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RESEARCH PAPERS: Forced Convection

Thermal Entrance Heat Transfer of an Adiabatically Prepared Fluid With Viscous Dissipation in a Tube With Isothermal Wall

[+] Author and Article Information
A. Barletta1

Dipartimento di Ingegneria Energetica, Nucleare e del Controllo Ambientale (DIENCA), Università di Bologna, Via dei Colli 16, I-40136 Bologna, Italyantonio.barletta@mail.ing.unibo.it

E. Magyari

 Institute of Building Technology, Swiss Federal Institute of Technology (ETH), Zürich, CH-8093 Zürich, Switzerland

1

Corresponding author.

J. Heat Transfer 128(11), 1185-1193 (Mar 13, 2006) (9 pages) doi:10.1115/1.2352784 History: Received August 29, 2005; Revised March 13, 2006

Forced convection in the thermal entrance region of a circular duct is analyzed. Viscous dissipation effects are taken into account under conditions of laminar hydrodynamically developed flow. The duct wall is assumed to be isothermal in the region downstream of the entrance cross section. The prescription of the initial condition at the entrance cross section is coherent with the assumption of a non-negligible viscous heating in the whole duct. The special case of an adiabatic-wall preparation of the fluid in the upstream region is considered. This adiabatic preparation results in a non-uniform entrance temperature distribution. The governing equations are solved analytically by separation of variables. Important differences are pointed out in the comparison of the solution with those available in the literature, which are based on the assumption of a uniform temperature distribution in the entrance cross section.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Circular duct and thermal boundary conditions

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Figure 2

Set of couples (z,Br) corresponding to Tw−Tb=0 (solid line); set of couples (z,Br) corresponding to qw=0 (dashed line)

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Figure 3

Local Nusselt number in the thermal entrance region (small values of ∣Br∣)

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Figure 4

Dimensionless wall heat flux ϕw and dimensionless bulk temperature θb versus z̃ for Br=0.2 (a), Br=0.4 (b), Br=1 (c), Br=5 (d) and Br→±∞ (e)

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Figure 5

Dimensionless wall heat flux ϕw and dimensionless bulk temperature θb versus z̃ for Br=−1 (a), Br=−2 (b), Br=−5 (c) and Br→±∞ (d)

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Figure 6

Dimensionless wall heat flux ϕw and dimensionless bulk temperature θb versus z̃ for positive values of Br. Comparison between adiabatic preparation (AP)(solid lines) and uniform entrance temperature (UET)(dashed lines).

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Figure 7

Dimensionless wall heat flux ϕw and dimensionless bulk temperature θb versus z̃ for negative values of Br. Comparison between adiabatic preparation (AP)(solid lines) and uniform entrance temperature (UET)(dashed lines).

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Figure 8

Dimensionless temperature k(T−Tw)∕(μum2) versus r̃ for Br=1 and z̃=10−3 (upper frame) or z̃=0.1 (lower frame). Comparison between adiabatic preparation (AP)(solid line) and uniform entrance temperature (UET)(dashed line).

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Figure 9

Dimensionless temperature k(T−Tw)∕(μum2) versus r̃ for Br=−1 and z̃=10−3 (upper frame) or z̃=0.1 (lower frame). Comparison between adiabatic preparation (AP)(solid line) and uniform entrance temperature (UET)(dashed line).

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