Special features of generalization of problems in heat transfer under conditions of heat protection of high-temperature firing walls by way of tangential injection

In the presence of additional heating of the wall to be protected by means of radiation heat flux, where the surface temperature may significantly exceed the temperature of coolant being injected, the temperature distribution in the wall zone of mixing of the main and injection flows becomes nonmonotonic. As a result, the Reynolds analogy is violated, i.e., the profiles of dimensionless temperature at the firing wall turn out to be dissimilar with the velocity profiles. In view of this, it is suggested to use the method of characteristic scales for generalizing the results of calculation of motion of ideal incompressible gas with due regard for the temperature dependence of the properties and for heat transfer under conditions of tangential injection on a high-temperature wall (in particular, at $T_w > T_{ad}$). The respective scales and the dimensionless form of equations are obtained for the problem under consideration. It is demonstrated that, in the case of tangential injection, strict similarity exists of velocity fields in turbulent flow, as well as of temperature fields for physically dissimilar liquids.