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Research Papers

Natural Convective Nanofluid Flow in an Annular Space Between Confocal Elliptic Cylinders

[+] Author and Article Information
Tahar Tayebi

Faculty of Sciences and Technology,
Mohamed El Bachir El Ibrahimi University,
Bordj Bou Arreridj, El-Anasser 34030, Algeria;
Energy Physics Laboratory,
Department of Physics,
Faculty of Science,
Constantine 1 University,
Constantine 25000, Algeria

Ali J. Chamkha

Mechanical Engineering Department,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia;
Prince Sultan Endowment for
Energy and Environment,
Prince Mohammad Bin Fahd University,
Al-Khobar 31952, Saudi Arabia
e-mail: achamkha@pmu.edu.sa

Mahfoud Djezzar, Abdeslem Bouzerzour

Faculty of Science,
Energy Physics Laboratory, Department of Physics,
Constantine1, University, 25000, Algeria

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received February 22, 2016; final manuscript received August 23, 2016; published online October 26, 2016. Assoc. Editor: Giulio Lorenzini.

J. Thermal Sci. Eng. Appl 9(1), 011010 (Oct 26, 2016) (9 pages) Paper No: TSEA-16-1046; doi: 10.1115/1.4034599 History: Received February 22, 2016; Revised August 23, 2016

The natural convection fluid flow and heat transfer in an annulus of two differentially heated confocal elliptic cylinders filled with the Cu–water nanofluid are investigated numerically. The outer cylinder is maintained at a constant temperature Tc while the inner cylinder is kept at a differentially higher constant temperature Th. Equations of continuity, momentum, and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional steady, laminar, and incompressible flow, which is expressed in terms of stream function, vorticity, and temperature. The basic equations are discretized using the finite-volume method. Using a developed code, calculations were performed for Rayleigh number (103 ≤ Ra ≤ 3 × 105), volume fraction of nanoparticles (0 ≤ ϕ  ≤ 0.12), and eccentricity of the inner ellipse, ε1 = 0.7, 0.8, and 0.9. The eccentricity of outer ellipse and the angle of orientation are fixed at 0.6 deg and 0 deg, respectively. Results are presented in the form of stream lines, isotherm plots, and local and average Nusselt numbers. The results discussed in this present work show the existence of a very good agreement between the present results and those from the previous researches.

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Figures

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Fig. 1

Problem schematic and boundary conditions

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Fig. 2

(a) Physical domain and (b) computational domain

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Fig. 3

Variation in the mean Nusselt number around inner cylinder with the Rayleigh number for different values of the nanoparticle volume fraction: (a) ε1 = 0.7, (b) ε1 = 0.8, and (c) ε1 = 0.9

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Fig. 4

Variation in the mean Nusselt number with the nanoparticle volume fraction for different Rayleigh: (a) ε1 = 0.7, (b) ε1 = 0.8, and (c) ε1 = 0.9

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Fig. 5

Local Nusselt number along inner and outer cylinder's walls for different values of the nanoparticle volume fraction when Ra = 105 and ε1 = 0.8

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Fig. 6

Isotherms (left) and streamlines (right) for different values of volume fraction when ε1 = 0.8 and Ra =  105

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Fig. 7

Isotherms (left) and streamlines (right) for different values of the Rayleigh number Ra at ε1 = 0.7 and ϕ = 0

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Fig. 8

Isotherms (left) and streamlines (right) for different values of the Rayleigh number Ra at ε1 = 0.8 and ϕ = 0

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Fig. 9

Isotherms (left) and streamlines (right) for different values of the Rayleigh number Ra at ε1 = 0.9 and ϕ = 0

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