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Research Papers: Natural and Mixed Convection

Rayleigh–Bénard Convection in a Nanofluid Layer Using a Thermal Nonequilibrium Model

[+] Author and Article Information
Shilpi Agarwal

Department of Mathematics,
Galgotias University,
Greater Noida, Uttar Pradesh 201306, India
e-mail: drshilpimath@gmail.com

Puneet Rana

Department of Mathematics,
Jaypee Institute of Information Technology,
Noida, Uttar Pradesh 201307, India
e-mail: puneetranaiitr@gmail.com

B. S. Bhadauria

Department of Applied
Mathematics and Statistics,
School for Physical Sciences,
Babasaheb Bhimrao Ambedkar University,
Lucknow 226025, India
e-mail: mathsbsb@yahoo.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 10, 2013; final manuscript received August 13, 2014; published online September 30, 2014. Assoc. Editor: Peter Vadasz.

J. Heat Transfer 136(12), 122501 (Sep 30, 2014) (14 pages) Paper No: HT-13-1634; doi: 10.1115/1.4028491 History: Received December 10, 2013; Revised August 13, 2014

This paper studies the effect of local thermal nonequilibrium (LTNE) on the thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two temperature model has been used for the effect of LTNE among the particle and fluid phases. The boundary condition involved assumes that the nano-concentration flux is zero thereat, including the effect of thermophoresis. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to obtain the thermal Nusselt number, whose variation with respect to various parameters has been depicted graphically.

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References

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Figures

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Fig. 1

Linear stability curves comparing LTNE and LTE onset of convection

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Fig. 2

Neutral stability curves for different values of (a) Rn, (b) Le, (c) NA, (d) NH, (e) γ, and (f) ε

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Fig. 3

Variation of critical thermal Rayleigh number Racr with NH for different values of (a) NA, (b) Rn, (c) γ, (d) ε, and (e) Le

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Fig. 4

Variation of critical wave number αc with NH for different values of (a) NA, (b) Rn, (c) γ, (d) ε, and (e) Le

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Fig. 5

Variation of Nusselt number Nu(fluid) with time t for different values of (a) γ, (b) NA, (c) Rn, (d) Le, (e) NH, (f) Pr, and (g) ε

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Fig. 6

Variation of Nusselt number Nu(particle) with time t for different values of (a) γ, (b) NA, (c) Rn, (d) Le, (e) NH, (f) Pr, and (g) ε

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Fig. 7

Variation in streamlines, isotherms(particle), and isotherms(fluid) at different time t for Rn = 2, Le = 10, NA = 2, Ra = 1500, NH = 50, Pr = 10, ε = 0.04, and γ = 0.5

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Fig. 8

Variation of Nusselt number Nu(fluid) with thermal Rayleigh number Ra for different values of (a) γ, (b) NH, (c) NA, (d) Rn, (e) Le, and (f) ε

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Fig. 9

Variation of Nusselt number Nu(particle) with thermal Rayleigh number Ra for different values of (a) γ, (b) NH, (c) NA, (d) Rn, (e) Le, and (f) ε

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Fig. 10

Variation in streamlines, isotherms(particle), and isotherms(fluid) at different thermal Rayleigh number Ra for Rn = 2, Le = 10, NA = 2, Ra = 1500, NH = 50, Pr = 10, ε = 0.04, and γ = 0.5

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