Research Papers: Natural and Mixed Convection

Effect of Phase Thermal Modulation Without Stationary Temperature Gradient on the Threshold of Convection

[+] Author and Article Information
K. Souhar

Laboratory of Energy Engineering,
Materials and Systems,
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

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 138(10), 102502 (Jun 07, 2016) (8 pages) Paper No: HT-15-1814; doi: 10.1115/1.4033644 History: Received December 24, 2015; Revised May 12, 2016

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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Donnelly, R. J. , 1964, “ Experiments on the Stability of Viscous Flow Between Rotating Cylinders,” Proc. R. Soc. A, 281(1384), p. 130. [CrossRef]
Venezian, G. , 1969, “ Effect of Modulation on the Onset of Thermal Convection, Part 2 Convective Instability,” J. Fluid Mech., 35(02), pp. 243–254. [CrossRef]
Rosenblat, S. , and Herbert, D. M. , 1970, “ Low Frequency Modulation of Thermal Instability,” J. Fluid Mech., 43(2), pp. 385–398. [CrossRef]
Rosenblat, S. , and Tanaka, D. A. , 1971, “ Modulation of Thermal Convection Instability,” Phys. Fluids, 14(7), pp. 1319–1322. [CrossRef]
Yih, C. S. , and Li, C. H. , 1972, “ Instability of Unsteady Flows or Configurations,” J. Fluid Mech., 54(01), pp. 143–152. [CrossRef]
Finucane, R. G. , and Kelly, R. E. , 1976, “ Onset of Instability in a Fluid Layer Heated Sinusoidally From Below,” Int. J. Heat Mass Transfer, 19(1), pp. 71–85. [CrossRef]
Roppo, M. N. , Davis, S. H. , and Rosenblat, S. , 1984, “ Benard Convection With Time-Periodic Heating,” Phys. Fluids, 27(4), pp. 796–803. [CrossRef]
Or, A. C. , and Kelly, R. E. , 1999, “ Time-Modulated Convection With Zero Mean Temperature Gradient,” Phys. Rev. E, 60(2), pp. 1741–1747. [CrossRef]
Bhadauria, B. S. , and Bhatia, P. K. , 2002, “ Time-Periodic Heating for Rayleigh-Benard Convection,” Phys. Scr., 66(1), pp. 59–65. [CrossRef]
Aniss, S. , Belhaq, M. , Souhar, M. , and Velarde, M. G. , 2005, “ Asymptotic Study of Rayleigh-Benard Convection Under Time Periodic Heating in Hele-Shaw Cell,” Phys. Scr., 71(4), pp. 395–401. [CrossRef]
Malashetty, M. S. , and Basavaraja, D. , 2005, “ Effect of Thermal Modulation on the Onset of Double Diffusive Convection in a Horizontal Fluid Layer,” Int. J. Therm. Sci., 44(4), pp. 323–332. [CrossRef]
Oukada, B. , Ouazzani, M. T. , and Aniss, S. , 2006, “ Effects of a Temperature Modulation in Phase at the Frontier on the Convective Instability of a Viscoelastic Layer,” C. R. Mec., 334(3), pp. 205–211. [CrossRef]
Malashetty, M. S. , and Swamy, M. , 2008, “ Effect of Thermal Modulation on the Onset of Convection in a Rotating Fluid Layer,” Int. J. Heat Mass Transfer, 51(11), pp. 2814–2823. [CrossRef]
Bhadauria, B. S. , 2008, “ Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium,” ASME J. Heat Transfer, 130(5), p. 052601. [CrossRef]
Bhadauria, B. S. , Bhatia, P. K. , and Lokenath, D. , 2009, “ Weakly Non-Linear Analysis of Rayleigh-Benard Convection With Time Periodic Heating,” Int. J. Non-Linear Mech., 44(1), pp. 58–65. [CrossRef]
Bhadauria, B. S. , Siddheshwar, P. G. , and Suthar, P. , 2012, “ Nonlinear Thermal Instability in a Rotating Viscous Fluid Layer Under Temperature/Gravity Modulation,” ASME J. Heat Transfer, 134(10), p. 102502. [CrossRef]
Bhadauria, B. S. , and Kiran, P. , 2014, “ Heat and Mass Transfer for Oscillatory Convection in a Binary Viscoelastic Fluid Layer Subjected to Temperature Modulation at the Boundaries,” Int. Commun. Heat Mass Transfer, 58, pp. 166–175. [CrossRef]
Nield, D. A. , and Kuznetsov, A. V. , 2016, “ The Effect of Pulsating Throughflow on the Onset of Convection in a Horizontal Porous Layer,” Transp. Porous Media, 111(3), pp. 731–740. [CrossRef]
Nield, D. A. , and Kuznetsov, A. V. , 2013, “ The Effect of Pulsating Deformation on the Onset of Convection in a Porous Medium,” Transp. Porous Media, 98(3), pp. 713–724. [CrossRef]
Aouidef, A. , Normand, C. , Stegner, A. , and Wesfreid, J. E. , 1994, “ Centrifugal Instability of Pulsed Flow,” Phys. Fluids, 6(11), pp. 3665–3676. [CrossRef]
Platten, J. K. , and Legros, J. C. , 1984, Convection in Liquids, Springer-Verlag, Heidelberg, Germany.
Aniss, S. , Souhar, M. , and Belhaq, M. , 2000, “ Asymptotic Study of Convective Parametric Instability in Hele-Shaw Cell,” Phys. Fluids, 12(2), pp. 262–268. [CrossRef]
Gershuni, G. Z. , and Zhukhovitskii, E. M. , 1979, Convective Stability of Incompressible Fluids, (translated from Russian by D. Louvish), Keter Publications, Jerusalem, Israel.
Gershuni, G. Z. , and Lyubimov, D. V. , 1997, Thermal Vibrating Convection, Wiley, Hoboken, NJ.


Grahic Jump Location
Fig. 1

Horizontal fluid layer of infinite extension in the x* and y* directions with a phase modulation of the temperature at the upper and lower surfaces

Grahic Jump Location
Fig. 2

Time evolution of the equilibrium temperature profile with respect to the vertical dimensionless coordinate z, for different values of the dimensionless frequency, ω, over half a period 0≤t≤T/2=π/ω

Grahic Jump Location
Fig. 3

Marginal stability curves for ω = 112.5 and Pr = 7. (a) Free–free boundaries and (b) rigid–rigid boundaries.

Grahic Jump Location
Fig. 4

Numerical evolution and asymptotic behavior of the critical Rayleigh number, Rac, versus 1/ω for free–free and rigid–rigid boundaries.  (1)Rac=8501.77 σ−2, (2)Rac=18670.99 σ−2,  (3)Rac=37776.99 σ−4, (4)Rac=81542.86 σ−4.

Grahic Jump Location
Fig. 5

Numerical evolution and asymptotic behavior of the critical wave number, qc, versus 1/ω for high frequencies. (a) Free–free boundaries, qc=0.373ω and (b) rigid–rigid boundaries, qc=0.44ω.

Grahic Jump Location
Fig. 6

Numerical evolution and asymptotic behavior of the critical Rayleigh number, Rac, versus 1/ω in the limit of high frequencies in the both cases of boundaries, free–free and rigid–rigid




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