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Forced Convection

A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids

[+] Author and Article Information
D. A. Cruz

 Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugaldiogo.cruz@fe.up.pt

P. M. Coelho1

 CEFT, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugalpmc@fe.up.pt

M. A. Alves

 CEFT, Departamento de Engenharia Química, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugalmmalves@fe.up.pt

1

Corresponding author.

J. Heat Transfer 134(9), 091703 (Jul 09, 2012) (6 pages) doi:10.1115/1.4006288 History: Received July 12, 2011; Revised March 01, 2012; Published July 09, 2012; Online July 09, 2012

In this work, we propose an approximate methodology to estimate the Nusselt number and friction factor in fully developed non-Newtonian laminar flow in circular pipes for a constant wall heat flux. The methodology was tested using several constitutive equations, including generalized Newtonian fluids and viscoelastic models such as the simplified Phan-Thien–Tanner (sPTT), Herschel–Bulkley, Bingham, Casson, and Carreau–Yasuda constitutive equations. The error of the approximate methodology was found to be smaller than 3.2%, except for the fluids with yield stress for which the maximum error increased to about 8% for the cases analyzed, which cover a wide range of shear viscosity curves.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Example of application of power law model to a point of a shear viscosity curve

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Figure 2

Variation of friction factor with the generalized Reynolds number. Symbols correspond to calculated values using the rigorous approaches for the fluids presented in Table 2. ◻, sPTT fluid; ×, Herschel–Bulkley fluid; +, Bingham fluid; ◇, Casson fluid; ○, Carreau–Yasuda fluid; — Simplified method (Eq. 6).

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Figure 3

Variation of Nusselt number with the dimensionless group ɛWi2 for sPTT fluids. ●, simplified method predictions; — analytical solution. The vertical bar shows the location and value of the maximum error.

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Figure 4

Influence of the dimensionless group K(U¯/R)n/τ0 on the Nusselt number for Herschel–Bulkley and Bingham fluids (K≡μ∞ and n = 1 for Bingham fluid). Simplified method predictions for the Herschel–Bulkley fluid, ♦ n = 0.5 and ● n = 1.5; simplified method predictions for the Bingham fluid, ■n = 1; — analytical solution. The vertical bars show the location and value of the maximum error.

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Figure 5

Influence of the dimensionless group μ∞U¯/τ0R on the Nusselt number for Casson fluids. ♦, simplified method predictions; — analytical solution. The vertical bar shows the location and value of the maximum error.

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Figure 6

Variation of Nusselt number with the dimensionless group ΛU¯/R for two different Carreau–Yasuda fluids. Simplified method predictions: ♦, n = 0.2, a = 1.5, μ∞/μ0=0.08; ■ n = 0.358, a = 2.0, μ∞/μ0=1.08×10-4. — Numerical solution. The vertical bar shows the location and value of the maximum error.

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