Premium
Three‐dimensional Hiemenz stagnation‐point flows
Author(s) -
Weidman Patrick D.
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900319
Subject(s) - stagnation point , rotational symmetry , shear (geology) , stagnation temperature , shear stress , stagnation pressure , strain rate , mechanics , shear rate , flow (mathematics) , point (geometry) , mathematics , geometry , physics , materials science , thermodynamics , viscosity , composite material , heat transfer , mach number
A modification of Hiemenz's two‐dimensional outer potential stagnation‐point flow of strain rate a is obtained by adding periodic radial and azimuthal velocities of the form b r sin 2 θ and b r cos 2 θ , respectively, where b is a shear rate. This leads to the discovery of a new family of three‐dimensional viscous stagnation‐point flows depending on the shear‐to‐strain‐rate ratio γ = b / a that exist over the range − ∞ < γ < ∞ with reflectional symmetry about γ = 0 . Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large‐γ asymptotic behaviors. Sample similarity velocity profiles are also presented. It is noted that the results presented here are in many ways similar to the results reported for non‐axisymmetric Homann stagnation‐point flow.