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Research Papers: Forced Convection

# Comparison Between Thermal Conductivity Models on Heat Transfer in Power-Law Non-Newtonian Fluids

[+] Author and Article Information
Botong Li

Department of Mathematics and Mechanics,  University of Science and Technology Beijing, Beijing 100083, China; School of Mechanical Engineering,  University of Science and Technology Beijing, Beijing 100083, China

Liancun Zheng1

Department of Mathematics and Mechanics,  University of Science and Technology Beijing, Beijing 100083, Chinaliancunzheng@163.com

Xinxin Zhang

School of Mechanical Engineering,  University of Science and Technology Beijing, Beijing 100083, China

1

Correspondence author.

J. Heat Transfer 134(4), 041702 (Feb 13, 2012) (7 pages) doi:10.1115/1.4004020 History: Received October 18, 2010; Revised April 15, 2011; Published February 13, 2012; Online February 13, 2012

## Abstract

This paper endeavors to complete a numerical research on forced convection steady heat transfer in power-law non-Newtonian fluids in a circle duct. Incompressible, laminar fluids are to be studied with a uniform wall temperature. A hydrodynamic entrance length is neglected which allows establishing a fully developed flow. The energy equation is solved by using a LU decomposition coupled with control volume technique based on finite difference method. Four thermal conductivity models are adopted in this paper, that is, constant thermal conductivity model, linear thermal conductivity varying with temperature, thermal conductivity varying as a function of velocity gradient, and thermal conductivity varying as a function of temperature gradient. The results are compared with each other and the physical characteristics for values of parameters are also discussed in details. It is shown that the heat transfer behaviors are strongly depending on the power-law index in all models. Comparisons of temperature and local Nusselt number between models are made. It reveals the increasing values of thermal conductivity parameter result in increasing the local Nusselt number when the thermal conductivity is a linear one. Furthermore, there is obvious difference in the local Nusselt number between the constant model and the power-law velocity-dependent model, but Nusselt number varies little from the constant model to the power-law temperature-dependent model.

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## Figures

Figure 1

Physical description of the problem

Figure 2

Control volume

Figure 3

Temperature profiles of different dimensionless axial coordinate with linear temperature- dependent thermal conductivity

Figure 4

Temperature profiles of different power-law index with linear temperature-dependent thermal conductivity

Figure 5

Temperature profiles of different dimensionless axial coordinate with velocity-dependent thermal conductivity

Figure 6

Temperature profiles of different power-law index with velocity-dependent thermal conductivity

Figure 7

Temperature profiles of different dimensionless axial coordinate with power-law temperature-dependent thermal conductivity

Figure 8

Temperature profiles of different power-law index with power-law temperature-dependent thermal conductivity

Figure 9

Effect of thermal conductivity parameter ɛ* on temperature profiles in a linear temperature-dependent thermal conductivity model

Figure 10

Comparison of temperature profiles between models

Figure 11

Effect of thermal conductivity parameter ɛ* on local Nusselt number in a linear temperature-dependent thermal conductivity model

Figure 12

Comparison of local Nusselt number between models

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