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Research Papers: Micro/Nanoscale Heat Transfer

# Effects of Variable Viscosity and Thermal Conductivity of CuO-Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation

[+] Author and Article Information

Intitut für Technishe Verbrennung, Leibniz Universtät Hannover, Welfengarten 1a, Hannover 30167, Germany; Department of Mechanical Engineering, Hashemite University, Zarqa 13115, Jordaneiyad@hu.edu.jo

J. Heat Transfer 132(5), 052401 (Mar 04, 2010) (9 pages) doi:10.1115/1.4000440 History: Received November 07, 2008; Revised September 30, 2009; Published March 04, 2010; Online March 04, 2010

## Abstract

Heat transfer enhancement in horizontal annuli using variable thermal conductivity and variable viscosity of CuO-water nanofluid is investigated numerically. The base case of simulation used thermal conductivity and viscosity data that consider temperature property dependence and nanoparticle size. It was observed that for $Ra≥104$, the average Nusselt number was deteriorated by increasing the volume fraction of nanoparticles. However, for $Ra=103$, the average Nusselt number enhancement depends on aspect ratio of the annulus as well as volume fraction of nanoparticles. Also, for $Ra=103$, the average Nusselt number was less sensitive to volume fraction of nanoparticles at high aspect ratio and the average Nusselt number increased by increasing the volume fraction of nanoaprticles for aspect ratios $≤0.4$. For $Ra≥104$, the Nusselt number was deteriorated everywhere around the cylinder surface especially at high aspect ratio. However, this reduction is only restricted to certain regions around the cylinder surface for $Ra=103$. For $Ra≥104$, the Maxwell–Garnett and the Chon et al. conductivity models demonstrated similar results. But, there was a deviation in the prediction at $Ra=103$ and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and the Brinkman model give completely different predictions for $Ra≥104$, where the difference in prediction of the Nusselt number reached 50%. However, this difference was less than 10% at $Ra=103$.

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## Figures

Figure 1

Sketch of the problem geometry

Figure 2

Comparison between viscosities calculated using Eq. 13 and the data of Nguyen (14)

Figure 3

Comparison of the present work (solid lines) and the experimental results of Kuehn and Goldstein (22); experimental data points: ◻: 0 deg, ◇: 90 deg, ○: 180 deg (Ra=4.7×104, Pr=0.706, and L/D=0.8)

Figure 4

Nusselt number distribution around the inner cylinder surface using various volume fractions of CuO nanoparticles (L/D=0.8): (a) Ra=105, (b) Ra=104, and (c) Ra=103

Figure 8

Nusselt number distribution around the inner cylinder surface using various volume fractions of CuO nanoparticles: (a) Ra=105(L/D=0.4), (b) Ra=105(L/D=0.2), (c) Ra=104(L/D=0.4), (d) Ra=104(L/D=0.2), (e) Ra=103(L/D=0.4), and (f) Ra=103(L/D=0.2)

Figure 5

Temperature isotherms for L/D=0.8: (a) Re=105(φ=9%), (b) Re=105(φ=1%) (c) Re=103(φ=9%), and (d) Re=103(φ=1%)

Figure 6

Tangential velocity for Re=105, L/D=0.8, and θ=90 deg: (a) Ra=105 and (b) Ra=103

Figure 7

Streamlines for Re=105 and L/D=0.8: (a) φ=9%, (b) φ=5%, and (c) φ=1%

Figure 9

Average Nusselt number: (a) L/D=0.8, (b) L/D=0.4, and (c) L/D=0.2

Figure 10

Effects of the conductivity and viscosity models on the Nusselt number (L/D=0.8): (a) Ra=105, (b) Ra=104, and (c) Ra=103

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