Asymptotic solution of the low Reynolds-number flow between two co-axial cones of common apex
The paper is concerned with the axi-symmetric, incompressible, steady, laminar and Newtonian flow between two, stationary, conical-boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier- Stokes' equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross-sectional Reynolds-number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displaced and they are demonstrated to be plausible and informative.
flow between two, stationary, conical-boundaries
scientific article; zbMATH DE number 3915862