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Article Citation - WoS: 1A NEW FORMULATION FOR THE BOUNDARY ELEMENT ANALYSIS OF HEAT CONDUCTION PROBLEMS WITH NONLINEAR BOUNDARY CONDITIONS(Turkish Soc thermal Sciences Technology, 2019) Baranoglu, BesimAn effective numerical method based on the boundary element formulation is presented to solve heat conduction equations which are governed by the Fourier equation, with nonlinear boundary conditions on one or more sections of the prescribed boundary. The solution involves the manipulation of the system matrices of the boundary element method and obtaining a smaller ranked matrix equation in which the unknown is only the temperature difference over the nonlinear boundary condition region. This way, the iterations to deal with the nonlinear conditions are performed faster. After finding the solution over the nonlinear boundary condition region, the solution over the entire boundary is obtained as a post-process through a prescribed relation. An example with a proven exact solution is employed to assess the results.Article Citation - WoS: 4Citation - Scopus: 4Multi Input Dynamical Modeling of Heat Flow With Uncertain Diffusivity Parameter(Taylor & Francis inc, 2003) Efe, MÖ; Özbay, HThis paper focuses on the multi-input dynamical modeling of one-dimensional heat conduction process with uncertainty on thermal diffusivity parameter. Singular value decomposition is used to extract the most significant modes. The results of the spatiotemporal decomposition have been used in cooperation with Galerkin projection to obtain the set of ordinary differential equations, the solution of which synthesizes the temporal variables. The spatial properties have been generalized through a series of test cases and a low order model has been obtained. Since the value of the thermal diffusivity parameter is not known perfectly, the obtained model contains uncertainty. The paper describes how the uncertainty is modeled and how the boundary conditions are separated from the remaining terms of the dynamical equations. The results have been compared with those obtained through analytic solution.
