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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.Conference Object Citation - WoS: 1Citation - Scopus: 3Boundary Element Method for Optical Force Calibration in Microfluidic Dual-Beam Optical Trap(Spie-int Soc Optical Engineering, 2015) Solmaz, Mehmet E.; Cetin, Barbaros; Baranoglu, Besim; Serhathoglu, Murat; Biyikh, NeemiThe potential use of optical forces in microfluidic environment enables highly selective bio-particle manipulation. Manipulation could be accomplished via trapping or pushing a particle due to optical field. Empirical determination of optical force is often needed to ensure efficient operation of manipulation. The external force applied to a trapped particle in a microfluidic channel is a combination of optical and drag forces. The optical force can be found by measuring the particle velocity for a certain laser power level and a multiplicative correction factor is applied for the proximity of the particle to the channel surface. This method is not accurate especially for small microfluidic geometries where the particle size is in Mie regime and is comparable to channel cross section. In this work, we propose to use Boundary Element Method (BEM) to simulate fluid flow within the micro-channel with the presence of the particle to predict drag force. Pushing experiments were performed in a dual-beam optical trap and particle's position information was extracted. The drag force acting on the particle was then obtained using BEM and other analytical expressions, and was compared to the calculated optical force. BEM was able to predict the behavior of the optical force due to the inclusion of all the channel walls.
