Unconventional solution of heat transfer equation and application thereof in inverse problems

Ilmars Iltins, Marija Iltina
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
more » ... ed 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.