Two-dimensional flow of chemically reactive viscoelastic fluids with or without the influence of thermal convection (original) (raw)
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Numerical Methods for Viscoelastic Fluid Flows
Annual Review of Fluid Mechanics, 2021
Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow instabilities and major modifications to the fluid dynamics. Recent developments in the numerical methods for the simulation of viscoelastic fluid flows, described by continuum-level differential constitutive equations, are surveyed, with a particular emphasis on the finite-volume method. This method is briefly described, and the main benchmark flows currently used in computational rheology to assess the performance of numerical methods are presented. Outstanding issues in numerical methods and novel and challenging applications of viscoelastic fluids, some of which require further developments in numerical methods, are discussed.
Convection in binary viscoelastic fluid
2002
Following the insight of P. Kolodner (J. Non-Newtonian Fluid Mech. 75 (1998) 167)on DNA solutions, a study of the Rayleigh-Bénard instability for a binary viscoelastic fluid is presented. We emphasize the role of the relaxation time typical of the Oldroyd-B model for a viscoelastic fluid and the Soret effect characteristic of binary fluids. Critical values of parameters for oscillatory convection are established. The results suggest that the aspect of binary fluids cannot be ignored when studying the convection of polymeric solutions.
Natural Convection of Viscoelastic Liquids
ASME Fluids Engineering Division Summer Meeting, Lake Tahoe, Nevada, USA, Volume: FED-Vol. 179, p. 31-41, 1994
ABSTRACT: Two dimensional natural convection of a nonlinear fluid of the differential type, in an inclined cavity of arbitrary aspect ratio is solved by a regular perturbation for small Grashof numbers. We show that the series are asymptotic in character. Non-Newtonian effects appear at the third order of the analysis even though the Giesekus-Tanner theorem is not valid. The relative contributions of the elastic and shear rate dependent viscosity characteristics of the liquid to the non-Newtonian behavior are investigated through a parametric study, together with the dependence of the Nusselt number on the nonlinear properties of the fluid. The effects of the aspect ratio and the inclination of the enclosure on the flow field and the heat transfer coefficient are also investigated. An interesting instability of the fluid of grade three triggered by elastic effects is discussed together with the implications concerning heat transfer characteristics.
Numerical simulation of a viscoelastic fluid with anisotropic heat conduction
1995
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Journal of Heat Transfer, 140 (10), 101701-1 / 101701-7, 2018
A semi-analytical solution of the thermal entrance problem with constant wall temperature for channel flow of Maxwell type viscoelastic fluids and Newtonian fluids, both with pressure dependent viscosity, is derived. A Fourier-Gauss pseudo-spectral scheme is developed and used to solve the variable coefficient parabolic partial differential energy equation. The dependence of the Nusselt number and the bulk temperature on the pressure coefficient is investigated for the Newtonian case including viscous dissipation. These effects are found to be closely interactive. The effect of the Weissenberg number on the local Nusselt number is explored for the Maxwell fluid with pressure-dependent viscosity. Local Nusselt number decreases with increasing pressure coefficient for both fluids. The local Nusselt number Nu for Newtonian fluid with pressure-dependent viscosity is always greater than Nu related to the viscoelastic Maxwell fluid with pressure-dependent viscosity.
Surface tension driven convection in viscoelastic liquids with thermorheological effect
International Communications in Heat and Mass Transfer, 2011
Oscillatory onset of convection is studied numerically for Rivlin-Ericksen, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and the destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to the Jeffreys description whereas the Rivlin-Ericksen liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system.
A Comparative Study for Flow of Viscoelastic Fluids with Cattaneo-Christov Heat Flux
PLOS ONE, 2016
This article examines the impact of Cattaneo-Christov heat flux in flows of viscoelastic fluids. Flow is generated by a linear stretching sheet. Influence of thermal relaxation time in the considered heat flux is seen. Mathematical formulation is presented for the boundary layer approach. Suitable transformations lead to a nonlinear differential system. Convergent series solutions of velocity and temperature are achieved. Impacts of various influential parameters on the velocity and temperature are sketched and discussed. Numerical computations are also performed for the skin friction coefficient and heat transfer rate. Our findings reveal that the temperature profile has an inverse relationship with the thermal relaxation parameter and the Prandtl number. Further the temperature profile and thermal boundary layer thickness are lower for Cattaneo-Christov heat flux model in comparison to the classical Fourier's law of heat conduction.
Physics of Fluids, 2023
The effect of viscoelasticity on the flow and heat transport in the Rayleigh-Bénard convection (RBC) in a rectangular with horizontal periodic boundary is investigated via direct numerical simulation. The working fluid is described by the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model that is able to capture some of the most important polymeric flow behaviors. Numerical simulations are conducted at a low concentration β = 0.9, where β = μs/μ0, μs is the solvent viscosity, μ0 = μs + μp is 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. It is found 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 elastic nonlinearity may make the flow transition irregular and even may bring about the relaminarization or lead to the convection cells traveling in the horizontal direction. The extension length L may induce multiple pairs of roll flow patterns at a specific setting of (Ra, Wi). Heat transport is reduced 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.
International Journal for Numerical Methods in Fluids, 2011
This paper applies the finite-volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three-dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau-Yasuda as also Upper-Convected Maxwell and Phan-Thien/Tanner differential models, with a Williams-Landel-Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects.
Rheologica Acta, 1998
A combined finite element / streamline integration method is presented for nonisothermal flows of viscoelastic fluids. The attention is focused on some characteristic problems that arise for numerical simulation of flows with high Deborah and Péclet numbers. The two most important problems to handle are the choice of an outflow boundary condition for not completely developed flow and the treatment of the dissipative term in the temperature equation. The ability of the numerical method to handle high Deborah and Péclet numbers will be demonstrated on a contraction flow of an LDPE melt with isotropic and anisotropic heat conductivity. The influence of anisotropic heat conduction and the difference between the stress work and mechanical dissipation will be discussed for contraction flows.