The oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted two-dimensional rectangular cavity with an aspect ratio of Γ = 2 was investigated for the first time via direct numerical simulation. A series of simulations were conducted in the plane of the Rayleigh number (Ra) and the tilt angle (α∈[0°, 5°]) with three Weissenberg numbers [Wi=(0.1,0.15,0.2)] at a fixed Prandtl number Pr = 7.0. The evolutionary path of the oscillating convection onset in the (Wi,α)-plane was determined, and the corresponding complex flow structures were observed. The inclination of the box delays the onset of the oscillations and the corresponding Rayleigh number Rac as compared to the horizontal configuration. Oscillating flow structures acquire the attributes of a traveling wave. A specific feature of the oscillating convection in the case of the horizontal cavity is that the periodicity in space and time exists in the inclined box case as well. However, the evolution of the oscillatory flow structure is very different from the horizontal case in that the counterclockwise cell assimilates the clockwise cell [Zheng et al., “Pattern selection in Rayleigh–Bénard convection with nonlinear viscoelastic fluids,” Phys. Rev. Fluids 7, 023301 (2022)].

The effect of viscoelasticity on the flow and heat transport in the Rayleigh–Bénard convection (RBC), a frequently encountered phenomenon in nature and industry, in a rectangular enclosure with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by a finitely extensible nonlinear elastic-Peterlin constitutive model almost all important features of viscoelastic fluid flow. Numerical simulations are conducted at a low concentration β=0.9, where β=μs/μ0, μs is the solvent viscosity, and μ0=μs+μp is the sum of μs and the polymer viscosity μp. A parametric analysis is performed to understand the influence of the Weissenberg number Wi, the viscosity ratio β, and the extension length L on the oscillating mode of the viscoelastic RBC. The results indicate that both Wi and β weakly inhibit the convection onset and the transition from steady to oscillatory convection. The amplitude and frequency of the oscillations in the oscillatory flow regime are both suppressed. However, the strongly elastic nonlinearity makes the flow transition irregular and even brings about the relaminarization or lead to the convection cells traveling in the horizontal direction. The increasing extension length L induces multiple pairs of roll flow patterns at a specific setting of (Ra, Wi). Heat transport is reduced (up to 8.5%) by elasticity but still obeys the power law with Ra if the flow pattern has one pair of rolls. However, heat transfer enhancement occurs if multiple pairs of rolls are induced.

The unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo–Fabrizio time-fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson–Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique used is new, leads to exact solutions, is completely different from those available in the literature, and applies to other similar problems. The new expression for the velocity field displays experimentally observed ‘velocity overshoot’ as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo–Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.

A comprehensive study of the rheological characterization of the aqueous solutions of PEO (Polyethylene Oxide) with molecular mass of 4×10⁶, 5×10⁶ and 8×10⁶ g/mol respectively named (4miDA), (5miDA) and (8miDA) was conducted. A large batch of samples of 4miDA PEO with concentrations varying from 0.1% to 3% representing the range of dilute solutions to very high viscous hydrated gels, were tested. Steady state shear flow and oscillatory measurements are reported. Cross, Carreau and Carreau-Yasuda models were used to describe the shear-thinning behaviour within the shear rate range (0.001 ≤ $γ•$ ≤ 3000 s^-1). Experimental findings were validated with published results under the same operating conditions within specified shear rate ranges (0.1≤ $γ•$ ≤100 s^-1). We find that the behaviour of PEO under shear is highly dependent on the rheometer, material and operating procedures. Oscillatory measurements were carried out to determine the complex properties of the PEO solutions in the frequency ω and strain amplitude γ ranges of (0.01 ≤ ω ≤100 rad/s) and (0.01 ≤ γ ≤1000 %), respectively. Higher magnitudes of dynamic moduli (G^/ & G^//), zero (η₀) and infinite (η_∞) shear rate viscosities, resonant frequencies (ω_res), linear viscoelastic regions (LVER), and higher relaxation time constants (λ) were observed with increasing concentration and molecular weight. The rheological response of the PEO polymeric solutions was further clarified via Lissajous curves. The aim of this work is to characterize the behaviour of the 4miDa PEO prior to its use in an experimental investigation of the secondary flows of viscoelastic fluids in non-circular channels.