Temperature effects in the Rayleigh problem for a convected Jeffreys fluid

Abstract

We use a thermodynamic approach to non-linear viscoelasticity which predicts a coupling between the stress tensor and the heat flux, to generalize the Rayleigh problem for an Oldroyd B model of a fluid. For a special choice of the external temperature gradient, we show that thermal effects do alter the hydrodynamic velocity field as well as the first and second normal stress differences. These quantities depend on renormalized parameters wich explicitly depend on temperature and on the strength of the coupling. In particular we find that in contrast to the isothermal situation, the second normal stress difference does not vanish. The possibility of an experimental verification of our theoretical predictions is also mentioned.