Browsing by Author "Karunathilake, N. G. A."

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Heat transfer in boundary layer regions of non-Newtonian nanofluid flows
(Faculty of Science, University of Kelaniya Sri Lanka, 2024) Gunathilaka, W. A. N. A.; Karunathilake, N. G. A.
Heat and mass transfer in Nanofluids exhibit unique properties, and therefore they are used in many industrial applications, specifically in fuel cells, hybrid power trains, vehicle thermal management, domestic refrigerators, chillers, heat exchangers, and grinding machinery. In many of these applications, thin boundary layers are formed, and hence the impact of the flow parameters in these regions are crucial to maintain the quality of industrial products. In this research work, we improve a mathematical model of the boundary layer formation in non-Newtonian nanofluids. The analysis begins with the governing equations of the fluid flow derived from the conservation of mass, momentum, energy, and nanoparticle volume fraction. The modified second-grade fluid model is employed as the rheological model to close the system. The governing set of partial differential equations has been converted into nonlinear ordinary differential equations using similarity transformations. The resulting nonlinear coupled system of ordinary differential equations has been solved numerically by using the shooting method. The qualitative impact of Lewis number, Brownian motion parameter, magnetic parameter, local thermal Grashof parameter, local solutal Grashof parameter, power law index, and the porous parameter on the radial and axial fluid velocities, temperature, and nanoparticle volume fraction profiles in the boundary layers have been investigated. The results have been simulated and presented graphically for comparison. Our observations indicate that the axial velocity decreases with increasing Lewis number and Brownian motion parameter, but it increases with increasing local solutal Grashof parameter and power law index. The axial velocity demonstrates mixed behaviour in different flow regions with the magnetic parameter, porous parameter, and local thermal Grashof parameter. The radial velocity decreases with increasing Lewis number and Brownian motion parameter, but it increases with increasing power law index. The radial velocity demonstrates mixed behaviour in different flow regions with the porous parameter, magnetic parameter, local solutal Grashof parameter, and local thermal Grashof parameter. The temperature decreases with increasing local solutal Grashof parameter and power law index, but it increases with increasing Lewis number, Brownian motion parameter, local thermal Grashof parameter, magnetic parameter, and porous parameter. The nanoparticle volume fraction decreases with increasing Lewis number, Brownian motion parameter, power law index, and local solutal Grashof parameter, but it increases with increasing local thermal Grashof parameter, magnetic parameter, and porous parameter.
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.
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.
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.
Viscous Dissipation and thermal radiation of Williamson fluid flow over an exponentially stretching sheet
(Karunathilake N. G. A.; Hansameenu W. P. T.; Wijesiri G. S. (2023), Viscous Dissipation and thermal radiation of Williamson fluid flow over an exponentially stretching sheet, Proceedings of the International Conference on Applied and Pure Sciences (ICAPS 2023-Kelaniya) Volume 3, Faculty of Science, University of Kelaniya Sri Lanka. Page 78., 2023) Karunathilake, N. G. A.; Hansameenu, W. P. T.; Wijesiri, G. S.
This study investigates the viscous dissipation and thermal radiation of Williamson fluid flow over an exponentially stretching sheet. The analysis has been started with the governing equations of the fluid flow derived from the conservation of mass, momentum, energy, and concentration. The internal heat generation and absorption effect in the view of getting the influence of temperature difference between the free stream and stretching sheet have been incorporated. The Rosseland approximation and Taylor series expansion formulate the radiative heat flux. The density difference which interacts with the gravitational force, resulting in a natural convection heat and mass transfer process is described by the mass transfer phenomenon with the homogeneous first-order chemical reaction effect. The boundary layer approximations have been introduced to focus on the fluid flow near the stretching sheet. Furthermore, the governing system of partial differential equations has been converted into a nonlinear ordinary differential equation by using similarity transformations. The resulting non-linear coupled system of ordinary differential equations has been solved numerically by shooting techniques. The graphs have simulated and presented the qualitative impact of different flow parameters such as magnetic field, Prandtl number, Williamson number, Grashof number, and thermal radioactive parameter on the radial velocity, temperature, and mass concentration profiles. The study reveals that the Prandtl number intensifies the radial velocity and has a mixed impact on the temperature and concentration, which decreases with an increase in the magnetic parameter but increases temperature and concentration. Further with the increase of the Prandtl number, the velocity and the temperature decrease in general but increase the concentration. The radial velocity increases with the Radioactive parameter but the temperature and the concentration display mixed reactions to the parameter. The Grashof parameter intensifies the radial velocity but reduces the temperature and the concentration. The Williamson parameter does not significantly impact radial velocity, temperature, and concentration.