2017•arXiv (Cornell University)Open access

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

Sergey Leble, Witold M. Lewandowski

Abstract

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

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Key concepts: Streamlines, streaklines, and pathlines, Vector field, Velocity vector, Fourier transform, Orthogonal coordinates, Mechanics, Temperature gradient, Field (mathematics)