Research Papers: Natural and Mixed Convection

Numerical Study on Mixed Convection and Entropy Generation of a Nanofluid in a Lid-Driven Square Enclosure

[+] Author and Article Information
R. K. Nayak

Department of Mathematics,
IIT Kharagpur,
Kharagpur 721302, India
e-mail: ranjanmath007@iitkgp.ac.in

S. Bhattacharyya

Department of Mathematics,
IIT Kharagpur,
Kharagpur 721302, India
e-mail: somnath@maths.iitkgp.ernet.in

I. Pop

Department of Mathematics,
Babes-Bolyai University,
Cluj-Napoca 400084, Romania
e-mail: popm.ioan@yahoo.co.uk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 19, 2014; final manuscript received July 6, 2015; published online August 25, 2015. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 138(1), 012503 (Aug 25, 2015) (11 pages) Paper No: HT-14-1820; doi: 10.1115/1.4031178 History: Received December 19, 2014; Revised July 06, 2015

A numerical investigation of mixed convection due to a copper–water nanofluid in an enclosure is presented. The mixed convection is governed by moving the upper lid of the enclosure and imposing a vertical temperature gradient. The transport equations for fluid and heat are modeled by using the Boussinesq approximation. A modified form of the control volume based SIMPLET algorithm is used for the solution of the transport equations. The fluid flow and heat transfer characteristics are studied for a wide range of Reynolds number and Grashof number so as to have the Richardson number greater or less than 1. The nanoparticle volume fraction is considered up to 20%. Heat flow patterns are analyzed through the energy flux vector. The rate of enhancement in heat transfer due to the addition of nanoparticles is analyzed. The entropy generation and Bejan number are evaluated to demonstrate the thermodynamic optimization of the mixed convection. We have obtained the enhancement rate in heat transfer and entropy generation in nanofluid for a wide range of parameter values.

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Fig. 1

Grid independence test and comparison with published results: (a) effect of grid size on local Nu along the lower wall at Re = 100, Ri = 1, and φ = 0.05 and (b) comparison of the present result for v-velocity profile with the numerical results for mixed convection of nanofluid in lid-driven cavity with horizontal temperature gradient with those of Talebi et al. [26] at Re = 100, Ra = 1.47 × 105, and φ = 0.05

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Fig. 2

Streamlines (left column) and isotherm contours (right column) for various values of Ri (=0.1, 1.0, and 3.0) for nanfluid and clear fluid cases when Re = 100: (a) and (b) Ri = 0.1; (c) and (d) Ri = 1.0; and (e) and (f) Ri = 3.0. Dotted lines, φ = 0 (clear fluid) and solid line, φ = 0.2 (nanofluid).

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Fig. 3

A benchmark study on the energy flux vectors for natural convection due to a clear fluid (φ = 0) with differentially heated cavity with adiabatic top and bottom walls for Ra = 103 as considered by Deng and Tang [34]

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Fig. 4

Energy flux vectors for different Ri at Re = 100. First row, Ri = 0.1; second row, Ri = 1.0; and third row, Ri = 3.0. Clear fluid, φ = 0 (left column) and nanofluid, φ = 0.20 (right column).

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Fig. 5

Distribution of the local Nusselt number on the bottom wall at different values of volume fraction (φ) when Re = 100 and Gr = 103 (Ri = 0.1)

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Fig. 6

Variation of the average Nusselt number at the bottom wall as a function of the volume fraction (φ) for (a) different values of Re (= 100, 500, 1000) when Gr = 103 and (b) different values of Gr (= 103, 104, 3 × 104) when Re = 100

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Fig. 7

Percentage enhancement in heat transfer at different values of φ as function of (a) Gr when Re = 100 and (b) Re when Gr = 103

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Fig. 8

Comparison of the local entropy generation contours due to heat transfer Sh and fluid friction Sf for the natural convection of clear fluid (φ = 0) in a differentially heated square cavity with horizontal adiabatic walls at Ra = 103 for Pr = 0.7 (bench mark problem). First row, present results and second row, results due to Ilis et al. [45]. Sh (left column) and Sf (right column).

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Fig. 9

Local entropy generation due to heat transfer (Sh) and fluid friction (Sf) for Re = 100 at Ri = 3.0 (i.e., Gr = 103): (a) Sh at φ = 0.0; (b) Sf at φ = 0.0; (c) Sh at φ = 0.20; and (d) Sf at φ = 0.20

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Fig. 10

Variation of the average entropy generation as a function of volume fraction of nanoparticle (φ) for various Re and Gr when (a) Gr = 103, Re = 100, 500, 1000 and (b) Re = 100, Gr = 103, 104, 3 × 104

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Fig. 11

Variation of nanofluid-to-clear fluid average heat transfer Nu av* and entropy generation S av* ratios due to the variation of Reynolds number at different values of φ : (a) Gr = 102; (b) Gr = 103; (c) Gr = 104; and (d) Gr = 3 × 104. Here, solid lines correspond to Nu av* and dashed lines for S av*.

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Fig. 12

Variation of the average Bejan number (Beav) with nanoparticle volume fraction (φ) for (a) different values of Re when Gr = 103 and (b) different values of Gr when Re = 100




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