Premium
An analytical solution of the Navier‐Stokes equations for unsteady backward stagnation‐point flow with injection or suction
Author(s) -
Shapiro Alan
Publication year - 2006
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.200510241
Subject(s) - streamlines, streaklines, and pathlines , stagnation point , suction , mechanics , boundary layer , vortex , flow (mathematics) , similarity solution , stagnation temperature , stagnation pressure , mathematics , physics , classical mechanics , thermodynamics , heat transfer , mach number
Abstract A particular solution of the unsteady axisymmetric incompressible Navier‐Stokes equations is obtained in the classical Birkhoff similarity framework. The solution describes a decelerating backward stagnation‐point flow with uniform injection or suction from a porous boundary (plate). Although the solution is completely analytical, it is limited in scope to one particular case each of injection and suction. In the case of suction, a single dividing streamline is found in the lee of the plate, while in the case of injection, two dividing streamlines are found. In this latter case, the dividing streamlines bound a nearly stagnant layer containing a weak vortex. Analytical results are also presented for the temperature field in the forced convection regime.