Stagnation-point flow and heat transfer over an exponentially shrinking sheet

Abstract An analysis is carried out to investigate the stagnation-point flow and heat transfer over an exponentially shrinking sheet. Using the boundary layer approximation and a similarity transformation in exponential form, the governing mathematical equations are transformed into coupled, nonlinear ordinary differential equations which are then solved numerically by a shooting method with fourth order Runge–Kutta integration scheme. The analysis reveals that a solution exists only when the velocity ratio parameter satisfies the inequality −1.487068 ⩽ c/a. Also, the numerical calculations exhibit the existence of dual solutions for the velocity and the temperature fields; and it is observed that their boundary layers are thinner for the first solution (in comparison with the second). Moreover, the heat transfer from the sheet increases with an increase in c/a for the first solution, while the heat transfer decreases with increasing c/a for the second solution, and ultimately heat absorption occurs.

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

[2]  T. Hayat,et al.  Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet , 2008 .

[3]  Eugen Magyari,et al.  Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface , 1999 .

[4]  Wei Liang,et al.  A new solution branch for the Blasius equation - A shrinking sheet problem , 2008, Comput. Math. Appl..

[5]  A. Gupta,et al.  Magnetohydrodynamic stagnation-point flow towards a stretching sheet , 2001 .

[6]  E. Elbashbeshy,et al.  Heat transfer over an exponentially stretching continuous surface with suction , 2001 .

[7]  K. Vajravelu,et al.  Viscous flow over a nonlinearly stretching sheet , 2001, Appl. Math. Comput..

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

[9]  Sujit Kumar Khan,et al.  Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet , 2005 .

[10]  I. Pop,et al.  STAGNATION-POINT FLOW OVER A SHRINKING SHEET IN A MICROPOLAR FLUID , 2010 .

[11]  Tasawar Hayat,et al.  On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet , 2007 .

[12]  G. Layek,et al.  Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet , 2011 .

[13]  Tiegang Fang,et al.  Closed-form exact solutions of MHD viscous flow over a shrinking sheet , 2009 .

[14]  C. Wang,et al.  Viscous flow due to a shrinking sheet , 2006 .

[15]  Abdul Aziz,et al.  Viscous flow over a shrinking sheet with a second order slip flow model , 2010 .

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

[17]  Ioan Pop,et al.  MHD stagnation-point flow towards a stretching sheet with prescribed surface heat flux , 2009 .

[18]  P. V. S. N. Murthy,et al.  Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface , 2005 .

[19]  Chaoyang Wang.  Liquid film on an unsteady stretching surface , 1990 .

[20]  G. Layek,et al.  Effects of suction/blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation , 2011 .

[21]  Sujit Kumar Khan,et al.  On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet , 2006 .

[22]  T. Hayat,et al.  Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface , 2008 .

[23]  I. Pop,et al.  Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet , 2006 .

[24]  T. C. Chiam.  Stagnation-Point Flow Towards a Stretching Plate. , 1994 .

[25]  Ioan Pop,et al.  Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet , 2004 .

[26]  R. Cortell.  Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet , 2008 .

[27]  Swati Mukhopadhyay,et al.  Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing , 2007 .

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

[29]  C. Wang,et al.  Stagnation flow towards a shrinking sheet , 2008 .

[30]  Rafael Cortell,et al.  On a certain boundary value problem arising in shrinking sheet flows , 2010, Appl. Math. Comput..

[31]  K. Vajravelu,et al.  Fluid flow over a nonlinearly stretching sheet , 2006, Appl. Math. Comput..

[32]  Sohail Nadeem,et al.  HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet , 2010 .

[33]  S. Yao,et al.  Slip Magnetohydrodynamic Viscous Flow over a Permeable Shrinking Sheet , 2010 .