Temperature Rise in Large-Amplitude Oscillatory Shear Flow from Shear Stress Measurements

Recently, we derived the temperature rise in a viscoelastic fluid undergoing large-amplitude oscillatory shear flow (LAOS) using the corotational Maxwell model [Giacomin et al. Phys. Fluids, 2012, 24, 103101]. The results of this derivation are used to estimate the temperature rise a priori. In the present paper, we show how to calculate the temperature rise in any liquid after measuring the shear stress response to LAOS. Specifically, if the measured response is represented by a Fourier series of odd harmonics, we can then combine this Fourier series with the equation of energy, written in terms of temperature, to calculate the temperature rise. This yields both a time-averaged contribution to the temperature rise, and an oscillating part. We find-both contributions to be significant. We estimate the oscillating part with an analytical solution for the worst case, LAOS between adiabatic plates. We can thus use this calculation to see if the +/-0.5 degrees C temperature requirement of the current standard for oscillatory shear flow testing [BS ISO 6721-10:1999] is satisfied. Our work proceeds without the choice of a constitutive equation, and can thus be used to estimate the temperature rise a posteriori for any LAOS measurement on any fluid.