Browsing by Author "Alsoy-Akgun, Nagehan"

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Implementation of Drbem for Coupled Sine-Gordon Equations
(Elsevier Sci Ltd, 2023) Alsoy-Akgun, Nagehan
In this study, two-dimensional, time dependent, nonlinear, coupled sine-Gordon equations (CSGE) is solved using the dual reciprocity boundary element method (DRBEM). The DRBEM provides to transform the domain integral, caused by the inhomogeneous terms, into the boundary integral by approximating with thin plate spline. DRBEM formulation is derived using the fundamental solution of the modified Helmholtz equations (MHE)'s. In order to write the original equations in the form of MHE, time dervatives are expanded using finite difference. The principle purpose of this study is to show that DRBEM is a successful alternative for the solution of CSGE. Method is tested with the examples which have the analitical solution. The study also includes the solutions of other examples in the literature. Numerical experiments show that obtained results are in good agreement with other studies where the problem has been solved before and thus DRBEM is effective and accurate for the solution of CSGE.
Numerical Simulation of Unsteady Mixed Convection of Nanofluid in a Lid-Driven Square Cavity
(Hacettepe Univ, Fac Sci, 2019) Alsoy-Akgun, Nagehan
The behavior of unsteady mixed convection flow of Cu-water based nanofluids is investigated numerically inside a square lid-driven partially heated flow below. Dual Reciprocity Boundary Element Method is used to solve stream function-vorticity form of the governing equations of the problem. The need of time integration scheme is eliminated by transforming the vorticity transport and energy equations to modified Helmholtz equations. This procedure also diminishes the stability problems. The numerical results are given for several values of Reynolds number (Re), Rayleigh number (Ra), heat source location (D), heat source length (B) and solid volume fraction (phi). The steady-state results are in good agreement with the results available in the literature.
Effect of an Uniform Magnetic Field on Unsteady Natural Convection of Nanofluid
(Taylor & Francis Ltd, 2019) Alsoy-Akgun, Nagehan
In this work, the problem of the unsteady natural convection in an Al2O3-water filled nanofluids influenced by an uniform magnetic field is analysed numerically. Governing equations are given in terms of the streamlines, the vorticity and the temperature of the fluid. Dual Reciprocity Boundary Element Method (DRBEM) is performed as a solution technique. Both the fundamental solutions of Laplace equation ((1/2 pi) ln(x)) and modified Helmholtz equation (1/2 pi)K-0(x)) are used in the derivation of the method. The numerical analysis are done for physical parameters Rayleigh number (10(3) <= Ra <= 10(6)), Hartmann number (0 <= Ha <= 75) and particle volume fraction (0 <= phi <= 0.2). From the results, it is observed that the behaviours of all the variables are influenced by the changing values of parameters. The solution procedure of the all variables needs considerably small number of iterations and large time increments with suitable values of relaxation parameters which occur in the argument of Bessel function K-0(x).
Application of Drbem for 2d Sine-Gordon Equation
(Taylor & Francis Ltd, 2021) Alsoy-Akgun, Nagehan
This research paper introduces an application of dual reciprocity boundary element method (DRBEM) for the solution of sine-Gordon equation (SGE) in two-space dimension. Initially, the time derivatives are expanded using central difference schemes. After inserting the finite difference approximations into the governing equation, the pattern of the modified Helmholtz equation is obtained. The fundamental solution of modified Helmholtz equation is employed in the integral equation formulation. The inhomogeneous terms of the equation cause a domain integral in the integral equation formulation which leads to loss of advantage of the method. The DRBEM provides to transform the domain integral into the boundary integral by approximating the inhomogeneous term of the equation with thin plate spline (r(2) ln r). First, code validation of the procedure is done using a test problem and then proposed method is applied for several cases involving line and ring solitons to display its capacity to treat the problem. Presented numerical results are observed to be in good agreement with other numerical results available in the literature.
Natural Convection Resulting from Exponentially Varying Wall Heating in a Square Enclosure
(Pergamon-Elsevier Science Ltd, 2025) Alsoy-Akgun, Nagehan
The numerical investigation in this study explores the effects of non-uniform wall heating in a square cavity and its influence on natural convection behavior. A non-uniform heat source is applied to the left vertical wall of the cavity, whereas the right vertical wall is uniformly cooled. The remaining horizontal walls are thermally isolated. The main focus is on the heat transfer and fluid mixing caused by the convection occurring within the cavity. The governing equations are tackled with the help of the Dual Reciprocity Boundary Element Method (DRBEM). In the DRBEM procedure, the fundamental solution of the Laplace equation is used for solving the stream function equation, while for the vorticity transport and temperature equations-initially converted into the modified Helmholtz form-the fundamental solution of the modified Helmholtz equation (MHD) is applied. In order to transform the equations into this form, a relaxation parameter is applied to the corresponding term within the Laplace terms, and a forward difference scheme is employed for the time derivatives. In addition to the benefit of solving smaller-sized systems resulting from the boundary discretization in DRBEM, there is no requirement for an additional time integration scheme for the vorticity transport and energy equations, thus removing any potential stability issues. Calculations were performed for Rayleigh numbers of 10(3), 10(4), 10(5) and 10(6) and beta parameters-2, -1, 0, 1, 2. Obtained results show that the average Nusselt number was found to increase with increasing Ra and beta parameter, indicating enhanced convective heat transfer. Thus, it has been concluded that the heater position is quite effective in heat transfer.