Jet flows of liquids and gases are used in various fields of technology as means of controlling the processes of heat and mass transfer, for the intensification and stabilization of the combustion process, as means of protecting structures from exposure to thermal fields, for coating, etc. The jets of liquids and gases in technology are formed by sources-nozzles of finite sizes with various distributions of the initial outflow velocities in the outlet section of the nozzle, therefore, the

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... ation of the aerodynamic and thermal characteristics of jet flows is reduced to solving non-self-similar problems. However, one of the methods for solving such problems is the method of asymptotic expansion of velocities and pressure in series in a small parameter, when the first member of this series is a self-similar solution to the jet source problem. This article proposes an asymptotic expansion for axisymmetric weakly swirling flows in a model of a viscous incompressible medium, which leads to nonlinear «boundary layer» equations that differ from the well-known classical equations [1]–[4] for flows with finite swirl. Self-similar solutions of these equations are constructed that describe the distribution of speed, pressure, and temperature in a weakly swirling jet. The results presented in the article complement the results of [3]–[7] by calculating the thermal field in the jet.