Homotopy perturbation and numerical solutions for MHD flow of PTT fluid through a channel embedded in a porous medium

An analysis is made of the steady one dimensional flow and heat transfer of an incompressible viscoelastic electrically conducting fluid (PTT model) in a channel embedded in a saturated porous medium. The pressure driven flow is subjected to a transverse magnetic field of constant magnetic induction (field strength). The heat transfer accounts for the viscous dissipation. The governing equation (a non-linear ordinary differential equation) is solved analytically (Homotopy Perturbation Method) and numerically (Runge-Kutta method with shooting technique) providing the consistency of the result. The role of Deborah number substantiates both Newtonian and non-Newtonian aspects of the flow model. The inclusion of two body forces affects rheological property of the flow model considered. Temperature distribution in the boundary layer is shown when the channel surfaces are held at constant temperatures. A novel result of the analysis is that the contribution of viscous dissipation is found to be negligible as the variation of temperature is almost linear across the flow field in the present PTT fluid model indicating preservation of thermal energy loss.

Exact solutions for n-layer concentric flow of PTT fluids through a cylindrical pipe

Flows of multiple layers of fluids are encountered in many industrial and manufacturing processes. This paper investigates the concentric n-layer flow for Phan–Thien–Tanner (PTT) fluids through a cylindrical pipe. Finitely many immiscible non-Newtonian fluids are considered to be flowing concentrically in a tube. The flow is modelled using the exponential PTT fluid model and exact solutions for velocity fields and volume flow rates are computed. It has been shown that the corresponding results for linear PTT fluid model as well as Newtonian fluids can be deduced from the obtained expressions, and that they match with the present literature. It has also been observed that for such layered flow, the non-Newtonian parameters significantly affect the flow of fluids in adjacent layers. The effects of involved parameters on the velocity profiles are also shown graphically. We show that a unique velocity maximum exists along the axis of the pipe. Moreover, it is observed with the help of an example that layer thickness can be adjusted to obtain maximal flow rate with a given pressure gradient.

A New Approach to the Numerical Modeling of the Viscoelastic Rayleigh-Benard Convection

A new approach to the numerical simulation of incompressible viscoelastic Rayleigh-Bénard convection in a cavity is presented. Due to the fact that the governing equations are of elliptic-hyperbolic type, a quasi-linear treatment of the hyperbolic part of the equations is proposed to overcome the strong instabilities that can be induced and is handled explicitly in time. The elliptic part related to the mass conservation and the diffusion is treated implicitly in time. The time scheme used is semi-implicit and of second order. Second-order central differencing is used throughout except for the quasi-linear part treated by third order space scheme HOUC. Incompressibility is handled by a projection method. The numerical approach is validated first through comparison with a Newtonian benchmark of Rayleigh-Bénard convection and then by comparing the results related to the convection set-up in a 2 : 1 cavity filled with an Oldroyd-B fluid. A preliminary study is also conducted for a PTT fluid and shows that PTT fluid is slightly more unstable than Oldroyd-B fluid in the configuration of Rayleigh-Bénard convection.

Manufacturing of Double Layer Optical Fiber Coating Using Phan-Thien-Tanner Fluid as Coating Material

Modern optical fiber required a double-layer resin coating on the glass fiber to provide protection from signal attenuation and mechanical damage. The most important plastics resin used in coating of fiber optics are plasticized polyvinyle (PVC), low/high density polyethylene (LDPE/HDPE), nylon, and polysulfone. Polymer flow during optical fiber coating in a pressure type coating die has been simulated under non-isothermal conditions. The flow dependent on the wire or fiber velocity, geometry of the die, and the viscosity of the polymer. The wet-on-wet coating process is an efficient process for two-layer coating on the fiber optics. In the present study, the constitutive equation of polymer flow satisfies viscoelastic Phan-Thien-Tanner (PTT) fluid, is used to characterize rheology of the polymer melt. Based on the assumption of the fully developed incompressible and laminar flow, the viscoelastic fluid model of two-immiscible resins-layers modeled for simplified-geometry of capillary-annulus where the glass fiber drawing inside the die at high speed. The equation describing the flow of the polymer melt inside the die was solved, analytically and numerically, by the Runge-Kutta method. The effect of physical characteristics in the problem has been discussed in detail through graphs by assigning numerical values for several parameters of interest. It is observed that velocity increases with increasing values of ε D 1 2 , ε D 2 2 , X 1 , and X 2 . The volume flow rate increases with an increasing Deborah number. The thickness of coated fiber optic increases with increasing ε D 1 2 , ε D 2 2 , and δ . Increase in Brinkman number and Deborah number enhances the rate of heat transfer. It is our first attempt to model PTT fluid as a coating material for double-layer optical fiber coating using the wet-on-wet coating process. At the end, the present study is also compared with the published work as a particular case, and good agreement is found.

Flow Characterization of Viscoelastic Fluids around Square Obstacle

This study focuses on the computational implementation of structured non-uniform finite volume method for the 2-D laminar flow of viscoelastic fluid past a square section of cylinder in a confined channel with a blockage ratio 1/4 for Re = 10-4, 5, 10 and 20. Oldroyd-B model (constant viscosity with elasticity) and the PTT model (shear-thinning with elasticity) are the constitutive models considered. In this study effects of the elasticity and inertia on the drag coefficients and stress fields around the square cylinder are obtained and discussed in detail. With an increase elasticity, drag coefficients get smaller due to stronger shear thinning effects for PTT fluid, however, the drag coefficients show slightly enhancement for the Oldroyd-B fluid.

High-Speed Optical-Fiber Coating with Viscoelastic PTT Fluid: Analytical and Numerical Solutions

Polymer flow during optical fiber coating in a pressure type coating die has been simulated under non-isothermal conditions. The flow dependent on the wire or fiber velocity, geometry of the die and the viscosity of the polymer. The wet-on-wet coating process is an efficient process for two-layer coating on the fiber optics. In the present study, the constitutive equation of polymer flow satisfies viscoelastic Phan-Thien Tanner (PTT) fluid, is used to characterize rheology of the polymer melt. Based on assumption fully developed incompressible and laminar flow, the viscoelastic fluid model of two-immiscible resins-layers modeled for simplified-geometry of capillary-annulus where the glass fiber drawing inside the die at high speed. The equation describing flow of polymer melt inside the die solved analytically and numerically by Runge-Kutta method. The effect of physical characteristics in problem has been discussed in detail through graphs by assigning numerical values for several parameters of interest. At the end, present study is also compared with the published work as a particular case and good agreement is found.