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Technical Brief

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
e-mail: khatyrrabha@gmail.com

Jaafar Khalid-Naciri

Laboratory of Mechanics,
Faculty of Sciences Aïn Chock,
B.P. 5366, Maarif,
Hassan II University,
Casablanca 20100, Morocco
e-mail: 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
e-mail: ilidrissi.a@gmail.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 26, 2016; final manuscript received May 4, 2017; published online June 1, 2017. Assoc. Editor: Amy Fleischer.

J. Heat Transfer 139(10), 104504 (Jun 01, 2017) (5 pages) Paper No: HT-16-1603; doi: 10.1115/1.4036690 History: Received September 26, 2016; Revised May 04, 2017

The asymptotic behavior of laminar forced convection in a circular duct for a Herschel–Bulkley fluid of constant properties is analyzed. The viscous dissipation and the axial heat conduction effects in the fluid are both considered. The asymptotic bulk and mixing temperature field, and the asymptotic values of the bulk and mixing Nusselt numbers 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 obtained results are compared to other existing solutions in the literature for Newtonian and non-Newtonian cases.

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Figures

Grahic Jump Location
Fig. 1

Evolution the Θ∞*(R) for various values of n: (a) a = 0 and (b) a = 0.8

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Fig. 2

Evolution of Θ∞(R)/Θ∞*(R) versus Peclet number

Grahic Jump Location
Fig. 3

Variation of Nu and Nu* versus Pe for n = 1/3, β = 1 and: (a) a = 0 and (b) a = 0.8

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