Search

A time-distributed order fractional continuity model is proposed to simulate the rotating electro-osmotic slip flow of generalized Maxwell fluids in an alternating electric field. The model fully exhibits the wider memory characteristics of viscoelastic fluid. Complex momentum equation is discretized by L1 and L2 algorithms and verified by constructing analytical solutions method. Due to the stronger memory of generalized Maxwell fluids, reverse flow is restrained, and the time for oscillation reaching the steady state is postponed. Moreover, with the increase of Debye–Hückle coefficient the velocity will increase rapidly. • The time-distributed fractional order model is introduced to describe the characteristics of viscoelastic fluid. • The effects of alternating current frequency and Debye–Hückle coefficient are considered. • The reverse flow is restrained due to the existence of viscoelastic characteristics. • The time to reach constant amplitude oscillation is later compared with Newtonian fluid. [ABSTRACT FROM AUTHOR]

The finite difference schemes for equations depicting the fluid flow, heat and mass transfer of viscoelastic fluid in porous media based on fractional constitutive model are analyzed, when Soret and Dufour effects are taken into account. Different from the conventional fractional partial differential equations, the governing momentum equation of this system not only contains convection terms, but also a term: D t β 0 (∂ 2 u / ∂ y 2) , which are great challenges when we do the stability analysis. In addition, the temperature equation and concentration equation are coupled with each other, which increases the difficulty of numerical analysis. By using the energy method, the stability and convergence of the finite difference schemes employed for the governing equations are obtained. The accuracy of the scheme for momentum equation is O (τ + h x 2 + h y 2) , while the one for temperature and concentration equations is O (τ 2 + h x 2 + h y). Finally, numerical examples are presented to verify methods and demonstrate the analysis effectiveness. [ABSTRACT FROM AUTHOR]

This study numerically simulates the two-dimensional flow of Oldroyd-B fluid around an isosceles right-angled triangular cylinder with five orientations. The log-conformation reformulation is employed to stabilize the numerical simulations. By adjusting the triangular orientation angle (θ), three types of fluids development process can be observed: from steady to vortex shedding at θ = 0 and π , keeping the vortex shedding at θ = π 4 and 3 π 4 , and from vortex shedding to steady state at θ = π 2 . When the triangular cylinder faces the incoming stream with the inclined plane, the elastic effect acting on the cylinder is strong, otherwise it is weak. For θ = π 2 , the effects of the viscosity ratio (β), the Reynolds number (R e), and the Weissenberg number (W i) are further investigated. When the elasticity is reduced by changing the viscosity ratio (β) that ranged from 0 to 0.9, the final flow state will transition from stable to vortex shedding state, which indicates the restraining effect of elasticity on wake instability. In the high elastic Oldroyd-B fluid, the critical Reynolds number for vortex shedding is about 110 for W i = 1. Besides, the Weissenberg numbers (W i) ranged from 0.25 to 8 are discussed at R e = 100. With the increase of W i , four different flow states of the wake are observed: periodic vortex shedding at low Weissenberg number W i = 0. 25 , stabilizing for W i ranged from 0.5 to 1, semi-periodic strong vortex shedding for W i is about 2, and chaos when W i ≥ 4. The results indicate that excessively strong elastic effects may also lead to unstable flows. Finally, the flow states corresponding to each Reynolds number and Weissenberg number in a certain range (90 ≤ R e ≤ 120 and 0. 125 ≤ W i ≤ 4) are given in this study. • The strong elasticity mainly acts on the hypotenuse of the leading edge of the triangular cylinder. • The vortex shedding can be inhibited by the elasticity. • Inertial elastic instability is observed at high Weissenberg numbers. [ABSTRACT FROM AUTHOR]

This paper mainly analyzes the heat transfer of Carreau fluid over an infinite rotating disk, and two models with variable thermal conductivity are considered. Firstly, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by similarity transformation. Then, the boundary value problem is solved by improved bvp4c method, which reduced sensitivity to the initial values. For shear-thinning and shear-thickening fluids, the effects of Carreau fluid index n and Prandtl number Pr on velocity and temperature fields are shown and analyzed when 0.5 ≤ n ≤ 1.5 , 1 ≤ P r ≤ 10. Furthermore, the thermal conductivity is computed under two cases. [ABSTRACT FROM AUTHOR]

• A Caputo fractional-order COVID-19 model with generalized incidence rate is established, and some dynamic behaviors are analyzed. • Identify the parameters of the model according to relevant statistical data, which verifies the effectiveness of the model for depicting the COVID-19 pandemic. • Based on the relevant statistical data, the corresponding fractional optimal control problem is proposed and analyzed. • The numerical format of Riemann–Liouville adjoint system with transversality condition is given, and the fractional optimal control problem of the COVID-19 model is solved numerically. In view of the spread of corona virus disease 2019 (COVID-19), this paper proposes a fractional-order generalized SEIR model. The non-negativity of the solution of the model is discussed. Based on the established threshold R 0 , the existence of the disease-free equilibrium and endemic equilibrium is analyzed. Then, sufficient conditions are established to ensure the local asymptotic stability of the equilibria. The parameters of the model are identified based on the statistical data of COVID-19 cases. Furthermore, the validity of the model for describing the COVID-19 outbreak is verified. Meanwhile, the accuracy of the relevant theoretical results are also verified. Considering the relevant strategies of COVID-19 prevention and control, the fractional optimal control problem (FOCP) is proposed. Numerical schemes for Riemann–Liouville (R–L) fractional-order adjoint system with transversal conditions is presented. Based on the relevant statistical data, the corresponding FOCP is numerically solved, and the control effect of the COVID-19 outbreak under the optimal control strategy is discussed. [ABSTRACT FROM AUTHOR]