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The thesis presents the theoretical analysis of wire coating extrusion process inside
pressure type die. Efforts at obtaining better insight into the process must be mainly
theoretical rather than experimental. But the hope, of course, is that the better insight than
experimental so gained will provide practical benefits such as better control of the
process and of product quality, higher rates and more accurate and less costly die design.
In this thesis, two types of problems have been studied, (i) problems within the die and
(ii) problems outside the die. The studies are performed with several elastic fluid models
such as Phan-Thien and Tanner, second grade, third grade, elastico-viscous and Oldroyd-
8-constant fluid models and for the inelastic power law fluid model. There are ten
chapters in this thesis.
Chapter 1 is introductory and discusses mainly mathematical modeling, wire coating
operation and the phenomena inbuilt to it, in detail. In addition, it discusses the physical
properties of the non-Newtonian fluids that have been considered here. Finally, it deals
with the literature related to the analysis of coating process.
Chapter 2 is concerned with the study of non-isothermal PTT fluid in wire coating
analysis in a finite length pressure type die. The analysis is carried out by neglecting the
exit and entrance effects. The expressions for axial velocity, average velocity, volume
flow rate, shear and normal stresses, thickness of coated wire, force on the total surface of
wire and the temperature distribution are obtained. The effects of the Deborah number,
Brinkman number, elongation parameter and the ratio of the pressure drop to that of
velocity of fluid are discussed. A domain for Dec2 is found such that outside this domain,
the shear and normal stresses show insignificant effects.
Chapter 3 is devoted to the study of wire coating for heat transfer flow of a viscoelastic
PTT fluid with slip boundary conditions. The investigations are carried out by
considering nonzero pressure gradient in the axial direction. The wall shear stress, flow
analysis and the role of slip parameter are the areas of investigation. The effect of Dec2
and the slip parameter on the velocity of melt polymer, volume flow rate, thickness of
coated wire, shear and normal stresses and on temperature distributions are studied. It is
observed that the shear stress across the gap must follows a linear variation irrespective
of the constitutive equation but its magnitude depends on the model parameters. In case
of normal stress, this reduction is in the form of parabolic and the profiles overshoot at
the centre of the annulus.
Chapter 4 is to explore the wire coating analysis in a pressure type die by considering
third grade fluid for constant and variable viscosity depends on temperature. For
temperature dependent viscosity, two models are under discussion (i) Reynolds model
and (2) Vogel’s model. The coupled momentum and energy equations are solved with the
help of regular perturbation method. The non-Newtonian behavior of the fluid is
discussed with the influence of perturbation parameter. Also, the solution of the problem
is discussed for different Reynolds and Vogel’s model parameters.
Chapter 5 is targeted to study the wire coating with a bath of Oldroyd 8-constant fluid
taking into account the effect of pressure variation in the axial direction. The influence of
pseudoplastic and dilatant parameters is investigated on the flow behavior such as
velocity, average velocity, volume flow rate and shear stress of the fluid and on the
temperature distributions. Also the influence of pressure gradient and the drag flow are
examined. Furthermore, the effect of viscosity parameter 0 is discussed on shear stress.
The aim of chapter 6 is to investigate an unsteady flow of a second grade fluid in a
cylindrical die of finite length. In this problem, wire is dragged in a pool of melt polymer
in the axial direction inside the die. The pressure gradient along the flow direction is
assumed to be zero. The flow phenomena satisfying the continuity equation are modeled
mathematically with the help of Navier Stokes equations and solutions for velocity
distribution is derived in two different cases (i) when the wire is dragged in the molten
polymer and (ii) when the wire is dragged with cosine oscillation in the melt polymer in a
die. An exact solution is obtained in case (i) and an Optimal Homotopy Asymptotic
Method (OHAM) is applied for handling solution of the problem in case (ii). The velocity
field has been examined with passage of time and the effect of oscillation is investigated
in the region of fluid flow. The stability analysis of this technique is discussed on some
examples related to the problem under discussion.
Chapter 7 gives an analytical investigation of post-treatment of wire coating with heat
transfer analysis. The fluid is considered as third grade fluid. The investigation is
performed by considering the slippage exists at the contact surfaces of wire, polymer and
the gas. The mathematical model is derived for the fluid flow in a die. The governing
equations are solved for the velocity field and temperature distribution using the regular
Perturbation Method (PM) and OHAM. The explicit expressions for the flow rate,
average velocity, force on total surface of wire and thickness of coated wire are derived.
The solutions are examined under the effect of various parameters.
The analysis of post-treatment of wire coating with heat transfer analysis is studied in
chapter 8. The fluid is assumed to be satisfies the power law model. For temperature
distribution, three different cases have been discussed (i) temperature of the wire is
constant while it is varying linearly on the surface of the coated wire (ii) temperature of
the wire varying linearly while it is constant on the surface of the coated wire (iii)
temperature of the wire and the surface of coated wire are varying linearly at the same
temperature gradient. The analysis for velocity field, volume flow rate, average velocity,
shear rate, force on total surface wire and thickness of coated wire are carried out for the
power law index parameter n is or is not equal to 1. Temperature distribution is studied
separately in each of the three cases. The maximum temperature rise is investigated
which depends upon the non-dimensional parameter S 0 .
Chapter 9 deals with the post-treatment of wire coating analysis with heat transfer
analysis. The fluid is assumed to be satisfies the elastico-viscous fluid model. The
pressure gradient is considered to be constant in the direction of drag of wire. The
analytical expressions for axial velocity, average velocity, volume flow rate, shear stress,
normal stress, thickness of coated wire, the force on the total wire and the temperature
distribution are derived by means of regular PM and Modified Homotopy Perturbation
Method (MHPM). The influences of elastic number Re , cross-viscous number c ,
velocity ratio U and the non-dimensional parameter S are studied on the solutions of the
problem. It is concluded that an increase in the elastic number decreases, the flow rate
whereas thickness of coated wire and force on the total wire increases.
Chapter 10 is devoted to briefly review our main conclusions and future work directions. |
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