The Thermoconvective Instability in Hydrodynamics of Relaxational Liquids

Abstract

The main purpose of this paper is to show the influence of relaxational characteristics on the beginning and development of thermal convection in non-Newtonian liquids. The thermoconvection in horizontal plane layer of viscoelastic liquid is considered. It shows that in this case the convective motion is described by Lorenz system with modified Prandtl number, which depends on relaxation times of liquid. Therefore the development of thermal convection in relaxational medium take place as well as in viscous Newtonian liquid. Only the critical values of Rayleigh number are changed quantitatively. The beginning and development of convective motion of relaxational liquid in horizontal porous layer is considered. The proper nonlinear dynamical system is deduced and it is showed that when relaxation about pressure gradient is absent this new system comes to the classical Lorenz system. The analytical and numerical research of this new system solutions depending on the Rayleigh number and relaxation time values is realized. In particular is noted that stability disturbance for Rayleigh number less than classical Darcy-modified Rayleigh critical value is possible in certain cases. The toroidal-shaped porous medium saturated with relaxational liquid is considered. It shows that the solution of thermoconvective problem in this case in approximated by above-stated nonlinear dynamical system exactly, so that the higher garmonics decreases exponentialy in time and their influence on lowest garmonics is equal to zero.