On the Exact Solution for Axisymmetric Flow and Heat Transfer over a Nonlinear Radially Stretching Sheet

We investigate the boundary-layer flow and heat transfer of a magnetohydrodynamic viscous fluid over a nonlinear radially porous stretching sheet within a porous medium. The flow is generated due to a nonlinear stretching sheet and influenced by a continuous suction/blowing of the fluid through the porous sheet. The governing momentum and thermal boundary layer equations are converted into ordinary differential equations by appropriate similarity transformations. The exact solution for the velocity and the temperature fields are derived in the form of an incomplete Gamma function. Also analytic solutions are found by the homotopy analysis method. The graphical results for velocity and temperature fields are presented and discussed. Further, the numerical values of the skin friction coefficient and the Nusselt number are calculated and discussed.

[1]  U. T. Bödewadt.  Die Drehströmung über festem Grunde , 1940 .

[2]  P. Donald Ariel,et al.  Axisymmetric flow due to a stretching sheet with partial slip , 2007, Comput. Math. Appl..

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

[4]  E. Magyari,et al.  Heat transfer characteristics of boundary-layer flows induced by continuous surfaces stretched with prescribed skin friction , 2006 .

[5]  Bikash Sahoo,et al.  Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet , 2010 .

[6]  Tiegang Fang.  Flow and heat transfer characteristics of the boundary layers over a stretching surface with a uniform-shear free stream , 2008 .

[7]  Z. Ji,et al.  Viscous Flow over an Unsteady Shrinking Sheet with Mass Transfer , 2009 .

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

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

[10]  Rafael Cortell Bataller,et al.  Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface , 2008 .

[11]  T. Hayat,et al.  Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet , 2007 .

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

[13]  T. Kármán.  Über laminare und turbulente Reibung , 1921 .

[14]  Kambiz Vafai,et al.  The role of porous media in modeling flow and heat transfer in biological tissues , 2003 .

[15]  S Nadeem,et al.  MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method , 2009 .

[16]  Ajay Singh.  Heat source and radiation effects on magneto-convection flow of a viscoelastic fluid past a stretching sheet: Analysis with Kummer's functions , 2008 .