A theoretical analysis for the laminar momentum and energy boundary layer on a moving flat surface in power law fluids is made. The results indicate that while the plate moves in the direction of the flow, the boundary layer problem has a unique solution. Both skin friction and shear stress decrease with the increase of the ratio of the surface velocity to the free stream velocity and the power law n, the thermal diffusion ratio increases with the increase of n and ξ. However, in the case of the plate moving opposite to the flow, it is shown that the boundary layer solutions do not exist when velocity ratio ξ is larger than a positive critical value ξ*. For 0 < ξ < ξ*, the boundary layer solutions are found to be non-unique. Both superior and inferior solutions are noticeable. Skin friction and shear force for the superior solution decrease with the increase of the velocity ratio ξ. This is opposite for the inferior solution. The skin friction for both superior solution and inferior solution decrease with the increase of power law n. The result reveal the relations between momentum and thermal transfer, as well as the effects of parameters Pr, n and ξ on the transport process.
Skin Friction and Heat Transfer on a Continuous Moving Flat Surface in Power Fluids
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Zhang, X, Zheng, L, & He, J. "Skin Friction and Heat Transfer on a Continuous Moving Flat Surface in Power Fluids." Proceedings of the ASME 2003 Heat Transfer Summer Conference. Heat Transfer: Volume 1. Las Vegas, Nevada, USA. July 21–23, 2003. pp. 419-425. ASME. https://doi.org/10.1115/HT2003-47339
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