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Research Papers: Forced Convection

Entrance and Temperature Dependent Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux

[+] Author and Article Information
Stefano Del Giudice1

Stefano Savino

Carlo Nonino

Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica,  Università degli Studi di Udine, Via delle Scienze 208, 33100 Udine, Italycarlo.nonino@uniud.it

1

Corresponding author.

J. Heat Transfer 133(10), 101702 (Aug 15, 2011) (11 pages) doi:10.1115/1.4004171 History: Received December 21, 2010; Revised May 03, 2011; Published August 15, 2011; Online August 15, 2011

In this paper a parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously, i.e., hydro-dynamically and thermally, developing laminar flows of liquids in straight ducts of constant cross sections. Uniform heat flux boundary conditions are imposed on the heated walls of the ducts. Different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (rectangular and trapezoidal) ducts. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Pearson and Prandtl numbers. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions. Correlations are also provided for the local Nusselt number and the apparent Fanning friction factor in simultaneously developing flows in ducts of different cross sections.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Graphical representation of the temperature dependence of the ratio Pr/Pre for different values of the Pearson number, Pn

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Figure 2

Axial distributions of the local Nusselt number Nuc for simultaneously developing flows of constant property fluids with different values of the Prandtl number Pre in (a) circular tubes, (b) concentric annular ducts with ri/ro=0.75, rectangular ducts with (c) γ=1 (square ducts), (d) γ=0.5 and (e) γ=0.25, (f) trapezoidal ducts with γ=0.414

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Figure 3

Axial distribution of (faRe)c for simultaneously developing flows of constant property fluids in ducts of different cross sections

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Figure 4

Axial distributions of the ratio Nu/Nuc for simultaneously developing flows with different Pearson and Prandtl numbers in (a) circular tubes, (b) concentric annular ducts with ri/ro=0.75, rectangular ducts with (c) γ=1 (square ducts), (d) γ=0.5 and (e) γ=0.25, (f) trapezoidal ducts with γ=0.414

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Figure 5

Distributions over the cross sections of the dimensionless axial velocity U at Xmax* in ducts with Pn=8 and different Prandtl numbers: (a) square duct, (b) rectangular duct with γ=0.5, (c) rectangular duct with γ=0.25, and (d) trapezoidal duct with γ=0.414. Contour value increment ΔU=0.1.

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Figure 6

Axial distributions of the ratio faPe/(faPe)c for simultaneously developing flows with different Pearson and Prandtl numbers in (a) circular tubes, (b) concentric annular ducts with ri/ro=0.75, rectangular ducts with (c) γ=1 (square ducts), (d) γ=0.5 and (e) γ=0.25, (f) trapezoidal ducts with γ=0.414

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