HEAT SOURCE IDENTIFICATION BASED ON ANALYTICAL SOLUTIONS OF THE HEAT-CONDUCTION PROBLEM
A. V. Eremin, Ekaterina Vasil'evna Stefanyuk, Lubov S Abisheva · Izvestiya Ferrous Metallurgy · 2016
On the base of the temperature perturbations front and additional boundary conditions the authors have obtained the approximate analytical solution of the heat-conduction problem for infinite plate by boundary conditions of the third kind and time-variable heat source. Heat-conduction process was divided into two stages according to the time, that (dividing) helps to find simple analytical solutions for each stage separately. Obtained solutions are in the form of algebraic power series with time-dependent coefficients, those (coefficients) defined major and an extra boundary conditions, specified at the boundary points and at the temperature perturbations front, but in such a way that their implementation of the desired solution was equivalent to executing differential equations boundary-value problem in the whole range of spatial and temporal variables. Using described method it is possible to obtain analytical solutions in the entire time range of the non-stationary process, including small and the smallest values, almost with a given degree of accuracy. Obtained in this work, an analytical solution was used to identify time-varying source of warmth by solving the inverse heat-conduction problem.