Analytic Solution of Three-Dimensional Viscous Flow and Heat Transfer Over a Stretching Flat Surface by Homotopy Analysis Method

In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.

[1]  Shijun Liao,et al.  On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..

[2]  Shijun Liao,et al.  Analytic solutions of the temperature distribution in Blasius viscous flow problems , 2002, Journal of Fluid Mechanics.

[3]  K. Cheung,et al.  Homotopy analysis of nonlinear progressive waves in deep water , 2003 .

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

[5]  A. Gupta,et al.  HYDROMAGNETIC FLOW AND HEAT TRANSFER OVER A STRETCHING SHEET , 1979 .

[6]  M. Zakaria.  Magnetohydrodynamic viscoelastic boundary layer flow past a stretching plate and heat transfer , 2004, Appl. Math. Comput..

[7]  Cha'o-Kuang Chen,et al.  Heat transfer of a continuous, stretching surface with suction or blowing , 1988 .

[8]  H. Andersson.  MHD flow of a viscoelastic fluid past a stretching surface , 1992 .

[9]  A. Bharali,et al.  Hydromagnetic flow and heat transfer between two horizontal plates, the lower plate being a stretching sheet , 1983 .

[10]  Kuppalapalle Vajravelu,et al.  Analytical and numerical solutions of a coupled non-linear system arising in a three-dimensional rotating flow , 2004 .

[11]  B. S. Dandapat,et al.  Flow and heat transfer in a viscoelastic fluid over a stretching sheet , 1989 .

[12]  K. Vajravelu.  Hydromagnetic flow and heat transfer over a continuous, moving, porous, flat surface , 1986 .

[13]  S. Liao.  An explicit, totally analytic approximate solution for Blasius’ viscous flow problems , 1999 .

[14]  M. B. Zaturska,et al.  Eigensolutions in Boundary-Layer Flow Adjacent to a Stretching Wall , 1986 .

[15]  Ali J. Chamkha.  Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption , 1999 .

[16]  F. Allan,et al.  On the analytic solutions of the nonhomogeneous Blasius problem , 2005 .

[17]  A. Mehmood,et al.  Analytic solution of generalized three-dimensional flow and heat transfer over a stretching plane wall , 2006 .

[18]  A. Jacobi.  A Scale Analysis Approach to the Correlation of Continuous Moving Sheet (Backward Boundary Layer) Forced Convective Heat Transfer , 1993 .

[19]  Shijun Liao,et al.  Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate , 2005 .

[20]  S. Liao.  An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate , 2006 .

[21]  I. Pop,et al.  Explicit analytic solution for similarity boundary layer equations , 2004 .

[22]  M. Ali,et al.  Heat transfer characteristics of a continuous stretching surface , 1994 .

[23]  P. S. Gupta,et al.  Heat and mass transfer on a stretching sheet with suction or blowing , 1977 .

[24]  B. K. Dutta,et al.  Temperature field in flow over a stretching sheet with uniform heat flux , 1985 .

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

[26]  P. S. Hiremath,et al.  Second-order fluid flow past a stretching sheet with heat transfer , 1987 .

[27]  Shijun Liao,et al.  On the explicit, purely analytic solution of Von Kármán swirling viscous flow , 2006 .

[28]  James P. Keener,et al.  Uniqueness of flow of a second-order fluid past a stretching sheet , 1987 .

[29]  Asif Ali,et al.  Homotopy analysis of unsteady boundary layer flow adjacent to permeable stretching surface in a porous medium , 2008 .

[30]  Ioan Pop,et al.  On the explicit analytic solution of Cheng-Chang equation , 2003 .

[31]  S. Liao.  A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate , 1999, Journal of Fluid Mechanics.

[32]  B. S. Dandapat,et al.  Flow of a power-law fluid film on an unsteady stretching surface , 1996 .

[33]  L. Crane.  Flow past a stretching plate , 1970 .

[34]  S. Liao.  On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet , 2003, Journal of Fluid Mechanics.

[35]  Buckling problems in finite plane elasticity-harmonic materials , 1984 .

[36]  Tariq Shah,et al.  Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method , 2008 .

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

[38]  P. D. Ariel,et al.  MHD flow of a viscoelastic fluid past a stretching sheet with suction , 1994 .

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

[40]  A. Mehmood,et al.  Unsteady boundary layer flow due to an impulsively started moving plate , 2007 .