Shear Heating in Couette Flow

The shearing action in Couette flow generates heat. Many organic and polymeric fluids have rather low thermal conductivity. Thus, the viscous dissipation results in a temperature rise in the fluid. Since viscosity decreases, typically exponentially, with tempera- 

For flow in a narrow gap viscometer, the energy equation and the momentum balance are coupled together by the temperature-dependent viscosity. These equations have been solved for the equilibrium temperature profile and the effect on shear stress by Gavis and Laurence (1968) for a power-law fluid and by Turian (1969) with the Ellis model. For the power law model, the effect on torque in a narrow gap instrument can be expressed in terms of a power series in the Brinkman number (see Example 2.6.1, eq. 2.6.15). The first term of the series is helpful to the experimentalist to indicate where shear heating can affect data. 

Viscosity versus shear rate data for Arochlor 1260, Broken lines are initial readings solid lines represent readings taken after equilibration of temperature profiles due to viscous dissipation. From Sukanek and Laurence (1974). 

Some typical values of b for polymer melts are 0.05-0.1 (Tadmor and Gogos, 1979). These can be somewhat higher for solutions. Further discussion of the temperature dependence of viscosity is given in Section 2.6. 

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