Overstability of a viscoelastic fluid layer heated from below

Abstract

The stability of a horizontal layer of Maxwellian fluid heated from below is considered. Critical Rayleigh numbers, wave-numbers, and frequencies for overstability are determined for both free and rigid boundaries. Elasticity is found to destabilize the fluid, and the presence of rigid boundaries is found to be slightly stabilizing.

Viscoelastic Natural Convection

“…The linear problem was investigated by Vest and Arpaci [66] for both free and solid walls and by Sokolov and Tanner [59] who present an integral model for the shear stress tensor which represent a number of non Newtonian fluids, including that of Maxwell. The linear equations in two-dimension use the stream function.…”

“…This constitutive equation has three versions, the upper convected, the lower convected and the corrotational Maxwell models, depending on the time derivative selected to describe the fluid behavior. The natural convection of the Maxwell fluid has been investigated by Vest and Arpaci [66] for free-free and solid-solid walls with fixed temperature. Sokolov and Tanner [59] investigated the linear problem of the Maxwell fluid, among other viscoelastic fluids, using an integral form of the stress tensor.…”

Effect of Magnetic Field on Thermal Instability of Oldroydian Viscoelastic Rotating Fluid in Porous Medium

“…The problem of convective instability of a viscoelastic fluid heated from below was first studied by Green (1968). Vest and Arpaci (1969) investigated the problem of overstability of a viscoelastic fluid heated from below. Bhatia and Steiner (1972) studied the problem of thermal instability of an Oldroydian visco-elastic fluid in hydromagnetics and found that the magnetic field has a stabilizing influence on the visco-elastic fluid just as in the case of a Newtonian fluid.…”

Linear macroscopic properties of polymeric liquids and melts. A new approach

“…cited therein) and more recently for e.g. thermal convection [6][7][8] and surface waves [9]. To give an accurate description of the experimental results a number of modifications of the classical Maxwell model (e.g.…”