Some Recent Developments in the Unsteady Flow of Dipolar Fluids with Hyperbolic Heat Conduction

摘要

In the recent articles [Acta Mech., Vol. 133, 145, 1999; Acta Mech., Vol. 137, 183, 1999; J. of Engng. Math., Vol. 36, 219, 1999] and the one entitled "Exact solutions for the unsteady plane Couette flow of a dipolar fluid" (to appear in Proc. R. Soc. London, Ser. A), the authors have presented a number of significant results on unsteady shearing flows of dipolar fluids under both isothermal and nonisothermal conditions. In this work a survey of some of these results is presented as well as a number of new findings. The specific problems considered here for dipolar fluids are Stokes' first and second problems with and without heat conduction. Exact solutions are obtained that are valid for arbitrary values of the dipolar constants d and J. In addition, solutions corresponding to fluids with couple stresses, Rivlin-Ericksen fluids, and viscous Newtonian fluids are derived as special cases. Some of the interesting results are (1) for special values of the physical parameters the flow instantly attains steady-state, (2) a back flow is possible when J > d, (3) when d > 0 the velocity field suffers a jump discontinuity on start-up, and (4) propagating jumps in the gradients of some components of the monopolar stress can occur under the Maxwell-Cattaneo-Fox (MCF) heat law.