Bifurcations, Chaos, and Heat Transmissions in Couple-Stress Nanoliquid Flows
Purbasha Deb, G. C. Layek
Abstract
This study focuses on the pre-chaotic, chaotic, heat transport, and intermittent demeanors for the natural convective flow of a shallow couple-stress nanofluid layer heated from underneath. A single-phase nanoliquid replica has been deployed. Both low-dimensional (3D) and comparatively higher-dimensional (5D) nonlinear systems are attained by employing low-order Galerkin approximations. We have found the critical value of the normalized Rayleigh quotient for the onset of stationary convection in both systems as [Formula: see text], where C is the couple-stress parameter and [Formula: see text], [Formula: see text], and [Formula: see text] are associated with different thermo-physical characteristics of base liquid and nanofragments. Enhancements of nanoflecks volume fraction ([Formula: see text]) and couple-stress parameter (C) delay the arrival of convection and suppress the chaotic motion. Unsteady convection and the chaotic emergence further detain in the 5D system. Oscillatory convective motion and its nature through projection algorithm are explored. Global dynamical features such as homoclinic explosions and chaotic transitions are investigated and explained physically at length. Heat transfer analysis is performed by computing the Nusselt number in every transitional zone for different values of C and [Formula: see text]. The novelty of this study is that the accessions of couple-stresses and nanoparticles reinforce the conductive mode of heat transfer and repress the unstable convective mode. Moreover, the conductive heat transmission in couple-stress fluid is more than that of the ordinary nanofluid. The study also discloses that the increment of [Formula: see text] intercepts the intermittent frequency in the chaotic regime, and the dynamics proceeds to the steady-state finally through periodic phases for higher values of [Formula: see text] and C.