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Research Papers: Micro/Nanoscale Heat Transfer

Thermocapillary Flow of a Thin Nanoliquid Film Over an Unsteady Stretching Sheet

[+] Author and Article Information
S. Maity

Department of Mathematics,
National Institute of Technology,
Arunachal Pradesh,
Yupia,
Papumpare 791112, India

Y. Ghatani

Department of Mathematics,
Sikkim Manipal Institute of Technology,
Majitar, East Sikkim,
Rangpo 737132, India

B. S. Dandapat

Department of Mathematics,
Sikkim Manipal Institute of Technology,
Majitar, East Sikkim,
Rangpo 737132, India
e-mail: bsdandapat@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 19, 2014; final manuscript received November 10, 2015; published online December 29, 2015. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(4), 042401 (Dec 29, 2015) (8 pages) Paper No: HT-14-1628; doi: 10.1115/1.4032146 History: Received September 19, 2014; Revised November 10, 2015

The two-dimensional flow of a thin nanoliquid film over an unsteady stretching sheet is studied under the assumption of planar film thickness when the sheet is heated/cooled along the stretching direction. The governing equations of momentum, energy are solved numerically by using finite difference method. The rate of film thinning decreases with the increase in the nanoparticle volume fraction. On the other hand, thermocapillary parameter influences the film thinning. A boundary within the film is delineated such that the sign of Tz changes depending on the stretching distance from the origin. Further the boundary for Tz > 0 enlarges when the volume fraction of the nanoparticle increases.

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References

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Figures

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Fig. 1

Schematic diagram of the flow problem

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Fig. 2

Comparison of numerical solution with analytical solution given by Dandapat et al. [12] for Re = 0.1. The numerical solution corresponding to Pr = 0, ϕ=0, and α = 0.

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Fig. 3

Variation of film thickness h with time t for different values of ϕ in case of Cu–water nanoliquid with Re = 1, Pr = 6.8, α = 0.5 and λ = −1

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Fig. 4

Variation of film thickness h with ϕ for different nanoliquid when Re = 1, Pr = 6.8, α = 1.0, t = 1.0, and λ = −1

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Fig. 5

Variation of film thickness h with time t in Cu–water nanoliquid for different values of thermocapillary parameter α when ϕ=0.01, Re = 0.1, Pr = 6.8, (a) for heating and (b) for cooling

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Fig. 6

Variation of velocity component F with respect to z when Re = 1, Pr = 6.8, α = 0.5, t = 1.0, and λ = −1 (a) for different values of nanoparticles volume fraction ϕ in Cu–water based nanoliquid and (b) for different water-based nanoliquids with ϕ=0.05

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Fig. 7

Variation of velocity component F with respect to t for different values of α at z = h in Cu–water nanoliquid in case of cooling when Re = 0.5, Pr = 6.8, ϕ=0.01, and λ = 1

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Fig. 8

Variation of temperature components M and N with respect to z for different values of ϕ in Cu–water nanoliquid in case of cooling when Re = 0.8, Pr = 6.8, α = 0.5, t = 2.0, X = 2, and λ = 1

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Fig. 9

Variation of Mz and Nz with respect to z for different values of ϕ in Cu–water nanoliquid in case of cooling when Re = 0.8, Pr = 6.8, α = 0.5, t = 2.0, X = 2, and λ = 1

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Fig. 10

Variation of temperature Tz with respect to z for different values of ϕ and t in Cu–water nanoliquid in case of cooling when Re = 0.81, Pr = 6.8, α = 0.5, X = 0.4, and λ = 1.0

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Fig. 11

Variation of Xc with respect to z for different values of ϕ and t in Cu–water nanoliquid in case of cooling when Re = 0.81, Pr = 6.8, α = 0.5, and λ = 1.0

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Fig. 12

Variation of temperature Tz with respect to X for different values of ϕ in Cu–water nanoliquid for cooling when Re = 0.81, Pr = 6.8, α = 0.5, t = 2.0, and z = 0.2h

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