Prediction of Heat Transfer to Fully Developed Pipe Flows with a Modified Power Law Viscosity Model

Author(s)

Abstract
Fully-developed forced convection heat transfer of a pseudoplastic fluid in a uniformly heated circular tube has been studied. The model used is a modification of the two-parameter Ostwald-de Waele power law, which correctly represents the upper and lower regions of Newtonian behavior shown by pseudoplastic or shear-thinning polymer melts and solutions. Results for a shear-thinning polymer solution, for which experimental data for the apparent viscosity is available over a large range of shear-rate magnitudes, predicted using the modified power-law viscosity model, have been presented. A new non-dimensional shear-rate parameter governing the flow has been identified. The non-Newtonian fluid mechanics community has been unaware of the existence of this parameter. The paradox in the prediction of boundary layer flows caused by lack of knowledge of this parameter has been well documented by our previous studies. In this paper, we discuss it for non-boundary-layer flows. The momentum and energy equations have been solved numerically, for fully developed pipe flow, by the trapezoidal rule and finite volume method respectively. The results indicate that there are three regimes of flow. When the shear-rate parameter is small, the fluid behaves like a Newtonian fluid and the Nusselt number is identical to that for a Newtonian fluid. At intermediate values of the shear-rate parameter, there are two regions of flow: a central region where the fluid behaves like a Newtonian fluid and an outer region where the fluid behaves like a power-law fluid. The Nusselt numbers predicted by the modified power law and power law models agree in this intermediate range of shear rates. When the shear-rate parameter is large, there are two Newtonian regions, one near the axis and one near the wall, with a middle power-law zone.

Keywords
Non-Newtonian fluid, modified power-law, forced convection heat transfer, Boger’s experimental data

Cite this paper
Md. Mamun Molla, S. Ghosh Moulic, Lun-Shin Yao, Prediction of Heat Transfer to Fully Developed Pipe Flows with a Modified Power Law Viscosity Model , SCIREA Journal of Mechanics. Volume 1, Issue 1, October 2016 | PP. 1-47.

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