Abstract
In this paper, we have studied the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic field has been analyzed analytically. The governing fundamental equations are approximated by a system of nonlinear locally similar ordinary differential equations which are solved analytically by applying homotopy analysis method (HAM). The effects of Darcy number, heat generation parameter and inertia coefficient parameter are determined on the flow. Convergence of the obtained series solution is discussed. The homotopy analysis method provides us with a new way to obtain series solutions of such problems. This method contains the auxiliary parameter which provides us with a simple way to adjust and control the convergence region of series solution. By suitable choice of the auxiliary parameter, we can obtain reasonable solutions for large modulus.
Similar content being viewed by others
Abbreviations
- Pr :
-
Prandtl Number
- L 1,L 2 :
-
Linear operator of HAM
- B 0 :
-
External magnetic field
- HAM:
-
Homotopy analysis method
- T :
-
Temperature
- ħ :
-
Auxiliary parameters
- K :
-
Thermal conductivity
- ρ :
-
Density of the fluid
- ν :
-
Kinematic viscosity
- η :
-
Dimensionless similarity variable
- α :
-
Inertia coefficient parameter
- ψ :
-
Stream function
- μ :
-
Dynamic viscosity
References
Eringen AC (1966) Theory of micropolar fluids. J Math Mech 16:1–18
Lukaszewicz G (1999) Micropolar fluids: theory and applications. Birkhauser, Boston
Allen SJ, Kline KA (1971) Lubrication theory for micropolar fluids. J Appl Mech 38(3):646–650
Tipei N (1979) Lubrication with micropolar liquids and its application to short bearings. J Lubr Technol 101(3):356–363
Sakiadis BC (1962) Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J 7(1):26–28
Kim YJ, Fedorov AG (2003) Transient mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate. Int J Heat Mass Transf 46(10):1751–1758
Raptis A (1998) Flow of a micropolar fluid past a continuously moving plate by the presence of radiation. Int J Heat Mass Transf 41(18):2865–2866
Raptis A (2000) Boundary layer flow of a micropolar fluid through a porous medium. J Porous Media 3(1):95–97
Liao SJ (1992) The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University
Liao SJ (1995) An approximate solution technique not depending on small parameters: a special example. Int J Non-Linear Mech 303:371–380
Liao SJ (1997) Boundary element method for general nonlinear differential operators. Eng Anal Bound Elem 202:91–99
Liao SJ (2003) Beyond perturbation: introduction to the homotopy analysis method. Chapman & Hall/CRC Press, Boca Raton
Hayat T, Khan M, Ayub M (2004) On the explicit analytic solutions of an oldroyd 6-constant fluid. Int J Eng Sci 42:123–135
Abbasbandy S Homotopy analysis method for heat radiation equations. Int Commun Heat Mass Transf 34, 380 (2007)
Ali A, Mehmood A (2008) Homotopy analysis of unsteady boundary layer flow adjacent to permeable stretching surface in a porous medium. Commun Nonlinear Sci Numer Simul 13(2):340
Ziabakhsh Z, Domairry G (2009) Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method. Commun Nonlinear Sci Numer Simul 14(4):1284
Sohouli AR, Domairry D, Famouri M, Mohsenzadeh A (2008) Analytical solution of natural convection of Darcian fluid about a vertical full cone embedded in porous media prescribed wall temperature by means of HAM. Int Commun Heat Mass Transf 35(10):1380–1384
Ziabakhsh Z, Domairry G, Ghazizadeh HR (2009) Analytical solution of the stagnation-point flow in a porous medium by using the homotopy analysis method. J Taiwan Inst Chem Eng 40:91–97
Domairry G, Nadim N (2008) Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation. Int Commun Heat Mass Transf 35(1):93–102
Ziabakhsh Z, Domairry G, Bararnia H, Babazadeh H (2010) Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. J Taiwan Inst Chem Eng 41:22–28
Mostaf AA, Manmoud M, Abd-elati M, Waheed SE (2006) Hydromagnetic boundary layer micropolar fluid flow over a stretching surface embedded in a non-Darcian porous medium with radiation. Math Probl Eng 39392:1–10
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Domairry, G., Ziabakhsh, Z. Solution of boundary layer flow and heat transfer of an electrically conducting micropolar fluid in a non-Darcian porous medium. Meccanica 47, 195–202 (2012). https://doi.org/10.1007/s11012-011-9429-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-011-9429-x