A note on viscous flow induced by half-line sources bounded by conical surfaces

TL;DR

This paper investigates axisymmetric viscous flows caused by a half-line source within conical boundaries, analyzing solution existence, boundary conditions, and flow transitions at different Reynolds numbers.

Contribution

It introduces a detailed analysis of flow solutions with two boundary condition types and explores their existence limits and transition behavior.

Findings

Solutions exist within specific Reynolds number ranges.

Two boundary condition types are identified and analyzed.

Flow transitions depend on boundary conditions and Reynolds number.

Abstract

In this paper axisymmetric solutions of the Navier-Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in which the radial velocity along the axis is prescribed, and the other in which the radial velocity along the axis is obtained as an eigenvalue of the problem. The existence of these solutions are limited to a range of Reynolds numbers and the transition from one case to the other are discussed in detail.