*Article* **Identification of Transient Steam Temperature at the Inlet of the Pipeline Based on the Measured Steam Temperature at the Pipeline Outlet**

**Karol Kaczmarski**

Department of Thermal Processes Air Protection and Waste Utilization, Cracow University of Technology, 31155 Cracow, Poland; karol.kaczmarski@pk.edu.pl

**Abstract:** A solution to the inverse heat transfer problem (IHP) occurring in steam pipelines is presented in the paper. The transient steam temperature at the pipeline inlet was determined from the steam temperature measured at the pipeline outlet. Temporary changes of steam temperature at the turbine inlet are set by the turbine manufacturer and result from the conditions of safe starting of the turbine and maintaining high durability of its components. The boiler start-up should be carried out so that the time-temperature changes at the boiler outlet equal the time-temperature changes determined using the inverse problem. In this paper, the inverse problem of heat transfer in the pipeline was solved by the finite volume method using data smoothing, future times steps, and Tikhonov regularization that stabilized the solution of the inverse problem. The determined transient steam temperature at the pipeline inlet was compared with the measured temperatures. The steam temperature at the inlet to the pipeline, which is the solution to the inverse problem, agrees very well with the measured temperature, as the absolute value of the relative difference *ε<sup>T</sup>* between measured and calculated temperature is between 0.045% and 0.3%, and the root mean square error RMSE is within the range of 0.038 K to 0.322 K.

**Keywords:** inverse heat conduction problem; numerical modelling; steam pipeline
