0
TECHNICAL PAPERS: Forced Convection

Transition in Homogeneously Heated Inclined Plane Parallel Shear Flows

[+] Author and Article Information
S. Generalis

School of Engineering and Applied Sciences, Division of Chemical Engineering and Applied Chemistry, Aston University, United Kingdom

M. Nagata

Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Japan

J. Heat Transfer 125(5), 795-803 (Sep 23, 2003) (9 pages) doi:10.1115/1.1599370 History: Received November 14, 2002; Revised May 16, 2003; Online September 23, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.

References

Horvat,  A., Kljenak,  I., and Marn,  J., 2001, “Two-Dimensional Large-Eddy Simulation of Turbulent Natural Convection Due to Internal Heat Generation,” Int. J. Heat Mass Transfer, 44, pp. 3985–3995.
Nourgaliev,  R. R., Dinh,  T. N., and Sehgal,  B. R., 1997, “Effect of Fluid Prandtl Number on Heat Transfer Characteristics in Internally Heated Liquid Pools With Rayleigh Number Up to 1012,” Nucl. Eng. Des., 169, pp. 165–184.
Worner,  M., Schmidt,  M., and Grotzbach,  G., 1997, “Direct Numerical Simulation of Turbulence in an Internally Heated Convective Fluid Layer and Implications for Statistical Modelling,” J. Hydraul. Res., 35, pp. 773–797.
Arpaci,  V. S., 1995, “Buoyant Turbulent Flow Driven by Internal Heat Generation,” Int. J. Heat Mass Transfer, 38, pp. 2761–2770.
Wilkie, D., and Fisher, S. A., 1961, “Natural Convection in a Liquid Containing a Distributed Heat Source,” International Heat Transfer Conference, Paper 119, University of Colorado, Boulder, pp. 995–1002.
Nagata,  M., and Generalis,  S., 2002, “Transition in Convective Flows Heated Internally,” ASME J. Heat Transfer, 124(4), pp. 635–642.
National Engineering Laboratory, 1998, “Prandtl Number for ZnCl2 Solutions,” private communication.
Gershuni, G. Z., and Zhukhovitskii, E. M., 1976, Convective Stability of Incompressible Fluids (Translated from the Russian by D. Lowish), Keterpress Enterprises, Jerusalem.
Gershuni,  G. Z., Zhukhovitskii,  E. M., and Yakimov,  A. A., 1974, “On Stability of Plane-Parallel Convective Motion Due to Internal Heat Sources,” Int. J. Heat Mass Transfer, 17, pp. 717–726.
Ehrenstein,  U., and Koch,  W., 1991, “Three-Dimensional Wavelike Equilibrium States in Plane Poiseuille Flow,” J. Fluid Mech., 228, pp. 111–148.
Pugh,  J. D., and Saffman,  P. G., 1988, “Two-Dimensional Superharmonic Stability of Finite Amplitude Waves in Plane Poiseuille Flow,” J. Fluid Mech., 194, pp. 295–307.
Heiber,  C. A., and Gebhart,  B., 1971, “Stability of Vertical Natural Convection Boundary Layers: Some Numerical Solutions,” J. Fluid Mech., 48, pp. 625–646.
Chait,  A., and Korpela,  S. A., 1989, “The Secondary Flow and Its Stability for Neutral Convection in a Tall Vertical Enclosure,” J. Fluid Mech., 200, pp. 189–216.
Busse,  F. H., and Glever,  R. M., 1979, “Instabilities of Convection Rolls in a Fluid of Moderate Prandtl Number,” J. Fluid Mech., 91, pp. 319–335.

Figures

Grahic Jump Location
The geometrical configuration exhibiting the basic symmetric velocity profile U*(z*) of the plane-parallel shear flow in an inclined fluid layer heated internally. The temperature T*(z*) is measured from the environment.
Grahic Jump Location
(a) The linear neutral curves in the (α,Gr) plane and for various values of the Prandtl number as indicated; (b) the critical wavenumber αc as a function of the Prandtl number; and (c) the critical Grashof number Grc as a function of the Prandtl number. χ=90 deg.
Grahic Jump Location
The critical Grashof number for the primary and the second closed connected neutral curves for transverse roll type perturbations. Pr=7, β=0, and χ≈4.95 deg
Grahic Jump Location
The closed neutral curves for (a) χ≈5.121 deg, (b) χ≈5.085 deg, and (c) χ≈4.95 deg. Pr=7. ⊗ corresponds to the value χ≈5.1273 deg.
Grahic Jump Location
The critical values of the Grashof number (right scale—continuous curve) and the wavenumber (left scale—dash-dotted curve) against the angle of inclination χ for transverse roll type perturbations (β=0). Pr=7. ⊗ corresponds to the value χ≈5.1273 deg.
Grahic Jump Location
The phase velocity (continuous curve—left scale) and real part of the leading eigenvalue, σ1r, (dashed curve—right scale) as a function of the Grashof number for the stability curve of Fig. 5 with χ≈4.95 deg and α=1.257, β=0, Pr=7
Grahic Jump Location
The phase velocity (continuous curve—left scale) and real part of the leading eigenvalue, σ1r, (dashed curve—right scale) as a function of the Grashof number for the second lower stability curve of Fig. 5 with χ≈4.95 deg and α=2.01, β=0, Pr=7
Grahic Jump Location
The neutral curve after the smooth merger of the two neutral curves for χ≈0.9 deg and β=0 with Pr=7
Grahic Jump Location
The critical Grashof number as a function of the angle of inclination for longitudinal roll type perturbations (α=0, continuous curve) and for transverse roll type perturbations (β=0, dash-dotted disconnected curves). Pr=7.
Grahic Jump Location
The critical wavenumber βc as a function of the angle of inclination χ for longitudinal roll type perturbations (α=0). Pr=7.
Grahic Jump Location
The stream function of (a) the velocity fluctuations ∂ϕ/∂x, (b) the disturbance ∂ϕ/∂x+∫−1zŬdz, (c) the total flow, ∂ϕ/∂x+∫−1zU⁁dz, (d) the total temperature, for the secondary state with α=1.21, Gr=23,000, Pr=7. Colder regions are represented by the lighter shade.
Grahic Jump Location
The total (a) mean flow (U⁁) profile and (b) mean temperature (T⁁) profile for various Grashof numbers and for a fixed wavenumber α=1.21. In (a) and (b) the dash-dotted, dashed, dash-dot-dotted and long-dashed curves correspond to Gr=4300, 12,000, 23,000 and 33,000, respectively. The solid curve in both figures represents the basic flow and temperature distributions. Pr=7.
Grahic Jump Location
The real part of the leading eigenvalue as function of d for α=1.227, Gr=2817, Pr=7 and for fixed values of the parameter b as indicated. Note that for α=1.227, linear stability analysis predicts a value of Grc=2816.8898.
Grahic Jump Location
Instability boundaries of secondary TWs for Pr=7. (1): d=0.01, (2): d=0.02, (3): d=0.03, (4): d=0.04, (a): b=0.2, (b): b=0.15, (c): b=0.1. For (1)–(4) b=0 and σ1i≠0. For (a)–(c) d=0 and σ1i=0. The outer curve represents the neutral curve.
Grahic Jump Location
Instability boundaries of secondary TWs for Pr=0.71. (1): d=0.01, (2): d=0.03, (3): d=0.04, (a): b=0.2, (b): b=0.15, (c): b=0.1. For (1)–(3) b=0 and σ1i≠0. For (a)–(c) d=0 and σ1i≠0. The outer curve represents the neutral curve.

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