An iterative algorithm for the stable solution of inverse heat conduction problems in multiply-connected domains

•Iterative algorithm for solving inverse problems of heat transfer combined with regularization of solution.•Automatic selection of the regularization parameter γ.•The use of an iterative algorithm to optimize gas turbine blade cooling.

The Cauchy problem for inverse heat conduction in a multiply-connected domain Ω was solved in this paper. To obtain this, an iterative algorithm which minimized a functional comprising the homogeneity of the outer domain surface temperature and the temperature gradient within the domain Ω was developed. Calculations were made for the known distribution of the heat transfer coefficient and surrounding temperature on the outer boundary of the domain, disturbed by the random error δ[%] = 0, 1, 5, 10. The influence of temperature gradient on time and accuracy of calculations was investigated. Taking into consideration the temperature gradient in the functional being minimized in the analytical process shortens the time of calculations and reduces oscillations of temperature and heat flux distributions on the inner boundary of the multiply-connected domain. An example of application of the algorithm presented in this paper can be the optimization problem in cooling of gas turbine blades.