A new type of the boundary condition allowing analytical solution of the thermal boundary layer equation

Outlined in this paper is a new analytical form of a non-monotone distribution of the wall temperature allowing solving the thermal boundary layer equation analytically. The thermal boundary layer equation in its integral form was solved for the temperature distribution at the wall, with the Nusselt number being specified as a boundary condition in the form of an arbitrary power-law function. The new solution, as illustrated on the example of a free rotating disk, can provide the analytical formulas for the wall temperature distributions having points of a maximum or a minimum, while the traditionally used power-law distributions behave as the monotone functions. The new solution includes earlier known power-law solutions for the wall temperature and the Nusselt number as a particular case. Numerical data computed using the proposed solution are in a better agreement with known experimental data than the traditionally used power-law functions.