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Fully developed laminar forced convection in a circular duct for Herschel-Bulkley fluids with viscous dissipation and axial heat conduction

[+] Author and Article Information
Rabha Khatyr

Laboratory of Mechanics, Faculty of Sciences Aïn Chock, B.P. 5366, Maarif, Hassan II University, Casablanca 20100, Morocco
khatyrrabha@gmail.com

Jaafar Khalid-Naciri

Laboratory of Mechanics, Faculty of Sciences Aïn Chock, B.P. 5366, Maarif, Hassan II University, Casablanca 20100, Morocco
naciriuh2c@gmail.com

Ali Il Idrissi

Laboratory of Mechanics, Faculty of Sciences Ben M'Sik, B.P. 7955, Sidi Othmane, Hassan II University, Casablanca 20100, Morocco
ilidrissi.a@gmail.com

1Corresponding author.

ASME doi:10.1115/1.4036690 History: Received September 26, 2016; Revised May 04, 2017

Abstract

The asymptotic behaviour of laminar forced convection in a circular duct for a Herschel- Bulkley fluid with constant properties is analysed. The viscous dissipation effects and the axial heat conduction in the fluid are considered. The asymptotic bulk and mixing temperature field, and the asymptotic value of the bulk and mixing Nusselt number are determined for every boundary condition enabling a fully developed region. In particular, it is proved that whenever the wall heat flux tends to zero, the asymptotic Nusselt number is zero. The comparison with other existing solutions in the literature for Newtonian and non-Newtonian cases are analysed.

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