Inverse analysis of heat conduction problems with relatively long heat treatment

•A hybrid technique for 1D IHCPs with relatively long time is proposed.•The mathematical process need not divide into several sub-time intervals.•Temperature and heat flux with entire time and space domains can be obtained. This paper proposes a solution method for one-dimensional inverse heat conduction problems that require a relatively long time. A hybrid technique is applied to analyze laser surface heating and spray cooling on a hot surface. In the present study, the unknown temperature in half-range expansions form is assumed, and the shifting function method is used to obtain an analytic solution. The coefficients of the half-range expansions could be determined with the least-squares method in conjunction with the analytic solution and measured temperatures. Mathematical and experimental examples are given to illustrate the analyses.