# MathSciDoc: An Archive for Mathematician ∫

#### Numerical Analysis and Scientific Computingmathscidoc:1610.25041

International Journal of Numerical Analysis and Modeling, 11, 525-540, 2014
In this work, we study the unsteady axisymmetric mixed convection boundary layer flow and heat transfer of non-Newtonian power law fluid over a cylinder. Different from most classical works, the temperature dependent variable fluid viscosity and thermal conductivity are taken into account in highly coupled velocity and temperature fields. The motion of the fluid can be modeled by a time-dependent nonlinear parabolic system in cylindrical coordinates, which is solved numerically by using Chebyshev spectral method along with the strong stability preserving (SSP) third order Runge-Kutta time discretization. We apply the numerical solver to problems with different power law indices, viscosity parameter, thermal conductivity parameter and Richardson numbers, and compute up to the steady state. The numerical solver is checked by testing the spectral convergence of the numerical approximation to a smooth exact solution of the PDEs with source terms. Moreover, the combined effects of pertinent physical parameters on the flow and heat transfer characteristics are analyzed in detail.
Unsteady mixed convection, power law fluid, temperature dependent fluid viscosity, variable thermal conductivity, Chebyshev spectral method
```@inproceedings{jiajia2014chebyshev,
title={Chebyshev spectral method for unsteady axisymmetric mixed convection heat transfer of power law fluid over a cylinder with variable transport properties},
author={Jiajia Niu, Liancun Zheng, Yang Yang, and Chi-Wang Shu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012043236607545159},
booktitle={International Journal of Numerical Analysis and Modeling},
volume={11},
pages={525-540},
year={2014},
}
```
Jiajia Niu, Liancun Zheng, Yang Yang, and Chi-Wang Shu. Chebyshev spectral method for unsteady axisymmetric mixed convection heat transfer of power law fluid over a cylinder with variable transport properties. 2014. Vol. 11. In International Journal of Numerical Analysis and Modeling. pp.525-540. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012043236607545159.