Effect of rotation on thermal instability of a viscoelastic fluid

Abstract

The thermal instability of a layer of OLDROYD fluid acted on by a uniform rotation is considered. The rotation is found to have destabilizing as well as stabilizing effect under certain conditions in eontrast to that of a Maxwell fluid where ir has a destabilizing effect. The analytic eonditions for non-existenee of overstability ate investigated. lntroductionThe problem of thermal instability of a fluid layer aeted on by a uniform rotation has been discussed in detail by Cn~,NnnASVKHAn [2]. BHATIX and ST~XN~n [1] have studied the problem of thermal instability of a Maxwell fluid in the presence of rotation and have found that the rotation has a destabilizing influence in eontrast to the stabilizing effect on ordinary fluid (Newtonian fluid). Here we attempt to study the effect of rotation on the stabi]ity of the layer of an OLDnOYV fluid heated from below.We consider ah infinite horizontal layer of fluid of depth d which is heated uniformly fr£ below and acted on by a uniform rotation ~ 91 (0, 0, f2) and gravity force g (0, 0,--g). The fluid is assamed to have a viscoelastic nature described by the OLVnOYD constitutive relation. Perturbation equationsThe constitutive relation for the fluid, as proposed by OLVROYD [3] iswhere Tij, eq, #, ~ and ~o denote respectively the shear stress tensor, the rate-of-strain tensor, the viscosity, the stress relaxation time and the strain retardation time. Let ~0, ~P, q (u, v, w) and 0 denote the perturbations in density 0, pressure p, velocity and temperature T, respectively; v and u denote, reActa Physica Acad~miae Scientiarum HungaricGe 40, 1976

Hydromagnetic thermosolutal instability of Rivlin-Ericksen rotating fluid permeated with suspended particles and variable gravity field in porous medium

“…Bhatia and Steiner [1] have studied the thermal instability of a Maxwellian visco-elastic fluid in the presence of magnetic field while the thermal convection in Oldroydian visco-elastic fluid has been considered by Sharma [14]. Veronis [20] has investigated the problem of thermohaline convection in a layer of fluid heated from below and subjected to a stable salinity gradient.…”

Double-diffusive convection in a viscoelastic fluid

“…is a non-trivial solution of the double eigen value problem for σ r and σ i described by the equations (12)- (15) with the boundary conditions (16) and (17).…”

“…Experimental demonstration by Toms and Strawbridge [15] has revealed that a dilute solution of methyl methacrylate in n-butyl acetate agrees well with the theoretical model of the Oldroyd fluid. The thermal instability of an Oldroydian viscoelastic fluid has been considered in the presence of rotation (Eltayeb [16], Sharma [17]) and magnetic field (Sharma [18]). The thermosolutal instability of an Oldroydian viscoelastic fluid in porous medium has been considered by Sharma and Bhardwaj [19].…”

Hall Effect on Thermal Instability of Viscoelastic Dusty Fluid in Porous Medium

“…Bhatia and Steiner (1972) studied the problem of thermal instability of a Maxwellian viscoelastic fluid in the presence of rotation and found that rotation has a destabilizing influence in contrast to the stabilizing effect on an ordinary viscous (Newtonian) fluid. The thermal instability of an Oldroydian viscoelastic fluid acted on by a uniform rotation was studied by Sharma (1976). There are many elastico-viscous fluids that cannot be characterized by Maxwell's or Oldroyd's constitutive relations.…”