Unconventional Solution of Heat Transfer Equation and Application thereof in Inverse Problems
International Journal of Mathematical Models and Methods in Applied Sciences 2014
Ilmārs Iltiņš, Marija Iltiņa

Abstract: There are several thermo-physical inverse problems discussed in the article, whose solution is based on non-stationery temperature field projection in the series. These series are obtained by means of separation of variables, which differs from a classic method of separation of variables and is especially convenient for solving various inverse thermo-physical problems. Abraham Temkin (1919 – 2007) was the first to apply this method for separation of variables. He has also created several methods for solving inverse problems. Those methods are not studied enough and are unknown to a wider circle of experts. Some of those methods are discussed in this article. Determination of heat transfer rule between a solid and its surroundings or environment is one of the inverse thermo-physical problems. Heat transfer rule can be determined much easier if average temperature of a solid and its rate of change are known. There is a way how average temperature of a solid can be found is described. When discussing inverse thermal conductivity problems, temperature measurements at the simplest possible temperature field mathematically in laboratory conditions are used as input data Therefore, a one-dimensional symmetric temperature field is described. One shows in the article that a point exists in such a temperature field that does not practically depend on time and where temperature is equal to average temperature of the solid.


Atslēgas vārdi
Keywords - temperature field; inverse problem; series; temperature conductivity; boundary conditions
Hipersaite
http://www.naun.org/main/NAUN/ijmmas/2014/a162001-081.pdf

Iltiņš, I., Iltiņa, M. Unconventional Solution of Heat Transfer Equation and Application thereof in Inverse Problems. International Journal of Mathematical Models and Methods in Applied Sciences, 2014, Vol.8, 22.-29.lpp. ISSN 1998-0140.

Publikācijas valoda
English (en)
RTU Zinātniskā bibliotēka.
E-pasts: uzzinas@rtu.lv; Tālr: +371 28399196