Within the framework of the theory of turbulent gas flows, the most frequently used mathematical models of gas dynamics and heat exchange in the heat exchanger of power plants have been analyzed. The Navier-Stokes equations in Helmholtz variables describing the plane flow of incompressible Newtonian viscous fluid with constant properties in the absence of external forces are taken as a basis for calculating the dynamics of gases in recuperative heat exchangers.  In order to systematize the analysis of the process of distribution of hydrodynamic parameters of gas in the inner tube, oscillations of nozzle elements and their influence on heat transfer, the problem is considered under conditions of gas flow turbulence. The nozzle elements are connected by an elastic wire through a certain distance. Due to the kinetic energy of the gas flow, the elements of the nozzle are driven in the longitudinal and transverse directions. At such problem statement, for physical interpretation of dynamics and heat exchange of gases, data on geometry of flow area, pipe dimensions, gas flow rate, temperature, physical and chemical parameters, elasticity of wire and oscillation (vibrability) of nozzle elements are required. Under the assumption that the temperature depends only on time and longitudinal coordinate, taking into account the heat transfer from the pipe wall to the gas, a simplified heat transfer equation is formulated. Possibilities of realization of the proposed model using computer mathematical systems of different levels are discussed.