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

TL;DR

This paper develops a coordinate transformation based on streamlines to simplify the Navier-Stokes and Fourier-Kirchoff equations in free convection, enabling explicit expressions for velocity in terms of temperature gradients.

Contribution

It introduces a novel transformation to streamline coordinates that accounts for viscosity effects, simplifying the analysis of free convection flows.

Findings

Derived explicit formulas for velocity magnitude and inclination in streamline coordinates.

Facilitated analysis of free convection by simplifying governing equations.

Enhanced understanding of temperature field impact on flow velocity.

Abstract

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.