Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method

Abstract This paper aims to present complete analytic solution to the unsteady heat transfer flow of an incompressible viscous fluid over a permeable plane wall. The flow is started due to an impulsively stretching porous plate. Homotopy analysis method (HAM) has been used to get accurate and complete analytic solution. The solution is uniformly valid for all time τ  ∈ [0, ∞) throughout the spatial domain η  ∈ [0, ∞). The accuracy of the present results is shown by giving a comparison between the present results and the results already present in the literature. This comparison proves the validity and accuracy of our present results. Finally, the effects of different parameters on temperature distribution are discussed through graphs.

[1]  K. Stewartson ON THE IMPULSIVE MOTION OF A FLAT PLATE IN A VISCOUS FLUID , 1951 .

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

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

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

[5]  C. Watkins Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate , 1975 .

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

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

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

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

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

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

[12]  S. Liao An analytic approximation of the drag coefficient for the viscous flow past a sphere , 2002 .

[13]  Shijun Liao,et al.  An analytic approach to solve multiple solutions of a strongly nonlinear problem , 2005, Appl. Math. Comput..

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

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

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

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

[18]  P. Hilton An Introduction to Homotopy Theory , 1953 .

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

[20]  Siddhartha Sen,et al.  Topology and geometry for physicists , 1983 .

[21]  Qiang Sun,et al.  Solving the Klein-Gordon equation by means of the homotopy analysis method , 2005, Appl. Math. Comput..

[22]  J. Williams,et al.  Boundary layer development on a wedge impulsively set into motion , 1980 .

[23]  K. Stewartson ON THE IMPULSIVE MOTION OF A FLAT PLATE IN A VISCOUS FLUID. II , 1973 .

[24]  H. Xu,et al.  An explicit analytic solution for free convection about a vertical flat plate embedded in a porous medium by means of homotopy analysis method , 2004, Appl. Math. Comput..

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

[26]  Qiang Du,et al.  Impulsive Stretching of a Surface in a Viscous Fluid , 1997, SIAM J. Appl. Math..

[27]  K. Vajravelu,et al.  Heat transfer in a second-order fluid over a continuous stretching surface , 1991 .

[28]  Louis Rosenhead,et al.  Boundary layer growth , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[29]  S. Dennis The Motion of a Viscous Fluid Past an Impulsively Started Semi-infinite Flat Plate , 1972 .

[30]  Ioan Pop,et al.  Unsteady flow past a stretching sheet , 1996 .

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

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

[33]  R. J. Goldstein,et al.  Flow and heat transfer in the boundary layer on a continuous moving surface , 1967 .

[34]  M. Hall The boundary layer over an impulsively started flat plate , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[35]  J. Means,et al.  Transient Convective Heat Transfer During and After Gas Injection Into Containers , 1975 .

[36]  Chun Wang,et al.  Solving the nonlinear periodic wave problems with the Homotopy Analysis Method , 2005 .

[37]  G. Nath,et al.  Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion , 2002 .

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

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

[40]  I. Pop,et al.  Unsteady boundary layer flow due to a stretching surface in a rotating fluid , 2004 .

[41]  B. K. Dutta Heat transfer from a stretching sheet with uniform suction and blowing , 1989 .