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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January 2009

Research Papers

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

M. M. Molla,

M. M. Molla

Department of Mechanical Engineering,

University of Glasgow

, Glasgow G12 8QQ, UK
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L. S. Yao

L. S. Yao

Department of Mechanical and Aerospace Engineering,

Arizona State University

, Tempe, AZ 85287
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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*. Jan 2009, 131(1): 012501 (6 pages)

**Published Online:**October 21, 2008

Article history

Received:

April 4, 2008

Revised:

June 17, 2008

Published:

October 21, 2008

Citation

Molla, M. M., and Yao, L. S. (October 21, 2008). "Non-Newtonian Natural Convection Along a Vertical Heated Wavy Surface Using a Modified Power-Law Viscosity Model." ASME. *J. Heat Transfer*. January 2009; 131(1): 012501. https://doi.org/10.1115/1.2977556

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