Flow and heat due to a surface formed by a vortical source

The existence of exact solutions relevant to the rotating incompressible fluid flows over surfaces formed by the superposition of a uniform source and an irrotational vortex, is described in the present paper. The interest lies in transport phenomena based approach to understanding vortical flows taking place in the vortex flows in geophysics. The vortex structure of the surface is not permitted to persist far away from the surface and the surface is also heated with a finite amount of energy. A treatment of Navier Stokes equations in cylindrical coordinates shows that such a motion imposes similarity solutions leading to two and three-dimensional flows. Closed-form solutions are proven to be available for zero Reynolds number (Stokes flow) and hence, perturbation solutions follow for small Reynolds numbers. For Reynolds number sufficiently large, numerical solutions clearly point to the formation of a viscous boundary layer near the surface. A continuous decay in the velocity field is anticipated for increasing Reynolds numbers, which, in turn, results in a pronounced thermal layer. The effects of source and vortex strength on the velocity and temperature distributions are eventually investigated. A hotter fluid is found when changing from a source to a sink of the same strength. (C) 2017 Elsevier Masson SAS. All rights reserved.