The study of temperature field impact on velocity of fluid in streamlines coordinates in free convection problem

A transition to coordinates formed by streamlines and orthogonal ones are convenient to simplify the Navier-Stokes and Fourier-Kirchoff system. We derive transformation to such coordinates, taking into account a necessity to introduce integrating factor that is not equal to unity in a viscous flow. The transition allows to express approximately velocity module and the velocity vector inclination to vertical direction in terms of temperature gradient in explicit form.