Weakly nonlinear analysis of Bénard–Marangoni instability in viscoelastic fluids

Finite-amplitude Rayleigh- Bénard convection for weakly shear thinning fluids

“…Readers are referred to Friedman [21], Eckhaus [22], Newell et al [23], and Cross & Hohenberg [24] for the general theory. The current derivation follows closely that developed by Parmentier et al [17] and Li & Khayat [18].…”

“…(see Shenoy and Mashelkar [6] for general review on the experiments on natural convection of shear thinning and viscoelastic fluids and Larson [7] for a general review on the instabilities in viscoelastic fluids). Nonlinear RB convection of non-Newtonian fluids was considered by Eltayeb [8], Rosenblat [9], Martinez-Mardones & Perez-Garcia [10], Martinez-Mardones et al [11], Harder [12], and, more recently by Khayat [4,[13][14][15], Park & Lee [16], Parmentier et al [17], Li & Khayat [18], and Zhang, Vola & Frigaard [19]. Khayat investigated nonlinear RB convection of viscoelastic [13][14][15] and shear-thinning [4] fluids by adopting a dynamical system constituting a generalization of the Lorenz model (Lorenz [20]) to include elastic normal stress effects.…”

Thermal convective instability of viscoelastic fluids in a rotating porous layer heated from below

“…Besides determining critical values, we can proceed to present a possible convection pattern which is limited to two-dimensional rolls, that is, the variables are independent of y-coordinate. Both experiment [26] and theory analysis [27] indicate that the prevalence of rolls should be expected at the onset of stationary or oscillatory convection. In this case, there exists a stream function to satisfy the continuity equation (10) and the solution of  which satisfies the symmetry condition at the axis of rotation is…”

Thermal convection thresholds in a Oldroyd magnetic fluid

“…In this model, the stress tensor is decomposed into both a polymeric contribution and a solvent contribution. Studies of convection in such fluids have been performed by various authors for different cases, either with freefree or rigid-rigid boundary conditions [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. It has been found that, besides the usual stationary convection, oscillatory states can also be obtained at onset.…”