A new model for flow and heat of a power law fluid in a pipe

Abstract

In this paper, a new model is proposed for flow and heat transfer of a power law fluid in a pipe. The flow is hydro-dynamically fully-developed and laminar while the characteristic of the fluid viscosity changes with the entrance distance considered. We assume that the power-law index is no longer a constant but a function of the entrance distance. Also, in terms of analogy between the viscous boundary layer and the thermal one, the thermal diffusion coefficient is considered as a power-law function of temperature gradient as Zheng?s model. A control volume technique based on the finite difference model coupled with the LU decomposition method is adopted and the least squares polynomial is used to approximate the non-linear item. The results show that the heat transfer behavior strongly depend on the value of the power law index.