Linear instability in viscoelastic fluid convection

Abstract

The onset of convection in a viscoelastic fluid that obeys the Jeffreys model is investigated. Two boundary conditions have been considered separately: free-free and rigid-rigid. The role played by the retardation time, characteristic of the Jeffreys model, is emphasised. The threshold values of the parameters (critical Rayleigh number, critical wavenumber, onset frequency, etc.) for stationary and oscillatory convection are obtained. The frontier between oscillatory and stationary convection is calculated and the possibility to obtain a codimension-two point is discussed.

Viscoelastic Natural Convection

“…The qualitative behavior of convection with fixed heat flux is the same, for both free-free and solid-solid boundaries, but with important differences in the magnitude of R C .T h e codimension-two point also occurs for different parameters. Interesting results have been obtained by Martínez-Mardones and Pérez-García [35] who calculated the codimension-two points with respect to L and E for both the free-free and the solid-solid boundary conditions. Besides, they calculated the dependance these points have on the Prandtl number.…”

On the double diffusive convection flow of Eyring-Powell fluid due to cone through a porous medium with Soret and Dufour effects

“…In general, the convection in viscoelastic fluids is categorized in two states: stationary convection and an oscillatory state that can be perceived experimentally such as travelling or standing waves and this state arises for definite values of the fluid parameters. [1][2][3][4] Recently, massive attention has been given to the double-diffusive convection in a porous medium evoked by local temperature and solute concentration gradients. Wide range applications of such kind of convection such as food processing, the transport of solutes in water-saturated soils, the transport of chemicals in packs bed reactors, etc., brought a great interest in this area.…”

On the linear stability analysis of a Maxwell fluid with double-diffusive convection

“…viscoelastic rather than Newtonian fluids are appropriate for modelling natural phenomena [1,2]. Although many models of non-Newtonian fluids (such as the Oldroyd and Jeffreys models) have been suggested in the literature, the simplest model that takes into account the stress tensor relaxation is the Maxwell viscoelastic model [3,4]. The Maxwell model is capable of describing stress relaxation effects and has been applied to problems having small dimensionless relation time [1].…”

“…The Maxwell model is capable of describing stress relaxation effects and has been applied to problems having small dimensionless relation time [1]. However, the model does not fully account for the elasticity of the fluid and typically fails to predict retardation effects as it lacks the retardation time scale that characterize other viscoelastic models such as Jeffreys model [1,3,5,6]. Some of the most recent contributions in this area include those of Hayat et al [1,2,[7][8][9], Fetecau and Fetecau [10][11][12][13] and Wang and Tan [14,15].…”