Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Solutions of Initial and Boundary Value Problems for Inhomogeneous Burgers Equations With Time-Variable Coefficients(Izmir Institute of Technology, 2016) Bozacı, Aylin; Atılgan Büyükaşık, ŞirinIn this thesis, we have investigated initial-boundary value problems on semiinfinite line for inhomogeneous Burgers equation with time-variable coecients. We have formulated the solutions for the cases with Dirichlet and Neumann boundary conditions. We showed that the Dirichlet problem for the variable parametric Burgers equation is solvable in terms of a linear ordinary dierential equation and a linear second kind singular Volterra integral equation. Then, for particular models with special initial and Dirichlet boundary conditions we found a class of exact solutions. Next, we considered the Neumann problem and showed that it reduces to a second order linear ordinary dierential equation and the standard heat equation with initial and nonlinear boundary conditions. Finally, we formulated the Cauchy problem for the variable parametric Burgers equation on the non-characteristic line, and obtained its solution in terms of a linear ODE and the series solution of the corresponding Cauchy problem for the heat equation. We gave examples to illustrate how some well known solutions of the Burgers equation can be recovered by solving a corresponding Cauchy problem.Master Thesis Heat and Fluid Flow Analysis in a Channel Partially Filled With Permeable Isotropic Porous Layer(Izmir Institute of Technology, 2012) Uçar, Eren; Mobedi, MoghtadaA theoretical study is performed on heat and fluid flow in a parallel plate channel completely and partially filled with porous medium. An asymmetric heat flux is imposed onto the boundary conditions of the channel fully filled with porous media. However, a symmetrical heat flux is applied to the channel partially filled with porous medium. Dimensional analysis is performed on three parallel plates having different permeability and effective thermal conductivity values. The dimensionless analysis is performed for parallel plates with different values of Da and thermal conductivity ratio. Darcy-Brinkman model is used to investigate the velocity distribution in porous media. The dimensional and dimensionless energy equation and appropriate boundary conditions are written for the analyzed channels. The dimensional equations of motion and heat are solved by numerical methods, while the dimensionless form of those equations are analytically solved to obtain analytical expressions for the velocity and temperature fields in the channel. The dimensional temperature and velocity profiles, obtained by numerical methods, are compared with the analytical expressions of dimensionless temperature and velocity profiles and good agreement between the results were observed. For both fully filled asymmetric heated channel and partially filled symmetrical heated channel, it is observed that the traditional temperature difference (difference between surface and mean temperatures) is not proper to be used in the individual heat transfer coefficient since heat transfer coefficient approaches to infinity and changes sign without changing of heat transfer direction. Hence, a proper temperature difference is required to be defined.