Jeffery–Hamel flow

In fluid dynamics Jeffery–Hamel flow is a flow created by a converging or diverging channel with a source or sink of fluid volume at the point of intersection of the two plane walls. It is named after George Barker Jeffery(1915) and Georg Hamel(1917), but it has subsequently been studied by many major scientists such as von Kármán and Levi-Civita, Walter Tollmien, F. Noether, W.R. Dean, Rosenhead, Landau, G.K. Batcheloretc.

Consider two stationary plane walls with a constant volume flow rate ${\displaystyle Q}$ is injected/sucked at the point of intersection of plane walls and let the angle subtended by two walls be ${\displaystyle 2\alpha }$. Take the cylindrical coordinate ${\displaystyle (r,\theta ,z)}$ system with ${\displaystyle r=0}$ representing point of intersection and ${\displaystyle \theta =0}$ the centerline and ${\displaystyle (u,v,w)}$ are the corresponding velocity components. The resulting flow is two-dimensional if the plates are infinitely long in the axial ${\displaystyle z}$ direction, or the plates are longer but finite, if one were neglect edge effects and for the same reason the flow can be assumed to be entirely radial i.e., ${\displaystyle u=u(r,\theta ),v=0,w=0}$.

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