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Motsa, S. S.

On an interpolation based spectral homotopy analysis method for PDE based unsteady boundary layer flows. (English) Zbl 1474.76022

Abstr. Appl. Anal. 2014, Article ID 848170, 7 p. (2014).
Summary: This work presents a new approach to the application of the spectral homotopy analysis method (SHAM) in solving non-linear partial differential equations (PDEs). The proposed approach is based on an innovative idea of seeking solutions that obey a rule of solution expression that is defined in terms of bivariate Lagrange interpolation polynomials. The applicability and effectiveness of the expanded SHAM approach are tested on a non-linear PDE that models the problem of unsteady boundary layer flow caused by an impulsively stretching plate. Numerical simulations are conducted to generate results for the important flow properties such as the local skin friction. The accuracy of the present results is validated against existing results from the literature and against results generated using the Keller-box method. The preliminary results from the proposed study indicate that the present method is more accurate and computationally efficient than more traditional methods used for solving PDEs that describe nonsimilar boundary layer flow.

Cited in 2 Documents

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics

Software:

BVPh; Matlab
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\textit{S. S. Motsa}, Abstr. Appl. Anal. 2014, Article ID 848170, 7 p. (2014; Zbl 1474.76022)
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References:

[1] Liao, S., Beyond Perturbation: Introduction to the Homotopy Analysis Method. Beyond Perturbation: Introduction to the Homotopy Analysis Method, CRC Series: Modern Mechanics and Mathematics, 2 (2004), Boca Raton, Fla, USA: Chapman & Hall/CRC Press, Boca Raton, Fla, USA · Zbl 1051.76001
[2] Liao, S. J., Homotopy Analysis Method in Nonlinear Differential Equations (2012), Berlin, Germany: Springer, Berlin, Germany
[3] Motsa, S. S.; Sibanda, P.; Shateyi, S., A new spectral-homotopy analysis method for solving a nonlinear second order BVP, Communications in Nonlinear Science and Numerical Simulation, 15, 9, 2293-2302 (2010) · Zbl 1222.65090
[4] Motsa, S. S.; Sibanda, P.; Awad, F. G.; Shateyi, S., A new spectral-homotopy analysis method for the MHD Jeffery-Hamel problem, Computers & Fluids, 39, 7, 1219-1225 (2010) · Zbl 1242.76363
[5] Motsa, S. S., On the practical use of the spectral homotopy analysis method and local linearisation method for unsteady boundary-layer flows caused by an impulsively stretching plate, Numerical Algorithms (2013) · Zbl 1299.76192
[6] Ali, A.; Mehmood, A., Homotopy analysis of unsteady boundary layer flow adjacent to permeable stretching surface in a porous medium, Communications in Nonlinear Science and Numerical Simulation, 13, 2, 340-349 (2008) · Zbl 1155.35408
[7] Ahmad, I.; Sajid, M.; Hayat, T.; Ayub, M., Unsteady axisymmetric flow of a second-grade fluid over a radially stretching sheet, Computers & Mathematics with Applications, 56, 5, 1351-1357 (2008) · Zbl 1155.76304
[8] Kumari, M.; Nath, G., Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface, Communications in Nonlinear Science and Numerical Simulation, 14, 8, 3339-3350 (2009) · Zbl 1221.76226
[9] Hayat, T.; Qasim, M.; Abbas, Z., Homotopy solution for the unsteady three-dimensional MHD flow and mass transfer in a porous space, Communications in Nonlinear Science and Numerical Simulation, 15, 9, 2375-2387 (2010) · Zbl 1222.76075
[10] Liao, S., An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Communications in Nonlinear Science and Numerical Simulation, 11, 3, 326-339 (2006) · Zbl 1078.76022
[11] Mehmood, A.; Ali, A.; Shah, T., Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation, 13, 5, 902-912 (2008) · Zbl 1221.76152
[12] Mehmood, A.; Ali, A.; Takhar, H. S.; Shah, T., Unsteady three-dimensional MHD boundary-layer flow due to the impulsive motion of a stretching surface, Acta Mechanica, 199, 1-4, 241-249 (2008) · Zbl 1311.76146
[13] Sajid, M.; Ahmad, I.; Hayat, T.; Ayub, M., Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet, Communications in Nonlinear Science and Numerical Simulation, 13, 10, 2193-2202 (2008)
[14] Sajid, M.; Ahmad, I.; Hayat, T.; Ayub, M., Unsteady flow and heat transfer of a second grade fluid over a stretching sheet, Communications in Nonlinear Science and Numerical Simulation, 14, 1, 96-108 (2009) · Zbl 1221.76022
[15] Tan, Y.; Liao, S.-J., Series solution of three-dimensional unsteady laminar viscous flow due to a stretching surface in a rotating fluid, Journal of Applied Mechanics, Transactions ASME, 74, 5, 1011-1018 (2007)
[16] Xu, H.; Liao, S. J.; Pop, I., Series solutions of unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface, Acta Mechanica, 184, 1-4, 87-101 (2006) · Zbl 1096.76004
[17] Xu, H.; Pop, I., Homotopy analysis of unsteady boundary-layer flow started impulsively from rest along a symmetric wedge, Zeitschrift für Angewandte Mathematik und Mechanik, 88, 6, 507-514 (2008) · Zbl 1138.76034
[18] Canuto, C.; Hussaini, M. Y.; Quarteroni, A.; Zang, T. A., Spectral Methods in Fluid Dynamics. Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics (1988), New York, NY, USA: Springer, New York, NY, USA · Zbl 0658.76001
[19] Trefethen, L. N., Spectral Methods in MATLAB. Spectral Methods in MATLAB, Software, Environments, and Tools, 10 (2000), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA · Zbl 0953.68643
[20] Williams, J. C.; Rhyne, T. B., Boundary layer development on a wedge impulsively set into motion, SIAM Journal on Applied Mathematics, 38, 2, 215-224 (1980) · Zbl 0443.76039
[21] Nazar, R.; Amin, N.; Pop, I., Unsteady boundary layer flow due to a stretching surface in a rotating fluid, Mechanics Research Communications, 31, 1, 121-128 (2004) · Zbl 1053.76017
[22] Seshadri, R.; Sreeshylan, N.; Nath, G., Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion, International Journal of Heat and Mass Transfer, 45, 6, 1345-1352 (2002) · Zbl 1121.76394
[23] Cebeci, T.; Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer (1984), New York, NY, USA: Springer, New York, NY, USA · Zbl 0545.76090
[24] Chamkha, A. J.; Abbasbandy, S.; Rashad, A. M.; Vajravelu, K., Radiation effects on mixed convection over a wedge embedded in a porous medium filled with a nanofluid, Transport in Porous Media, 91, 1, 261-279 (2012)
[25] Chamkha, A. J.; Abbasbandy, S.; Rashad, A. M.; Vajravelu, K., Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid, Meccanica, 48, 2, 275-285 (2013) · Zbl 1293.76123
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