Abstract
Mechanical engineering has its own specifics when it comes to describing the thermal state of cylinders. The heating and cooling of bodies with a cylinder surface as their heat exchange area can be considered an important technical task that requires appropriate mathematical foundation. The purpose of this work is to construct a mathematical description of the thermal state of a thermally massive cylinder cooled by a liquid passing through a coaxially located channel. The study proposed a one-dimensional mathematical model for the numerical study of the thermal state of a thermally massive cylinder cooled by a liquid passing through a coaxially arranged channel inside the body under consideration. The mesoscopic modeling scale is the basis of the mathematical model, which employs the mathematical approach of Markov chains theory. The numerical evaluation of cooling scenarios in the flow and looping mode of the cooling fluid movement is carried out. The operability of the mathematical model was investigated by performing a series of numerical experiments. The numerical experiments with the model have shown the possibility of a qualitatively consistent analysis of possible cooling scenarios and their significant differences. The qualitative reliability of the results allows us to consider the proposed model as a reliable scientific basis for describing more complex cooling systems used, for example, in transport technologies and processes.