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Research Papers: Natural and Mixed Convection

Non-Newtonian Natural Convection Along a Vertical Heated Wavy Surface Using a Modified Power-Law Viscosity Model

[+] Author and Article Information
M. M. Molla

Department of Mechanical Engineering, University of Glasgow, Glasgow G12 8QQ, UK

L. S. Yao

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287

J. Heat Transfer 131(1), 012501 (Oct 21, 2008) (6 pages) doi:10.1115/1.2977556 History: Received April 04, 2008; Revised June 17, 2008; Published October 21, 2008

Natural convection of non-Newtonian fluids along a vertical wavy surface with uniform surface temperature has been investigated using a modified power-law viscosity model. An important parameter of the problem is the ratio of the length scale introduced by the power-law and the wavelength of the wavy surface. In this model there are no physically unrealistic limits in the boundary-layer formulation for power-law, non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge removed; hence, the boundary-layer equations can be solved straightforwardly by marching downstream from the leading edge. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluid in terms of the viscosity, velocity, and temperature distribution, and for important physical properties, namely, the wall shear stress and heat transfer rates in terms of the local skin-friction coefficient and the local Nusselt number, respectively. Also results are presented for the variation in surface amplitude and the ratio of length scale to surface wavelength. The numerical results demonstrate that a Newtonian-like solution for natural convection exists near the leading edge where the shear-rate is not large enough to trigger non-Newtonian effects. After the shear-rate increases beyond a threshold value, non-Newtonian effects start to develop.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 9

(a) Skin-friction coefficient and (b) Nusselt number for the different α while Pr=100, δ=1.0, and n=1.4 (shear-thickening fluid)

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Figure 8

(a) Skin-friction coefficient and (b) Nusselt number for the different δ while Pr=100, α=0.3, and n=0.6

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Figure 7

Velocity distribution at the crest and trough of the wavy surface while Pr=100, n=0.6, α=0.3, and δ=1

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Figure 6

Temperature distribution at (a) X=1.0 and (b) X=100 while Pr=100, α=0.3, and δ=1

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Figure 5

Velocity distribution at (a) X=1.0 and (b) X=100 while Pr=100, α=0.3, and δ=1

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Figure 4

Velocity distribution at (a) X=1.0 and (b) X=100 while Pr=100 and δ=1

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Figure 3

Viscosity distribution at (a) X=1.0 and (b) X=100 while Pr=100 and δ=1

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Figure 2

Modified power-law correlation for the power-law index n (=0.6, 0.8, 1.0, 1.2, and 1.4) while γ1=0.1 and γ2=105

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Figure 1

Physical model and coordinate system

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Figure 10

(a) Skin-friction coefficient, (b) Nusselt number, and (c) average Nusselt number for the different n while Pr=100, α=0.3, and δ=1.0

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