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Series Solutions of Unsteady Boundary‐Layer Flows over a Stretching Flat Plate
Author(s) -
Liao Shijun
Publication year - 2006
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.1467-9590.2006.00354.x
Subject(s) - convergent series , mathematics , dimensionless quantity , series (stratigraphy) , mathematical analysis , boundary layer , boundary value problem , homotopy analysis method , nonlinear system , perturbation (astronomy) , similarity (geometry) , homotopy , power series , physics , mechanics , pure mathematics , computer science , paleontology , quantum mechanics , artificial intelligence , image (mathematics) , biology
An analytic technique, namely, the homotopy analysis method, is applied to give series solution of the unsteady boundary‐layer flows over an impermeable stretching plate. Different from all previous perturbation solutions, our series solutions are convergent in the whole time region 0 ≤τ < +∞. To the best of our knowledge, such kind of series solution has never been reported for this problem. Besides, two kinds of new similarity transformations about dimensionless time are proposed. Using these two different similarity transformations, we obtain the same convergent solution valid in the whole time region 0 ≤τ < +∞. Furthermore, it is shown that a nonlinear initial/boundary‐value problem can be replaced by an infinite number of linear boundary‐value subproblems.