × – quasi-parallel approximation; ○ – local nonparallel model
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Velocity disturbance profiles, v and w, of the neutral vortex mode (Rx tan θ=24.26, ω=0, γδx=1.292). Pr=5.5.
Grahic Jump Location
Eigenvalue maps (ω=0, γδx=1.292). Quasi-parallel approximation. Pr=5.5.
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Velocity disturbance profiles, v and w, of the second unstable vortex mode (Rx tan θ=242.6, ω=0, γδx=1.292). Pr=5.5.
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Neutral curves for the traveling mode, γ=0. Solid symbols (P)–quasi-parallel approximation; open symbols (NP)–nonparallel flow theory. Pr=5.5.
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Growth rates for the traveling modes: (a) θ=0°; (b) θ=12°. Solid symbols–quasi-parallel approximation; open symbols–nonparallel flow theory. Pr=5.5.
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Comparison of growth rates for different models of the steady vortex mode (Rx tan θ=24.26, ω=0, γδx=1.292): □ – quasi-parallel; ⋄ – local nonparallel; • – perturbation method (term No. 1 in Eq. (29) only); ○ – conventional nonparallel theory (both terms in Eq. (29)). Pr=5.5.
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Effect of spanwise wave number and Reynolds number on the growth rate of the vortex instability mode: (a) Rx tan θ=60; (b) Rx tan θ=120. □ – quasi-parallel; ⋄ – local nonparallel; • – perturbation method (term No. 1 in Eq. (22) only); ○ – conventional nonparallel theory (both terms in Eq. (22)). Pr=6.7.
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Comparison of the disturbance velocity profiles at ξ0=0.22 used in two runs (RL tan θ=145,γδL=1.5): + – 1st run; × – 2nd run. Pr=5.5.
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Effect of initial data on umax(RL tan θ=145,γδL=1.5): + – 1st run; × – 2nd run. Pr=5.5.
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Comparison of growth rates (RL tan θ=145,γδL=1.5): × – quasi-parallel approximation; + – nonparallel normal mode consideration; ○ – marching method (run 1). Pr=5.5.
Grahic Jump Location
Comparison of growth rates at ξ=1. RL tan θ=145, Pr=5.5: × – quasi-parallel approximation; ○ – marching method (run 1).

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