Iranian researchers managed to solve heat conduction governing equations in a nano-scale element and obtain a continuous solution.
Seyed Hojjatollah Momeni-Masuleh, one of the scientists, pointed to the increasing usage of thin films in various industries on one hand, and the high costs or lack of high precision instruments for temperature measurement at such scales on the other hand as motivations for their research.
“Regarding the weaknesses in the available discrete methods, the main purpose of the research was to find an approximate analytical continuous solution (not proposed yet) for heat conduction equations in nano-scale,” Momeni said to the news service of INIC.
Momeni and his colleague first defined the operator compatible with the problem and then performed their numerical simulations using Maple software.
Elaborating on the advantages of their research work, he said, “The conducted research can bypass high costs of experimental works and avoid their related probable hazards. Also, it is more time-saving to use simulations than to perform experiments.”
"By using this method, it is possible to solve the problem without imposing any conditions that gaps between model and reality. In addition, unlike dependent methods, the solution obtained form Adomian Decomposition is applicable for all point in domain. To find the solution for points rather than network points via discrete methods, one must repeat the calculations or accept interpolation,” Momeni added.
A detailed article on this research work has been published in the Physics Letter A, volume 374, pages 595 to 604, 2010.