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Viscous heating and heat transfer in cone-and-plate rheogoniometry

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Summary

At higher shear rates the relation between shear stress and shear rate appears to deviate from the for Newtonian fluids expected linear behaviour. In cone-and-plate rheogoniometry one of the most important causes of that is the effect of viscous heating. Accurate measurements carried out with a 10 cm diameter cone and plate lead to a semi-logarithmic, linear relationship between temperature increase and time for a Newtonian oil which dynamic viscosity varies approximately linearly with time. A simple model based on a heat balance describes this behaviour quantitatively.

Zusammenfassung

Bei newtonschen Flüssigkeiten weisen die Experimente eine Abweichung vom linearen Zusammenhang zwischen Schubspannung und Schergeschwindigkeit auf. Im Kegel-Platte-Meßsystem ist die Wärmeproduktion durch innere Reibung die wichtigste Ursache der Abweichung. Bei newtonschen Flüssigkeiten, deren dynamische Viskosität sich ungefähr linear mit der Temperatur verändert, ergeben sorgfältig ausgeführte Messungen mit einem Kegel von 10 cm Durchmesser einen linearen Zusammenhang zwischen der Zeit und dem Logarithmus der Temperaturzunahme. Ein aus der Wärmebilanz abgeleitetes Modell vermag dieses Verhalten quantitativ zu beschreiben.

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Abbreviations

A :

platen surface (m2)

B :

viscosity constant from eq. [1] (Pa s K−1)

S B :

standard deviation ofB (Pa s K−1)

S t0 :

standard deviation oft 0 (s)

S t′0 :

standard deviation oft′ 0 (s)

S η0 :

standard deviation ofη 0 (Pa s)

t :

time (s)

t 0 :

time def. by eq. [5] (s)

t′ 0 :

time def. by eq. [11] (s)

T :

temperature (°C)

T 0 :

temperature of the surrounding air (°C)

T ∞ :

highest experimental temperature (°C)

V :

volume of the fluid between the platen (m3)

W :

heat capacity of the system (J K−1)

α :

heat transfer coefficient (W m−2 K−1)

\(\dot \gamma \) :

shear rate (s−1)

η :

dynamic viscosity (Pa s)

η 0 :

dynamic viscosity atT 0 (Pa s)

θ :

dimensionless temperature def. by eq. [4a] (−)

τ :

dimensionless time def. by eq. [4b] (−)

τ′ :

dimensionless time def. by eq. [10] (−)

References

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  2. Bird et al., Transport Phenomena, J. Wiley & Sons Inc. (London 1960).

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  3. Welty et al., The Fundamentals of Momentum, Heat and Mass Transfer, J. Wiley & Sonc Inc. (London 1976).

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  4. Turian et al., Chem. Eng. Sci.18, 689–696 (1963).

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Authors and Affiliations

  1. Laboratory of Chemical Technology, University of Amsterdam, Plantage Muidergracht 30, Amsterdam, The Netherlands

    P. -J. Klijn, J. Ellenberger & J. M. H. Fortuin

Authors
  1. P. -J. Klijn
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  2. J. Ellenberger
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  3. J. M. H. Fortuin
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With 4 figures and 2 tables

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Klijn, P.J., Ellenberger, J. & Fortuin, J.M.H. Viscous heating and heat transfer in cone-and-plate rheogoniometry. Rheol Acta 18, 303–307 (1979). https://doi.org/10.1007/BF01542778

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  • DOI: https://doi.org/10.1007/BF01542778

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