Calculation of the velocity of second-order thermal slip using the model kinetic equation with a variable collision frequency

The problem on the calculation of the second-order thermal slip velocity is solved. For this purpose, an exact solution of an inhomogeneous model Boltzmann kinetic equation with the collision operator in the form corresponding to the BGK model with the collision frequency proportional to the module of intrinsic velocity of gas molecules is constructed. Comparison with the available results is performed.