In this work, a mathematical model of cylindrical nano-beam with constant elastic parameters with fractional order heat conduction will be constructed. The governing equations of the mathematical model will be taken when the beam is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a certain model when the beam is subjected to thermal load. Inversion of Laplace transforms will be obtained numerically, and the results will be presented graphically with some comparisons to study the impact of thermal load and the effect of the fractional order parameter on the speed of progress of mechanical and thermal waves through the beam.
Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam
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Youssef, HM, Elsibai, KA, & El-Bary, AA. "Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam." Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 8C: Heat Transfer and Thermal Engineering. San Diego, California, USA. November 15–21, 2013. V08CT09A010. ASME. https://doi.org/10.1115/IMECE2013-62876
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