Abstract
The objective of the present study is to analyze the effect of heat generation/absorption on magnetohydrodynamic stagnation point flow and heat transfer over a porous stretching surface, with prescribed surface heat flux. The governing coupled partial differential equations are non-dimensionalized and solved analytically by homotopy perturbation method employing Padé technique. The effects of involved parameters (stretching velocity, magnetic parameter, porosity parameter, suction or injection parameter, heat flux index, heat source or sink parameter, Prandtl number) on velocity, temperature profiles are presented graphically and analyzed. The obtained results are compared with the numerical solution and with other results obtained in previous works so that the high accuracy of present results is clear.
Similar content being viewed by others
References
Weidman P, Paullet J (2007) Analysis of stagnation point flow toward a stretching sheet. Int J Non-Linear Mech 42:1084–1091
Hiemenz K (1911) Die Grenzschicht an einem in den gleichformingen Flussigkeitsstrom eingetauchten graden Kreiszylinder. Dinglers Polytech J 236:321–324
Crane LJ (1970) Flow past a stretching plate. J Appl Math Phys (ZAMP) 21:645–647
Chiam TC (1994) Stagnation-point flow towards a stretching plate. J Phys Soc Jpn 63(6):2443–2444
Gupta PS, Gupta AS (1977) Heat and mass transfer on a stretching sheet with suction and blowing. J Chem Eng 55:744–746
Mahapatra TR, Gupta AS (2002) Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Transf 38:517–521
Mahapatra TR, Gupta AS (2003) Stagnation-point flow towards a stretching surface. Can J Chem Eng 81:258–263
Lok YY, Amin N, Pop I (2006) Non-orthogonal stagnation point flow towards a stretching sheet. Int J Nonlinear Mech 41:622–627
Wang CY (1984) The three-dimensional flow due to a stretching flat surface. Phys Fluids 27:1915–1917
Char MI, Chen CK (1988) Temperature field in non-Newtonian flow over a stretching plate with variable heat flux. Int J Heat Mass Transf 31:917–921
Chen CK, Char MI (1988) Heat transfer of a continuous, stretching surface with suction or blowing. J Math Anal Appl 135:568–580
Elbashbeshy EMA (1998) Heat transfer over a stretching surface with variable surface heat flux. J Phys D Appl Phys 31:1951–1954
Ishak A, Nazar R, Pop I (2008) Heat transfer over a stretching surface with variable heat flux in micropolar fluids. Phys Lett A 372:559–561
Anjali Devi SP, Ganga B (2008) Dissipation effects on MHD nonlinear flow and heat transfer past a porous surface with prescribed heat flux. J Appl Fluid Mech 3:1–6
Hayat T, Javed T, Abbas Z (2009) MHD flow of a micropolar fluid near a stagnation point towards a non-linear stretching surface. Nonlinear Anal Real World Appl 10:1514–1526
Rashidi MM, Abelman S, Freidoonimehr N (2013) Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int J Heat Mass Transf 62:515–525
Ishak A, Jafar K, Nazar R, Pop I (2009) MHD stagnation point flow towards a stretching sheet. Physica A 388:3377–3383
Mohyud-Din ST, Yıldırım A, Sezer SA, Usman M (2010) Modified variational iteration method for free-convective boundary-layer equation using Pade´ approximation. Math Probl Eng 318298:1–11
Mirgolbabaei H, Ganji DD, Etghani MM, Sobati A (2009) Adapted variational iteration method and axisymmetric flow over a stretching sheet. World J Model Simul 5:307–314
Sajid M, Hayat T (2009) The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. Chaos Solitons Fract 39:1317–1323
Liao SJ (1992) The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D., Shanghai Jiao Tong University
Rashidi MM (2009) The modified differential transform method for solving MHD boundary-layer equations. Comput Phys Commun 180:2210–2217
He JH (1999) Homotopy perturbation technique. Comput Math Appl Mech Eng 178:257–262
He JH (2000) A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int J Non-Linear Mech 35:37–43
He JH (2003) Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 135:73–79
He JH (2006) Homotopy perturbation method for solving boundary value problems. Phys Lett A 350:87–88
Fathizadeh M, Rashidi F (2009) Boundary layer convective heat transfer with pressure gradient using homotopy perturbation method (HPM) over a flat plate. Chaos Solitons Fract 42:2413–2419
Ganji DD, Ganji SS, Karimpour S, Ganji ZZ (2010) Numerical study of homotopy-perturbation method applied to Burgers equation in fluid. Numer Methods Partial Differ Eq 26:917–930
Ariel PD, Hayat T, Asghar S (2006) Homotopy perturbation method and axisymmetric flow over a stretching sheet. Int J Nonlinear Sci Numer Simul 7:399–406
Yıldırım A, Sezer SA (2010) Non-perturbative solution of the MHD flow over a non-linear stretching sheet by HPM-Pade technique. Z Naturforsch A J Phys Sci 65:1106–1110
Domairry D, Ziabkhsh Z, Domiri H (2011) Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM. Therm Sci 15(5):111–115
Torabi M, Yaghoobi H, Saedodin S (2011) Assessment of homotopy perturbation method in nonlinear convective-radiative non-fourier conduction heat transfer equation with variable coefficient. Therm Sci 15(2):263–274
Inc M (2010) He’s homotopy perturbation method for solving Korteweg–de Vries Burgers equation with initial condition. Numer Methods Partial Differ 26:1224–1235
Baker GA (1975) Essentials of Padé approximants. Academic, London
Boyd J (1997) Padé approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Comput Phys 11(3):299–303
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Francisco Ricardo Cunha.
Rights and permissions
About this article
Cite this article
Jalilpour, B., Jafarmadar, S. & Ganji, D.D. MHD stagnation flow towards a porous stretching sheet with suction or injection and prescribed surface heat flux. J Braz. Soc. Mech. Sci. Eng. 37, 837–847 (2015). https://doi.org/10.1007/s40430-014-0218-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40430-014-0218-z