Abstract
The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves.
Highlights
Driven flows represent a vast category of phenomena with extensive background applications in various technological realms and industrial areas
We focus on a layer of viscoelastic (FENE–CR) fluid with Prg = 8, ξ = 0.5, and θ = 0.1 subjected to either sinusoidal or square vibrations having frequency Ω = 25
Relevant examples are represented by a class of water-based polymer dilute solutions at ambient or moderate temperatures, e.g., water between 25 °C and 50 °C with limited amount of a polymer such a PAM, PEG, PEO, PVP, Xanthan Gum, etc., for which the Prandtl number would be similar to that considered in the present work (Prg ∼= 8) and ξ < 1
Summary
Driven flows represent a vast category of phenomena with extensive background applications in various technological realms and industrial areas. Time-varying (with variable sign and/or direction) body forces can support similar density-driven mechanisms and excite other fascinating forms of thermal convection [1,2]. Such apparently innocuous observation is at the basis of a well-known dichotomy in the literature, that is, the distinction between the classical fluid motion of thermogravitational nature and the so-called “thermovibrational” convection. The latter is called in this way as the simplest approach to have a fluid undergoing an acceleration that changes continuously sign in time is to “shake” the system containing the fluid itself. Constant amplitude vibrations can produce an acceleration signal that displays no mean value (i.e., the related time-averaged value over a period of the vibrations is zero [3])
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