Solution of the Falkner-Skan wedge flow by HPM-Padé method. (English) Zbl 1376.76055

Summary: In this paper, the temperature and velocity fields associated with the Falkner-Skan boundary-layer problem have been studied. The nonlinear boundary-layer equations are solved analytically by the homotopy perturbation method (HPM) employing the Padé technique. Analytical results for the temperature and velocity of the flow are presented through graphs and tables for various values of the wedge angle and Prandtl number. It is seen that the current results in comparison with the numerical ones are in excellent agreement and the HPM-Padé solution provides a convenient way to control and adjust the convergence region of a system of nonlinear boundary-layer problems.


76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI


[1] Falkner, V. M.; Skan, S. W.: Some approximate solutions of the boundary layer equations, Philos mag 12, No. 80, 865-896 (1931) · Zbl 0003.17401
[2] Hartree, D. H.: On an equation occurring in Falkner and Skan’s approximate treatment of the equations of the boundary layer, Proc cambr philos soc 33, No. Part II, 223-239 (1937) · Zbl 0017.08004
[3] Na, T. Y.: Computational methods in engineering boundary value problems, (1979) · Zbl 0456.76002
[4] Rajagopal, K. R.; Gupta, A. S.; Na, T. Y.: A note on the Falkner – Skan flows of a non-Newtonian fluid, Int J non-linear mech 18, 313-320 (1983) · Zbl 0527.76010
[5] Lin, H. T.; Lin, L. K.: Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number, Int J heat mass transfer 30, 1111-1118 (1987)
[6] Hsu, C. H.; Chen, C. S.; Teng, J. T.: Temperature and flow fields for the flow of a second grade fluid past a wedge, Int J nonlinear mech 32, No. 5, 933-946 (1997) · Zbl 0894.76003
[7] Asaithambi, A.: A finite-difference method for the Falkner – Skan equation, Appl math comput 92, 135-141 (1998) · Zbl 0973.76581
[8] Hsu, C. H.; Hsiao, K. L.: Conjugate heat transfer of a plate fin in a second-grade fluid flow, Int J heat mass transfer 41, No. 8-9, 1087-1102 (1998) · Zbl 0940.76534
[9] Soleimani, Soheil; Ghasemi, E.; Ganji, D. D.; Jalaal, M.; Bararnia, H.: Meshless LRBF-DQ for 2D heat conduction: a comparative study, J therm sci 15, S117-S121 (2011)
[10] Jalaal, M.; Jalali, P.; Ganji, D. D.; Ghasemi, E.; Soleimani, Soheil; Bararnia, H.: Effect of temperature-dependency of surface emissivity on heat transfer: A PPM investigation, J therm sci 15, S123-S125 (2011)
[11] Jalaal, M.; Nejad, M. G.; Jalili, P.; Bararnia, H.; Ghasemi, E.; Soleimani, Soheil: Homotopy perturbation method for motion of a spherical solid particle in plane Couette fluid flow, Comput math appl 61, 2267-2270 (2011) · Zbl 1219.76036
[12] Hesameddini, E.; Latifizadeh, H.: An optimal choice of initial solutions in the homotopy perturbation method, Int J nonlinear sci num 10, 1389-1398 (2009) · Zbl 1191.65177
[13] Hesameddini, E.; Latifizadeh, H.: A new vision of the he’s homotopy perturbation method, Int J nonlinear sci num 10, 1415-1424 (2009) · Zbl 1191.65177
[14] Miansari, Mo; Miansari, Me; Barari, A.; Domairry, G.: Analysis of Blasius equation for flat-plate flow with infinite boundary value, Int J comput methods eng sci mech 11, No. 2, 79-84 (2010) · Zbl 1372.76039
[15] Yıldırım, A.; Sezer, S. A.: Effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel, Math comput modell 52, No. 3 – 4, 618-625 (2010) · Zbl 1201.76318
[16] Omidvar, M.; Barari, A.; Momeni, M.; Ganji, D. D.: New class of solutions for water infiltration problems in unsaturated soils, Geomech geoeng: int J 5, 127-135 (2010)
[17] He, J. H.: Homotopy perturbation method: a new nonlinear analytical technique, Appl math comput 135, 73-79 (2003) · Zbl 1030.34013
[18] Ganji, D. D.: The application of he’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys lett A 355, 337-341 (2006) · Zbl 1255.80026
[19] Ganji, D. D.; Afrouzi, G. A.; Hosseinzadeh, H.; Talarposhti, R. A.: Application of homotopy-perturbation method to the second kind of nonlinear integral equations, Phys lett A 371, 20-25 (2007) · Zbl 1209.65145
[20] Esmaeilpour, M.; Ganji, D. D.: Application of he’s homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate, Phys lett A 372, 33-38 (2007) · Zbl 1217.76029
[21] Ganji, D. D.; Kachapi, Seyed H. Hashemi: Analysis of nonlinear equations in fluids, Prog nonlinear sci 2, 1-293 (2011) · Zbl 1305.74002
[22] Ganji, D. D.; Kachapi, Seyed H. Hashemi: Analytical and numerical methods in engineering and applied sciences, Prog nonlinear sci 3, 1-579 (2011) · Zbl 1335.00001
[23] Bararnia, H.; Ghasemi, E.; Domairry, G.; Soleimani, S.: Behavior of micropolar flow due to linear stretching of porous sheet with injection and suction, Adv eng softw 41, 893-897 (2010) · Zbl 1346.76192
[24] Moghimi, S. M.; Domairry, G.; Soleimani, S.; Ghasemi, E.; Bararni, H.: Application of homotopy analysis method to solve MHD Jeffery – Hamel flows in non-parallel walls, Adv eng softw 42, 108-113 (2011) · Zbl 1316.76078
[25] Wazwaz, A. M.; El-Sayed, S. M.: A new modification of the Adomian decomposition method for linear and nonlinear operators, Appl math comput 122, 393-405 (2001) · Zbl 1027.35008
[26] Baker, G. A.: Essentials of Padé´ approximants, (1975) · Zbl 0315.41014
[27] Bararnia, H.; Ghasemi, E.; Soleimani, Soheil; Baraei, A.; Ganji, D. D.: HPM – Padé method on natural convection of darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature, J porous media 14, No. 6, 545-553 (2011)
[28] He, J. H.: A simple perturbation approach to Blasius equation, Appl math comput 140, 217-222 (2003) · Zbl 1028.65085
[29] Ganji, D. D.; Sahouli, A. R.; Famouri, M.: A new modification of he’s homotopy perturbation method for rapid convergence of nonlinear undamped oscillators, J appl math comput 30, 181-192 (2009) · Zbl 1180.34011
[30] Boyd, J.: Pad´e approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain, Comput phys 11, 299-303 (1997)
[31] White, F. M.: Viscous fluid flow, (1991)
[32] Adomian, G.: Solving frontier problems of physics: the decomposition method, (1994) · Zbl 0802.65122
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