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Date of download: 12/21/2017 Copyright © ASME. All rights reserved.

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1 Date of download: 12/21/2017 Copyright © ASME. All rights reserved. From: A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids J. Heat Transfer. 2012;134(9): doi: / Figure Legend: Example of application of power law model to a point of a shear viscosity curve

2 Date of download: 12/21/2017 Copyright © ASME. All rights reserved. From: A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids J. Heat Transfer. 2012;134(9): doi: / Figure Legend: Variation of friction factor with the generalized Reynolds number. Symbols correspond to calculated values using the rigorous approaches for the fluids presented in Table . ◻, sPTT fluid; ×, Herschel–Bulkley fluid; +, Bingham fluid; ◇, Casson fluid; ○, Carreau–Yasuda fluid; — Simplified method (Eq. ).

3 Date of download: 12/21/2017 Copyright © ASME. All rights reserved. From: A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids J. Heat Transfer. 2012;134(9): doi: / Figure Legend: 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.

4 Date of download: 12/21/2017 Copyright © ASME. All rights reserved. From: A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids J. Heat Transfer. 2012;134(9): doi: / Figure Legend: 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.

5 Date of download: 12/21/2017 Copyright © ASME. All rights reserved. From: A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids J. Heat Transfer. 2012;134(9): doi: / Figure Legend: 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.

6 Date of download: 12/21/2017 Copyright © ASME. All rights reserved. From: A Simplified Method for Calculating Heat Transfer Coefficients and Friction Factors in Laminar Pipe Flow of Non-Newtonian Fluids J. Heat Transfer. 2012;134(9): doi: / Figure Legend: 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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