ISSN 打印: 1064-2285
ISSN 在线: 2162-6561

# 传热学

DOI: 10.1615/HeatTransRes.2017018876
pages 1165-1178

## MIXED CONVECTION HEAT TRANSFER OF VISCOELASTIC FLUID ALONG AN INCLINED PLATE OBEYING THE FRACTIONAL CONSTITUTIVE LAWS

Jinhu Zhao
Fuyang Normal University
Liancun Zheng
School of Mathematics and Physics, University of Science and Technology Beĳing, Beĳing 100083, China
Xinxin Zhang
School of Energy and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China; Beijing Key Laboratory of Energy Saving and Emission Reduction for Metallurgical Industry, University of Science and Technology Beijing, Beijing 100083, China
Fawang Liu
School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

### ABSTRACT

The fractional constitutive laws are introduced into the study of mixed convection heat transfer of viscoelastic fluid along an inclined plate. Nonlinear fractional boundary layer governing equations are formulated and solved by a finite difference algorithm combined with the shifted Grünwald–Letnikov formula. The results show that the inclination angle, Prandtl number, and the temperature fractional derivative parameter have remarkable impacts on both temperature and velocity fields, while the effect of the velocity fractional derivative parameter on temperature is ignorable. With decrease of the inclination angle and Prandtl number, the temperature profile rises and the thermal boundary layer becomes thicker significantly. The average Nusselt number increases remarkably with the augmentation of the temperature fractional derivative parameter. For larger velocity fractional derivative parameter, the intersections of velocity profiles demonstrate the strengthened viscoelasticity of the fluid. The average skin friction coefficient increases slowly first and then declines dramatically with the rise of the velocity fractional derivative parameter.

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