Dual solutions for flow and radiative heat transfer of a micropolar fluid over stretching/shrinking sheet

Abstract A boundary layer analysis is presented for the flow and radiative heat transfer of an incompressible micropolar fluid over stretching/shrinking sheet with power-law surface velocity and temperature distributions. Dual solutions are analytically obtained firstly by homotopy analysis method (HAM). It is found that dual solutions not only exist for the shrinking flow as reported in the previous literatures, but also exist for the stretching flow. The special case of the first branch (K = 0, classical Newtonian fluid) is compared with the existing numerical results of stretching flow in good agreement. Our results show that both solutions are physically meaningful (two solutions are closely related to each other), unlike the results previously reported that only one solution is acceptable. Moreover, the effects of the material parameter K, the radiative Prandtl number Prn, the velocity exponent parameter m and the temperature exponent parameter λ on the flow and heat transfer characteristics are analyzed in detail.

[1]  A. Cemal Eringen,et al.  Theory of thermomicrofluids , 1972 .

[2]  M. Ali,et al.  On thermal boundary layer on a power-law stretched surface with suction or injection , 1995 .

[3]  Goodarz Ahmadi,et al.  Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate , 1976 .

[4]  I. Pop,et al.  Dual solutions in mixed convection boundary layer flow of micropolar fluids , 2009 .

[5]  Shijun Liao,et al.  A new branch of solutions of boundary-layer flows over a permeable stretching plate , 2007 .

[6]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[7]  S. Liao.  A new branch of solutions of boundary-layer flows over an impermeable stretched plate , 2005 .

[8]  L. Kumar,et al.  Finite element analysis of combined heat and mass transfer in hydromagnetic micropolar flow along a stretching sheet , 2009 .

[9]  Tasawar Hayat,et al.  MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface , 2009 .

[10]  Shanshan Yao,et al.  Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions , 2011 .

[11]  S. Liao,et al.  A new branch of the temperature distribution of boundary-layer flows over an impermeable stretching plate , 2008 .

[12]  Ioan Pop,et al.  Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet , 2012 .

[13]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[14]  Chuei-Tin Chang,et al.  Petri-net based scheduling strategy for semiconductor manufacturing processes , 2011 .

[15]  S. Liao.  An approximate solution technique not depending on small parameters: A special example , 1995 .

[16]  I. Pop,et al.  Boundary-layer flow of a micropolar fluid on a continuously moving or fixed permeable surface , 2007 .

[17]  W. H. H. Banks,et al.  Similarity solutions of the boundary-layer equations for a stretching wall , 1983 .

[18]  Z. Abbas,et al.  Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet , 2011 .

[19]  I. Pop,et al.  MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux , 2009 .

[20]  G. Domairry,et al.  Analytical solution of non-Newtonian micropolar fluid flow with uniform suction/blowing and heat generation , 2009 .

[21]  Tiegang Fang,et al.  Boundary layer flow over a shrinking sheet with power-law velocity , 2008 .

[22]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[23]  A. Raptis.  Flow of a micropolar fluid past a continuously moving plate by the presence of radiation , 1998 .

[24]  Rafael Cortell,et al.  Viscous flow and heat transfer over a nonlinearly stretching sheet , 2007, Appl. Math. Comput..

[25]  I. Pop,et al.  Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid , 2011 .

[26]  Anuar Ishak,et al.  MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux , 2011 .

[27]  S. Goldstein.  On backward boundary layers and flow in converging passages , 1965, Journal of Fluid Mechanics.

[28]  K. Das,et al.  Slip effects on MHD mixed convection stagnation point flow of a micropolar fluid towards a shrinking vertical sheet , 2012, Comput. Math. Appl..

[29]  I. Pop,et al.  Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier–Stokes equations , 2011 .