*Article* **Numerical Study of Heat Transfer in a Gun Barrel Made of Selected Steels**

**Mateusz Zieli ´nski \*, Piotr Koniorczyk, Zbigniew Surma, Janusz Zmywaczyk and Marek Preiskorn**

Faculty of Mechatronics, Armament and Aerospace, Military University of Technology, ul. gen. S. Kaliskiego 2, 00-908 Warsaw, Poland; piotr.koniorczyk@wat.edu.pl (P.K.); zbigniew.surma@wat.edu.pl (Z.S.); janusz.zmywaczyk@wat.edu.pl (J.Z.); marek.preiskorn@wat.edu.pl (M.P.) **\*** Correspondence: mateusz.zielinski@wat.edu.pl; Tel.: +48-261-839-647

**Abstract:** The results of numerical simulations of transient heat transfer in the barrel wall of a 35 mm caliber cannon for a single shot and the sequences of seven shots and sixty shots for chosen barrel steels are presented. It was assumed that the cannon barrel was made of one of the three types of steel: 38HMJ (1.8509), 30HN2MFA and DUPLEX (1.4462). To model the thermal phenomena in the barrel, the barrel wall material was assumed to be homogeneous and the inner surface of the barrel had no protective chromium or nitride layer. The calculations were made for temperature-dependent thermophysical parameters, i.e., thermal conductivity, specific heat and thermal expansion (in the range from RT up to 1000 ◦C) of the selected barrel steels. A barrel with a total length of 3150 mm was divided into 6 zones (*i* = 1, ... , 6) and in each of them, the heat flux density was calculated as a function of time . *qi* (*t*) on the inner surface of the barrel. Using lumped parameter methods, an internal ballistic code was developed to compute in each zone the heat transfer coefficient as a function of time *hi*(*t*) and bore gas temperature as a function of time *Tg*(*t*) to the cannon barrel for given ammunition parameters. A calculation time equaling 100 ms per single shot was assumed. The results of the calculations were obtained using FEM implemented in COMSOL Multiphysics ver. 5.6 software.

**Keywords:** anti-aircraft cannon barrel; modeling; heat transfer; numerical simulation; temperature field
