IRSPAS 2017

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Author: search.filters.author.Karunathilake, N. G. A.

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    Modeling Non-Isothermal wire-coating from a bath using Giesekus fluid.
    (International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Karunathilake, N. G. A.; Panda, S.; Mallawaarachchi, D. K.; Wijesiri, G. S.; Hansameenu, W. T. P.
    In this paper we extend the recent analysis of Giesekus isothermal viscoelastic fluid model by inclusion of temperature in the uni-axial flow which occurs in the wire-coating process. The wire-coating flow of incompressible non-Newtonian fluid is described by the boundary value problem in terms of the equation of continuity, momentum, and energy with Giesekus constitutive equation. The equations of the uni-axial flow are written in the cylindrical coordinates and the analytical solution for the velocity is obtained. The energy equation which takes into account the viscous dissipation term is then solved to understand the temperature distribution in the flow region. The influences of non-Newtonian rheological parameters like Deborah number, Giesekus parameter and Brinkman number on velocity and temperature distributions are discussed. A comparison of the approximated solutions and the numerical solutions of the exact model equation for the velocity field is given to verify the validity of the approximated solutions. It is observed that the Giesekus parameter influences the temperature profile in the entire fluid domain.
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    A mathematical model for a lubricant approximation of the wet thin tear film.
    (International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Ranathunga, G. P.; Karunathilake, N. G. A.
    The classical description of the tear film resides on the anterior surface of the eye between the upper and lower lids is a wet thin film. Various fluid dynamic model have been developed for the evolution of the surfactant concentration and the thickness of precorneal thin tear film on the eye surface after each blink. In this work we model tear film as an incompressible Newtonian fluid together with the surfactant equations with appropriate boundary conditions. On a lubricant framework we formulate the motion of the tear film mathematically using mass, momentum and transport equations with free surface boundary conditions. The conjoining pressure in the film is modelled by the standard Van der Waals force with Hamaker constant. The non-dimensional model is discretized using Finite volume method together with nonlinear multigrid approach. This Multigrid approach to the mathematical model with the conjoining pressure improves the results of the model. Study reveals that near the lower lid the thickness comes down from the initial condition but subsequently it advances to reach a maximum at somewhere around the middle and gradually decreases to its equilibrium level to the end. The surfactant concentration in contrast drops steady to zero from lower lid to upper lid. Several dry spots resulting from the evaporation can be observed in the numerical results.
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    A study on the convergence of Σ.. in terms of the convergence of Σ...
    (International Research Symposium on Pure and Applied Sciences, 2017 Faculty of Science, University of Kelaniya, Sri Lanka., 2017) Mampitiya, M.A.U.; Karunathilake, N. G. A.; Arachchi, D. K. M.
    The convergence or divergence of a given series is determined by the behavior of its partial sum. Various tests can be used to examine the convergence or the divergence of the series even in the absence of an explicit analytic expression for the corresponding partial sums of the series. In this paper, we study on the convergence of the series Σ...in terms of a given series of non-negative terms. We first prove that the series is divergent if the given series is convergent. When the given series is convergent, we study the behavior of Σ.. under three possible cases on the limiting value and then prove that the series is divergent in two of these cases. By giving two counterexamples, we show that the convergence outcome is inconclusive in the other case.