The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.
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Transition in Convective Flows Heated Internally
Masato Nagata,
Masato Nagata
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Japan
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Sotos Generalis
Sotos Generalis
School of Engineering and Applied Sciences, Division of Chemical Engineering and Applied Chemistry, Aston University, U.K.
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Masato Nagata
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Japan
Sotos Generalis
School of Engineering and Applied Sciences, Division of Chemical Engineering and Applied Chemistry, Aston University, U.K.
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division July 13, 2001; revision received November 21, 2001. Associate Editor: P. S. Ayyaswamy.
J. Heat Transfer. Aug 2002, 124(4): 635-642 (8 pages)
Published Online: July 16, 2002
Article history
Received:
July 13, 2001
Revised:
November 21, 2001
Online:
July 16, 2002
Citation
Nagata, M., and Generalis, S. (July 16, 2002). "Transition in Convective Flows Heated Internally ." ASME. J. Heat Transfer. August 2002; 124(4): 635–642. https://doi.org/10.1115/1.1470169
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