Heat transfer analysis on the Hiemenz flow of a non-Newtonian fluid: a homotopy method solution. (English) Zbl 1291.76036

Summary: The mathematical model for the incompressible two-dimensional/axisymmetric non-Newtonian fluid flows and heat transfer analysis in the region of stagnation point over a stretching/shrinking sheet and axisymmetric shrinking sheet is presented. The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely, the homotopy perturbation method (HPM) with general form of linear operator is used to solve dimensionless nonlinear ordinary differential equations. The series solution is obtained without using the diagonal Padé approximants to handle the boundary condition at infinity which can be considered as a clear advantage of homotopy perturbation technique over the decomposition method. The effects of the pertinent parameters on the velocity and temperature field are discussed through graphs. To the best of authors’ knowledge, HPM solution with general form of linear operator for two-dimensional/axisymmetric non-Newtonian fluid flows and heat transfer analysis in the region of stagnation point is presented for the first time in the literature.


76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
35C05 Solutions to PDEs in closed form
Full Text: DOI


[1] Hiemenz, K., Die Grenzschict neinem in den gleichformigen flussigkeitsstrom eingetauchten geraden Kreiszylinder, Dingler’s Polytechnic Journal, 326, 321-410 (1911)
[2] Howann, F., Der Einfluss grosser Zahigkeit bei der Stromung um den Zylinder und um die Kugel, Zeitschrift für Angewandte Mathematik und Mechanik, 16, 153-164 (1936) · JFM 62.0984.02
[3] Wang, C. Y., Stagnation flow towards a shrinking sheet, International Journal of Non-Linear Mechanics, 43, 5, 377-382 (2008)
[4] Wang, C. Y., Similarity stagnation point solutions of the Navier-Stokes equations—review and extension, European Journal of Mechanics, B/Fluids, 27, 6, 678-683 (2008) · Zbl 1151.76425
[5] Yildirim, A.; Sezer, S. A., Analytical solution of MHD stagnationpoint flowin porous media by means of the homotopy perturbation method, Journal of Porous Media, 15, 1, 83-94 (2012)
[6] Attia, H. A., Hydromagnetic stagnation point flow with heat transfer over a permeable surface, Arabian Journal for Science and Engineering, 28, 1, 107-112 (2003)
[7] Massoudi, M.; Ramezan, M., Boundary layers heat transfer analysis of a viscoelastic fluid at a stagnation point, Journal of Heat Transfer, 130, 81-86 (1990)
[8] Garg, V. K., Heat transfer due to stagnation point flow of a non-Newtonian fluid, Acta Mechanica, 104, 3-4, 159-171 (1994) · Zbl 0815.76007
[9] He, J. H., Homotopy perturbation method for solving boundary value problems, Physics Letters A, 350, 1-2, 87-88 (2006) · Zbl 1195.65207
[10] Khan, Y.; Faraz, N.; Yildirim, A.; Wu, Q., A series solution of the long porous slider, Tribology Transactions, 54, 2, 187-191 (2011)
[11] Xu, L., He’s homotopy perturbation method for a boundary layer equation in unbounded domain, Computers and Mathematics with Applications, 54, 7-8, 1067-1070 (2007) · Zbl 1267.76089
[12] Ariel, P. D., Homotopy perturbation method and the natural convection flow of a third grade fluid through a circular tube, Nonlinear Science Letters A, 1, 2, 43-52 (2010)
[13] Khan, Y.; Wu, Q., Homotopy perturbation transform method for nonlinear equations using He’s polynomials, Computers and Mathematics with Applications, 61, 8, 1963-1967 (2011) · Zbl 1219.65119
[14] Khan, Y., A method for solving nonlinear time-dependent drainage model, Neural Computing and Applications, 23, 2, 411-415 (2013)
[15] Khan, Y.; Wu, Q.; Faraz, N.; Yildirim, A., The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet, Computers and Mathematics with Applications, 61, 11, 3391-3399 (2011) · Zbl 1222.76014
[16] He, J. H., Asymptotic methods for solitary solutions and compactons, Abstract and Applied Analysis, 2012 (2012) · Zbl 1257.35158
[17] Madani, M.; Khan, Y.; Mahmodi, Gh.; Faraz, N.; Yildirim, A.; Nasernejad, B., Application of homotopy perturbation and numerical methods to the circular porous slider, International Journal of Numerical Methods for Heat and Fluid Flow, 22, 6, 705-717 (2012) · Zbl 1356.76205
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.