Chemically reactive solute transfer in a boundary layer slip flow along a stretching cylinder

Abstract

This paper presents the distribution of a solute undergoing a first order chemical reaction in an axisymmetric laminar boundary layer flow along a stretching cylinder. Velocity slip condition at the boundary is used instead of no-slip condition. Similarity transformations are used to convert the partial differential equations corresponding to momentum and concentration into highly nonlinear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. The velocity decreases with increasing slip parameter. The skin friction as well as the mass transfer rate at the surface is larger for a cylinder than for a flat plate.

Key words： boundary layer; stretching cylinder; partial slip; mass transfer; similarity solution

References

1 Chambré P L, Young J D. On diffusion of a chemically reactive species in a laminar boundary layer flow. Physics of Fluids, 1958, 1(1): 48–54

2 Andersson H I, Hansen O R, Holmedal B. Diffusion of a chemically reactive species from a stretching sheet. International Journal of Heat and Mass Transfer, 1994, 37(4): 659–664

3 Takhar H S, Chamkha A J, Nath G. Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species. International Journal of Engineering Science, 2000, 38(12): 1303–1314

4 Afify A A. MHD free convective flow and mass transfer over a stretching sheet with chemical reaction. Heat and Mass Transfer, 2004, 40(6-7): 495–500

5 Liu I C. A note on heat and mass transfer for a hydromagnetic flow over a stretching sheet. International Communications in Heat and Mass Transfer, 2005, 32(8): 1075–1084

6 Akyildiz F T, Bellout H, Vajravelu K. Diffusion of chemically reactive species in a porous medium over a stretching sheet. Journal of Mathematical Analysis and Applications, 2006, 320(1): 322–339

7 Cortell R. MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species. Chemical Engineering and Processing, 2007, 46(8): 721–728

8 Kandasamy R, Ismoen M, Saim H B. Lie group analysis for the effects of temperature-dependent fluid viscosity and chemical reaction on MHD free convective heat and mass transfer with variable stream conditions. Nuclear Engineering and Design, 2010, 240(1): 39–46

9 Lin H T, Shih Y P. Laminar boundary layer heat transfer along static and moving cylinders. European Journal of Scientific Research, 1980, 3(1): 73–79

10 Lin H T, Shi Y P. Buoyancy effects on the laminar boundary layer heat transfer along vertically moving cylinders. European Journal of Scientific Research, 1981, 4(1): 47–51

11 Ishak A, Nazar R. Laminar boundary layer flow along a stretching cylinder. European Journal of Scientific Research, 2009, 36(1): 22–29

12 Grubka L G, Bobba K M. Heat transfer characteristics of a continuous stretching surface with variable temperature. Journal of Heat Transfer, 1985, 107(1): 248–250

13 Ali M E. Heat transfer characteristics of a continuous stretching surface. Heat and Mass Transfer, 1994, 29(4): 227–234

14 Yoshimura A, Prudhomme R K. Wall slip corrections for Couette and parallel disc viscometers. Journal of Rheology (New York, N.Y.), 1988, 32(1): 53–67

15 Wang C Y. Flow due to a stretching boundary with partial slip—an exact solution of the Navier-Stokes equations. Chemical Engineering Science, 2002, 57(17): 3745–3747

16 Andersson H I. Slip flow past a stretching surface. Acta Mechanica, 2002, 158(1-2): 121–125

17 Ariel P D, Hayat T, Asghar S. The flow of an elastico-viscous fluid past a stretching sheet with partial slip. Acta Mechanica, 2006, 187(1-4): 29–35

18 Ariel P D. Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip. Zeitschrift für Angewandte Mathematik und Mechanik, 2008, 88(4): 320–324

19 Abbas Z, Wang Y, Hayat T, Oberlack M. Slip effects and heat transfer analysis in a viscous fluid over an oscillatory stretching surface. International Journal for Numerical Methods in Fluids, 2009, 59(4): 443–458

20 Crane L J. Flow past a stretching plate. Zeitschrift für Angewandte Mathematik und Physik, 1970, 21(4): 645–647