Heat transfer in Couette flow corrected for energy dissipation by the third kind boundary conditions

The analytical solution of the non-linear heat transfer problem for laminar flow of liquid in plane-parallel channel (Coutte flow) corrected for energy dissipation by the third kind boundary conditions on the moving wall is obtained by the Kantorovich and the orthogonal Bubnov-Galerkin methods. The solution allows to estimate the temperature state of liquid for the small values of longitudinal coordinate, where the displacement of temperature profile to the immovable wall takes place as the investigations have shown.