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Self‐Similar “Stagnation Point” Boundary Layer Flows with Suction or Injection
Author(s) -
King J. R.,
Cox S. M.
Publication year - 2005
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2005.01563
Subject(s) - stagnation point , streamlines, streaklines, and pathlines , suction , boundary layer , mechanics , similarity solution , flow (mathematics) , monotonic function , viscous liquid , stagnation pressure , mathematics , stagnation temperature , boundary (topology) , physics , thermodynamics , mathematical analysis , heat transfer , mach number
Multiple solutions are reported for the two‐dimensional boundary layer flow of a viscous fluid near a permeable wall through which fluid is uniformly withdrawn. In the limit of large wall suction, three flows of similarity form are found: the first is the well‐known monotonic solution of Terrill; the second exhibits flow reversal, with the streamlines being separated into three distinct cells; the third also exhibits flow reversal, but has multiple cells only when the fluid withdrawal speed is less than some threshold. The wall injection problem is also briefly studied, only Terrill's branch of solutions being found. Numerical and asymptotic solutions are presented and compared; the large‐suction asymptotics of the third solution branch are found to be rather subtle.