Abstract
The thermomechanical coupling in circular Couette rheometers is investigated Asymptotic solutions of second order in the Brinkman number, Br, are developed for Newtonian fluids whose viscosity and thermal conductivity can be expressed as quadratic functions of temperature. The derived solutions are validated by comparison to previously published series solutions as the limit of planar flow is approached as well as to numerical solutions and are found to be reliable for a practical range of the Nahme number. These solutions are explicit in Br and in the properties of the fluid and thus provide valuable insight into the functionality of the relevant dependences, something that is lost in purely numerical solutions.
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Abbreviations
- Br:
-
Brinkman number [Eq. (3)]
- k :
-
Thermal conductivity
- R :
-
Radius
- r :
-
Radial distance
- T :
-
Temperature
- T 0 :
-
Reference temperature
- u :
-
Dimensionless tangential velocity
- u 0 :
-
Tangential velocity
- u 0−u 2 :
-
Terms of series solution for velocity
- x :
-
Dimensionless radial distance
- α i :
-
Coefficients in the thermal conductivity model [Eq. (4)]
- β i :
-
Coefficients in the viscosity model [Eq. (5)]
- μ:
-
Viscosity
- κ:
-
Eccentricity of the Couette (inner radius/outer radius)
- Θ:
-
Dimensionless temperature
- Θ1−Θ3 :
-
Terms of series solution for temperature
- Ω:
-
Angular velocity
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Papathanasiou, T.D., Caridis, K.A. & Bijeljic, B. Thermomechanical coupling in frictionally heated circular Couette flow. Int J Thermophys 18, 825–843 (1997). https://doi.org/10.1007/BF02575136
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DOI: https://doi.org/10.1007/BF02575136