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A transition to coordinates formed by streamlines and orthogonal ones areconvenient to simplify the Navier-Stokes and Fourier-Kirchoff system. We derivetransformation to such coordinates, taking into account a necessity tointroduce integrating factor that is not equal to unity in a viscous flow. Thetransition allows to express approximately velocity module and the velocityvector inclination to vertical direction in terms of temperature gradient inexplicit form.

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