The convective instability of a horizontal fluid layer subject to a time varying gradient of temperature is investigated. The stationary component of the temperature gradient is considered equal to zero and the oscillating components imposed on the horizontal boundaries are in phase and with the same amplitude. The aim of the present paper is to examine the effect of this type of modulation on the onset of convective instability. We show that unlike the case where the equilibrium configuration is stable in the absence of modulation, we have instability when the temperature at the horizontal boundaries is modulated in phase. Also, we observe that in the limit of low and high dimensionless frequency of modulation, ω < 0.5 and ω > 140, the basic state tends to a stable equilibrium configuration and for an intermediate dimensionless frequency, the system is potentially unstable. The results obtained from analytical asymptotic study for low and high dimensionless frequency are in good agreement with the numerical ones.
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Effect of Phase Thermal Modulation Without Stationary Temperature Gradient on the Threshold of Convection
K. Souhar,
K. Souhar
Laboratory of Energy Engineering,
Materials and Systems,
ENSA,
Ibn Zohr University,
Agadir 80000, Morocco
e-mail: k.souhar@uiz.ac.ma
Materials and Systems,
ENSA,
Ibn Zohr University,
Agadir 80000, Morocco
e-mail: k.souhar@uiz.ac.ma
Search for other works by this author on:
S. Aniss
S. Aniss
Laboratory of Mechanics,
Faculty of Sciences,
University Hassan II Casablanca,
20100, Morocco
e-mail: s.aniss@etude.univcasa.ma
Faculty of Sciences,
University Hassan II Casablanca,
20100, Morocco
e-mail: s.aniss@etude.univcasa.ma
Search for other works by this author on:
K. Souhar
Laboratory of Energy Engineering,
Materials and Systems,
ENSA,
Ibn Zohr University,
Agadir 80000, Morocco
e-mail: k.souhar@uiz.ac.ma
Materials and Systems,
ENSA,
Ibn Zohr University,
Agadir 80000, Morocco
e-mail: k.souhar@uiz.ac.ma
S. Aniss
Laboratory of Mechanics,
Faculty of Sciences,
University Hassan II Casablanca,
20100, Morocco
e-mail: s.aniss@etude.univcasa.ma
Faculty of Sciences,
University Hassan II Casablanca,
20100, Morocco
e-mail: s.aniss@etude.univcasa.ma
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 24, 2015; final manuscript received May 12, 2016; published online June 7, 2016. Assoc. Editor: Andrey Kuznetsov.
J. Heat Transfer. Oct 2016, 138(10): 102502 (8 pages)
Published Online: June 7, 2016
Article history
Received:
December 24, 2015
Revised:
May 12, 2016
Citation
Souhar, K., and Aniss, S. (June 7, 2016). "Effect of Phase Thermal Modulation Without Stationary Temperature Gradient on the Threshold of Convection." ASME. J. Heat Transfer. October 2016; 138(10): 102502. https://doi.org/10.1115/1.4033644
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