An analytic solution for the problem of Williams–Brinkmann axisymmetric steady flow in the vicinity of a stagnation point at a blunt body is proposed. The boundary conditions are embedded in the main system of equations by means of the Boubaker polynomials expansion scheme (BPES). These differential equations are solved analytically and yield continuous and differentiable solutions compared to some published ones.
Similar content being viewed by others
References
H. Nasr, I. A. Hassanien, and H. M. El-Hawary, Chebyshev solution of laminar boundary-layer flow, Int. J. Comput. Math., 33, 127–132 (1990).
S. A. Orszag, Spectral methods for problems in complex geometries, J. Comp. Phys., 37, 70–92 (1980).
F. M. White, Viscous FIuid Flow, McGraw-Hill Inc., New York (1974).
A. R. Wadia and F. R. Payne, A boundary value technique for the analysis of laminar boundary layer flows, Int. J. Comput. Math., 9, 163–172 (1981).
L. Rosenhead, Laminar Boundary Layers, Oxford University Press (1963).
P. M. Beckett, Finite difference solution of boundary layer type equation, Int. J. Comput. Math., 14, 83–190 (1983).
T. Mahapatra and A. S. Gupta, Stagnation-point flow towards a stretching surface, Can. J. Chem. Eng., 81, 258–263 (2003).
T. Mahapatra and A. S. Gupta, Heat transfer in stagnation-point flow towards a stretching sheet, Heat Mass Transfer, 38, 517–521 (2002).
Y. Lok, N. Amin, and I. Pop, Non-orthogonal stagnation point flow towards a stretching sheet, Int. J. Nonlinear Mech., 41, 622–627 (2006).
C. Y. Wang, Stagnation flow towards a shrinking sheet, Int. J. Nonlinear Mech., 43, 377–382 (2008).
O. D. Oyodum, O. B. Awojoyogbe, M. Dada, and J. Magnuson, On the earliest definition of the Boubaker polynomials, Eur. Phys. J.–Appl. Phys., 46, 21201–21203 (2009).
J. Ghanouchi, H. Labiadh, and K. Boubaker, An attept to solve the heat transfer equation in a model of pyrolysis spray using 4q-order Boubaker polynomials, Int. J. Heat Technol., 26(1), 49–53 (2008).
S. Slama, J. Bessrour, M. Bouhafs, and K. B. Ben Mahmoud, Numerical distribution of temperature as a guide to investigation of melting point maximal front spatial evolution during resistance spot welding using Boubaker polynomials, Numer. Heat Transfer. Part A, 55, 401–408 (2009).
S. Fridjine and M. Amlouk, A new parameter: An ABACUS for optimizing functional materials using the Boubaker polynomials expansion scheme, Modern Phys. Lett. B, 23, 2179–282 (2009).
S. Tabatabaei, T. Zhao, O. Awojoyogbe, and F. Moses, Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme, Heat Mass Transfer, 45, 1247–1251 (2009).
A. Belhadj, O. Onyango, and N. Rozibaeva, Boubaker polynomials expansion scheme-related heat transfer investigation inside keyhole model, J. Thermophys. Heat Transfer, 23, 639–640 (2009).
N. Guezmir, T. Ben Nasrallah, K. Boubaker, M. Amlouk, and S. Belgacem, Optical modeling of compound CuInS2 using relative dielectric function approach and Boubaker polynomials expansion scheme BPES, J. Alloys Comp., 481, 543–548 (2009).
Q. Wu, S. Weinbaum, and Y. Andreopoulus, Stagnation-point flows in a porous medium, Chem. Eng. Sci., 60, 123–134 (2005).
V. Kumaran, R. Tamizharasi, and K. Vajravelu, Approximate analytic solutions of stagnation point flow in a porous medium, Commun. Nonlinear Sci. Numer. Simul., 14, 2677–2688 (2009).
S. E. El-Gendi, Chebyshev solution of differential, integral and integro-differential equations, Comput. J., 12, 282–287 (1969).
I. A. Hassanien, Chebyshev solution of stagnation point flow, Energy Convers. Mgmt., 38, 839–845 (1997).
H. W. Cheng, M. N. Ozisik, and J. C. Williams, III. Nonsteady three-dimensional stagnation-point flow, ASME J. Appl. Mech., 38, 282–287 (1960).
H. Schlichting, Boundary Layer Theory, McGraw-Hill, New York (1960).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 84, No. 3, pp. 571–575, May–June, 2011.
Rights and permissions
About this article
Cite this article
Zhang, D.H., Li, F.W. A Boubaker polynomials expansion scheme (BPES) related analytical solution to the Williams–Brinkmann stagnation point flow equation at a blunt body. J Eng Phys Thermophy 84, 618–623 (2011). https://doi.org/10.1007/s10891-011-0513-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-011-0513-9