Browsing by Subject "Heat equation"

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    A novel method for thermal conductivity measurement of two dimensional materials
    (2019-09) Çakıroğlu, Onur
    Thermal conductivity is a quantity which governs the heat transfer in a material. After increasing importance of efficiency in power generation systems and cooling mechanisms in micro-structures, many measurement methods have been developed to explore the thermal conductivity in micro and nano-sized materials. However, complexity in experimental setups, difficulties in the fabrication of devices required for measurements, and lacking exact solutions to thermal equations limit the usability of the methods to a class of materials. It is particularly challenging to study atomically thin metallic materials. To tackle this challenge, we have developed a new thermal conductivity measurement method based on the temperature dependent electrical resistance change and analyzed our method analytically and numerically by finite element method. We applied our method to 2H-TaS2 and found thermal conductivity as 9.55 1.27 W/m.K. Thermal conductivity value of TaS2, a metallic transition metal dichalcogenide was measured for the first time. This is supported by Wiedemann-Franz law and thermal conductivity of similar materials such as 2H-TaSe2 and 1T-TaS2. The method can be applied to semiconducting thin materials as well and is superior to other methods in various ways.
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    Numerical computation of Neumann controls for the heat equation on a finite interval
    (IEEE, 2024-01) Kalimeris, Konstantinos; Özsarı, Türker; Dikaios, Nikolaos
    This article presents a new numerical method, which approximates Neumann type null controls for the heat equation and is based on the Fokas method. This is a direct method for solving problems originating from the control theory, which allows the realization of an efficient numerical algorithm that requires small computational effort for determining the null control with exponentially small error. Furthermore, the unified character of the Fokas method makes the extension of the numerical algorithm to a wide range of other linear partial differential equations and different type of boundary conditions straightforward.
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    Stability analysis of the heat equation with time-delayed feedback
    (IFAC, 2009-06) Çalışkan, Sina Yamaç; Özbay, Hitay
    In this paper we consider the heat equation with time delayed feedback. Recently, stability analysis of this system, with possibly time-varying delay, is done by Fridman and Orlov (2007, 2009); and a sufficient condition is obtained for stability in terms of a linear matrix inequality. Here we consider the same system, but with constant delay, and perform the stability analysis in the frequency domain. A necessary and sufficient condition is obtained in terms of the system parameters. The result is illustrated with numerical examples. © 2009 IFAC.