Progress in Rheology: Theory and Applications (original) (raw)

Analytical solution for fully developed channel and pipe flow of Phan-Thien–Tanner fluids

Journal of Fluid Mechanics, 1999

Analytical expressions are derived for the velocity vector, the stress components and the viscosity function in fully developed channel and pipe flow of Phan-Thien–Tanner (PTT) fluids; both the linearized and the exponential forms of the PTT equation are considered. The solution shows that the wall shear stress of a PTT fluid is substantially smaller than the corresponding value for a Newtonian or upper-convected Maxwell fluid, with implications for comparing predicted and measured values in a non-dimensional form.

Semi-Analytical Solutions for the Poiseuille–Couette Flow of a Generalised Phan-Thien–Tanner Fluid

Fluids

This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille–Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien–Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien–Tanner constitutive equation. This generalised version considers the Mittag–Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification.

Analytical and numerical studies for slip flows of a generalised Phan‐Thien–Tanner fluid

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2020

This work presents analytical and numerical studies for pure Couette and combined Poiseuille-Couette flows under slip. The fluid behaviour is described by the recently proposed viscoelastic model, known as the generalised simplified Phan-Thien-Tanner constitutive equation, that considers the Mittag-Leffler function instead of the classical linear and exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The solutions derived in this work allow a better understanding of the model and its influence on the slippery behaviour of some complex fluids, contributing in this way to improve the modeling of complex fluids.

Steady Secondary Flows of Phan-Thien-Tanner Fluids in Pipes of Complex Shapes

ABSTRACT Secondary flows of Phan-Thien-Tanner fluids in channels formed by two intersecting walls, and driven by a pressure gradient parallel to the intersection line, are studied by means of perturbation analysis, where the perturbing parameter is the relaxation time. The velocity field is analysed in relation to the opening angle and distance from the corner within the fluid region. An analytically exact solution is found at 0(λ3 ), through the mathematical structure of which is possible to draw some general and important conclusions about the dynamics of the transversal flow. Such results are of potential interest in the design of devices aimed at exploiting the transport capacity of secondary flows.

Analysis of forced convection in pipes and channels with the simplified Phan-Thien–Tanner fluid

International Journal of Heat and Mass Transfer, 2000

Analytical solutions are derived for the temperature distribution and heat transfer coecient in forced convection of a viscoelastic¯uid obeying the simpli®ed Phan-Thien±Tanner constitutive equation in laminar pipe and plane channel¯ows. The results are valid for fully developed thermal and hydrodynamic¯ow conditions with a constant heat¯ux imposed at the wall and include the investigation of the eects of viscous dissipation. A nonvanishing value of the extensional parameter of the¯uid model is shown to be essential for the solution to dier signi®cantly from that for a Newtonian, or an elastic¯uid without extensibility. Elasticity, only when combined with extensibility, is shown to increase the heat transfer and to reduce the range of temperatures present inside a duct. These bene®cial eects of¯uid elasticity are enhanced by viscous dissipation. 7

Heat Transfer of Simplified Phan-Thien���tanner Fluids in Pipes and Channels

The rheology of some concentrated solutions of polymers and polymer melts is predicted adequately by the Phan-Thien-Tanner (PTT) constitutive equation (Larson, 1988, Quinzani et al, 1995). Such model fluids are frequently used to simulate real fluids encountered in industry, in processes involving high temperatures and heat transfer operations, and are also useful to assess the performance of numerical codes. For the simplified version of the PTT fluid model, an exact solution is derived for thermal and hydrodynamic fully-developed pipe and channel flows. The analysis considers a constant wall heat flux boundary condition and shows that fluid elasticity is responsible for an enhancement in heat transfer of at most 15.8% for the pipe flow and of 11.1% for the channel flow.

Constant Wall Temperature Forced Convection in Pipes with the Simplified Phan-Thien—Tanner Fluid

2000

The fully-developed thermal and hydrodynamic steady laminar pipe flow of the SPTT fluid is here investigated for the constant wall temperature boundary condition, assuming constant properties and negligible axial conduction. Two limiting conditions were identified: the solution pertaining to the equilibrium between axial convection and radial conduction of thermal energy, and the solution of the equilibrium of radial conduction of

Friction Effects in Pipe Flow of Phan-Tien Tanner Fluids

An analytical study of the friction law for rectilinear flow a Phan-Thien-Tanner fluid is presented. The flow is assumed steady and the pipe circular. The equations of motion are solved and the velocity, rate of flow, and friction factor are determined. Friction effects are related to the Reynolds number and to other flow parameters, such as the Deborah number.