Differential quadrature method for steady flow of an incompressible second-order viscoelastic fluid and heat transfer model

The two-dimensional steady flow of an incompressible second-order viscoelastic fluid between two parallel plates was studied in terms of vorticity, the stream function and temperature equations. The governing equations were expanded with respect to a small parameter to get the zeroth- and first-order approximate equations. By using the differential quadrature method with only a few grid points, the high-accurate numerical results were obtained.

[1]  S. Barış Steady Three-Dimensional Flow of a Second Grade Fluid towards a Stagnation Point at a Moving Flat Plate , 2002 .

[2]  C. Tiu,et al.  Entry flow behaviour of viscoelastic fluids in an annulus , 1977 .

[3]  W. Schultz,et al.  NON-ISOTHERMAL FLOWS OF NEWTONIAN SLENDER GLASS FIBERS , 1998 .

[4]  Unsteady convective diffusion in viscoelastic fluid flowing through a tube , 1998 .

[5]  C. Bert,et al.  A NEW APPROACH TO THE DIFFERENTIAL QUADRATURE METHOD FOR FOURTH‐ORDER EQUATIONS , 1997 .

[6]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATION , 1971 .

[7]  Hejun Du,et al.  Numerical study of grid distribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximation , 2001 .

[8]  P. Malekzadeh,et al.  DQM analysis of skewed and trapezoidal laminated plates , 2003 .

[9]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE: A TECHNIQUE FOR THE RAPID SOLUTION OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS , 1972 .

[10]  Application of differential quadrature method to simulate natural convection in a concentric annulus , 1999 .

[11]  Zhu Zheng-you,et al.  Application of differential quadrature method to solve entry flow of viscoelastic second‐order fluid , 1999 .

[12]  T. W. Patten,et al.  Collocation and galerkin finite element methods for viscoelastic fluid flow—I.: Description of method and problems with fixed geometry , 1979 .

[13]  C. Shu Differential Quadrature and Its Application in Engineering , 2000 .

[14]  C. Shu,et al.  Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method , 2001 .

[15]  Charles W. Bert,et al.  The differential quadrature method for irregular domains and application to plate vibration , 1996 .