## Explicit series solution for the Glauert-jet problem by means of the homotopy analysis method.(English)Zbl 1115.76065

Summary: We consider the self-similar wall jet over an impermeable resting plane surface (Glauert jet). Through an analytic technique to solve nonlinear problems, namely the homotopy analysis method, we obtain an explicit series solution for the Glauert-jet problem. This series solution converges efficiently to the closed-form solution found by Glauert in the whole region $$0 \leqslant \xi < + \infty$$ . In the frame of the homotopy analysis method, it is shown that the convergence region of the explicit series solution may be adjusted to obtain more accurate results.

### MSC:

 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 76D25 Wakes and jets 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 76M55 Dimensional analysis and similarity applied to problems in fluid mechanics

### Keywords:

boundary layer; convergence region
Full Text:

### References:

 [1] Akatnov, N. I., Development of 2d laminar fluid jet along a solid surface, Proc LPI Techn Hydrodyn, 5, 24-31 (1953) [2] Glauert, M. B., The wall jet, J Fluid Mech, 1, 625-643 (1956) [3] Liao, S. J., Beyond perturbation: introduction to homotopy analysis method (2003), Chapman & Hall/ CRC Press: Chapman & Hall/ CRC Press Boca Raton [4] Liao, S. J., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, J Fluid Mech, 488, 189-212 (2003) · Zbl 1063.76671 [5] Liao, S. J., On the homotopy analysis method for nonlinear problems, Appl Math Computat, 147, 499-513 (2004) · Zbl 1086.35005 [6] Liao, S. J.; Cheung, K. F., Homotopy analysis of nonlinear progressive waves in deep water, J Eng Math, 45, 2, 105-116 (2003) · Zbl 1112.76316 [7] Magyari, E.; Keller, B., The algebraically decaying wall jet, Eur J Mech B/Fluids, 23, 601-605 (2004) · Zbl 1093.76017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.