Forced convection heat transfer of a Giesekus fluid in circular micro-channels subjected to a constant wall temperature

[+] Author and Article Information
Mahmood Norouzi

Mechanical Engineering Department, Shahrood University of Technology, Shahrood, Iran Shahrood, Semnan 3619995161 Islamic Republic Of Iran norouzi.mahmood@gmail.com

Mohammad Reza Rezaie

Haftom Tir Square University Bulv. Shahrood, Semnan 3619995161 Islamic Republic Of Iran mohamadreza.rezaie@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Thermal Science and Engineering Applications. Manuscript received August 10, 2018; final manuscript received June 21, 2019; published online xx xx, xxxx. Assoc. Editor: Yit Fatt Yap.

ASME doi:10.1115/1.4044346 History: Received August 10, 2018; Accepted June 21, 2019


In this paper, an exact analytical solution for forced convective heat transfer of non-linear viscoelastic fluid in isothermal circular micro-channel is presented. The nonlinear Giesekus constitutive equation is used to model the Giesekus fluid heat transfer in micro-channel with constant wall temperature which is the main innovative aspect of current study. This constitutive equation is a powerful tool and able to model the fractional viscometric functions, extensional viscosity and elastic property. The solution of temperature profile and Nusselt number is obtained based on the Frobenius method. The effects of Weissenberg number, mobility factor, slip coefficient and Navier index on temperature distribution, velocity profile and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause to increases in slip velocity and maximum dimensionless temperature at wall and the micro-channel center, respectively. Moreover, the Nusselt number has upward trend with increases in slip coefficient and Navier index parameters. The results are indicated that the flow and temperature fields have complex relation with mobility factor which is control the level of nonlinearity of Giesekus model. Additionally, three correlations for Nusselt number of Giesekus flow in micro-channel are presented.

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