On a method for calculating heat transfer in a moving fluid taking into account energy dissipation

An approximate analytical solution to the heat transfer problem for a moving fluid in a cylindrical channel is obtained using an additional new function and additional boundary conditions in the heat balance integral method and taking into account energy dissipation under a first-order boundary condition that varies along the longitudinal coordinate. The use of the additional new function that determines the temperature change along the longitudinal variable in the center of the channel makes it possible to reduce the solution of the partial differential equation to the integration of the ordinary differential equation. The additional boundary conditions are found in such a way that their satisfaction for the new solution is equivalent to the satisfaction of the differential equation at boundary points.