Numerical solution to the flow of a second grade fluid over a stretching sheet using the method of quasi-linearization

In this short work we look at the flow of a second grade fluid due to a stretching sheet coinciding with the plane y=0. Two equal and opposite forces are applied along the x-axis (horizontal plane) in such a way that the origin remains fixed and the velocity of stretching is proportional to the distance from the origin. This problem was studied by Rajagopal et al. [Rheol. Acta 23 (1984) 213; Meccanica 19 (1984) 158] where a perturbation scheme was used to obtain the solution. Using the same similarity transformation given by Rajagopal et al., we solve the full equation numerically, using the method of quasi-linearization of Bellman and Kalaba [Quasilinearization and Non-Linear Boundary Value Problems, American Elsevier, New York, 1965]. Results will be given for the velocity distribution and the shear stress at the wall.

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

[2]  V. G. Fox,et al.  Heat and Mass Transfer on Moving Continuous Flat Plate with Suction or Injection , 1966 .

[3]  Vijay K. Garg,et al.  Flow of a non-Newtonian fluid past a wedge , 1991 .

[4]  Vijay K. Garg,et al.  Stagnation point flow of a non-Newtonian fluid , 1990 .

[5]  J. E. Dunn,et al.  Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade , 1974 .

[6]  I. A. Hassanien,et al.  Flow and heat transfer in a power-law fluid over a nonisothermal stretching sheet , 1998 .

[7]  L. T. Fan,et al.  The laminar boundary layer on a moving continuous flat sheet immersed in a non‐Newtonian fluid , 1969 .

[8]  Kumbakonam R. Rajagopal,et al.  Flow of a viscoelastic fluid over a stretching sheet , 1984 .

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

[10]  M. Ramezan,et al.  Effect of injection or suction on the Falkner-Skan flows of second grade fluids , 1989 .

[11]  I. Grant.  Quasilinearization and Non-Linear Boundary Value Problems , 1968, The Mathematical Gazette.

[12]  Kumbakonam R. Rajagopal,et al.  Flow of an Oldroyd-B fluid due to a stretching sheet in the presence of a free stream velocity , 1995 .

[13]  K. Walters,et al.  THE MOTION OF AN ELASTICO-VISCOUS LIQUID CONTAINED BETWEEN COAXIAL CYLINDERS (II) , 1960 .

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

[15]  D. W. Beard,et al.  Elastico-viscous boundary-layer flows I. Two-dimensional flow near a stagnation point , 1964, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  K. Rajagopal,et al.  An exact solution for the flow of a non-newtonian fluid past an infinite porous plate , 1984 .

[17]  D. Whiffen.  Thermodynamics , 1973, Nature.

[18]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[19]  P. D. McCormack,et al.  Physical Fluid Dynamics , 1973 .

[20]  B. Rao.  Flow of a fluid of second grade over a stretching sheet , 1996 .

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

[22]  Hari M. Srivastava,et al.  Some boundary-layer growth problems associated with a flat plate with suction or injection , 2001, Appl. Math. Comput..

[23]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[24]  V. Garg.  Improved shooting techniques for linear boundary value problems , 1980 .

[25]  M. S. Abel,et al.  Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer , 1986 .

[26]  P. Ariel.  Axisymmetric flow of a second grade fluid past a stretching sheet , 2001 .

[27]  M. Pakdemirli,et al.  Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet , 1999 .

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

[29]  T. Roper,et al.  Flow and heat transfer in a second grade fluid over a stretching sheet , 1999 .