The temperature field in rotational rheometers and flow curve correction for viscous dissipation |
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Authors: | Antoní n tpá nek |
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Affiliation: | (1) Department of Physics, Faculty of Mechanical Engineering, Technical University, Prague, Czechoslovakia |
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Abstract: | A solution is presented for incompressible non-Newtonian liquids of the one-dimensional stationary temperature field which arises due to heat dissipation between two concentric cylinders, the outer fixed and thermostated, the inner rotating at a constant angular velocity. The object of the study is to outline a simple procedure for determining the temperature rise of the liquid and, primarily, to ascertain the corrections of the consistent variables and D which enable the experimenter to rectify the rheogram on the basis of measurement of the shear stress and the angular velocity . The results obtained are summarized in graphical form as diagrams of the temperature and velocity fields and, to facilitate practical application of the correction procedure, in a table relating the dimensionless temperature function (, n, ) to the geometry , the flow behaviour index n, and the coefficient of temperature rise and showing the function (1) as well.List of symbols a radius of the inner cylinder - b radius of the outer cylinder - constant angular velocity of the inner cylinder - r* dimensionless radial coordinate r/b - * dimensionless angular velocity of the liquid - K fluid consistency index - n flow behaviour index - dimensionless temperature rise (T–T0)/T0 - T temperature of measured liquid (K) - T0 temperature of the thermostated bath - Br Brinkman criterion - f thermal conductivity of liquid - C constant of integration - coefficient of sensitivity in consistency-temperature law - coefficient of sensitivity divided by flow behaviour index: /n - (r*) dimensionless temperature function - coefficient of temperature rise; =Br· - ratio of the radii of inner and outer cylinder - T(1) temperature on the inner wall of the outer cylinder, i.e. for r*=1 - outer cylinder wall thickness - coefficient of heat transfer - q heat flux - k overall heat transfer coefficient - h height of measured liquid - s thermal conductivity of the outer cylinder - (1) derivative of the dimensionless temperature function at point r*=1 - dimensionless heat transfer constant - i(r*) dimensional temperature function calculated for isothermal wall; T(1)=T0 - dynamic viscosity - i() maximum value of the dimensionless temperature function - dimensionless symbol — ratio of C/C0 - D rate of shear - shear stress - rate of shear (not considering dissipation) - shear stress (not considering dissipation) - D+ rate of shear corrected for the inner cylinder temperature - + shear stress on the inner cylinder obtained by measurement on the rheometer used - j rate of shear on the inner cylinder for j-th measurement referred to a single constant temperature |
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