Slip Effects on Mixed Convection Flow Along A Stretching Cylinder

Page:

19-24

DOI:

https://doi.org/10.18280/ijht.300203

OPEN ACCESS

Abstract:

An analysis for the axi-symmetric laminar boundary layer mixed convection flow of a viscous incompressible fluid towards a stretching cylinder is presented. Instead of no-slip boundary condition, velocity slip is assumed at the boundary. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and heat equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that for buoyancy aided flow, velocity increases with increasing mixed convection parameter whereas the temperature decreases in this case but opposite trend is noted in case of buoyancy opposed flow. Due to velocity slip, fluid velocity decreases initially but the temperature increases. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to those for a flat plate.

Keywords:

*boundary layer, mixed convection, stretching cylinder, heat transfer, velocity slip, similarity solution.*

1. Introduction

2. Equations of Motion

3. Numerical Method for Solution

4. Results and Discussion

5. Conclusions

References

[1] A. Yoshimura and R. K. Prudhomme, Wall slip corrections for Couette and parallel disc viscometers, J. Rheol., Vol. 32, pp.53-67, 1998.

[2] C. L. M. H. Navier, Sur les lois du mouvement des fluids, Men. Acad. R. Sci. Inst. Fr., Vol. 6, pp. 389-440, 1827.

[3] C. Y. Wang, Flow due to a stretching boundary with partial slip – an exact solution of the Navier-Stokes equations, Chem. Eng. Sci., Vol. 57, pp. 3745-3747, 2002.

[4] H. I. Andersson, Slip flow past a stretching surface, Acta Mech., Vol. 158, pp. 121-125, 2002.

[5] P. D. Ariel, T. Hayat and S. Asghar, The flow of an elastico-viscous fluid past a stretching sheet with partial slip, Acta Mech., Vol. 187, pp. 29-35, 2006.

[6] P. D. Ariel, Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip, Z. Angew. Math. Mech., Vol. 88, pp. 320-324, 2008.

[7] Z. Abbas, Y. Wang, T. Hayat and M. Oberlack, Slip effects and heat transfer analysis in a viscous fluid over an oscillatory stretching surface, Int. J. of Numer. Meth.Fluids, Vol. 59, pp. 443-458, 2009.

[8] S. Mukhopadhyay, Effects of slip on unsteady mixed convective flow and heat transfer past a porous stretching surface, Nucl. Eng. Des., 2011 doi:10.1016/j.nucengdes.2011.05.007.

[9] K. Bhattacharyya, S. Mukhopadhyay and G. C. Layek, MHD boundary layer slip flow and heat transfer over a flat plate, Chin. Phys. Lett., Vol. 28(2), 024701, 2011.

[10] K. Bhattacharyya, S. Mukhopadhyay and G.C. Layek, Slip Effects on unsteady boundary layer stagnation-point flow and heat transfer towards a stretching sheet, Chin. Phys. Lett., Vol. 28(9), 094702, 2011.

[11] L. J. Crane, Flow past a stretching plate, Z. Angew Math. Phys., Vol. 21, pp. 645-647, 1970.

[12] P.S. Gupta and A.S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng., Vol. 55, pp. 744-746, 1977.

[13] B. K. Datta, P. Roy and A. S. Gupta, Temperature field in the flow over a stretching sheet with uniform heat flux, Int. Comm. Heat Mass Transfer, Vol. 12, pp. 89-94, 1985.

[14] C. K. Chen and M. I. Char, Heat transfer of a continuous stretching surface with suction or blowing, J. Math Anal. Appl., Vol. 135, pp. 568-580, 1988.

[15] H. Xu and S. J. Liao, Series solutions of unsteady magnetohydrodynamics flows of non-Newtonian fluids caused by an impulsively stretching plate, J. Non-Newtonian Fluid Mech., Vol. 129, pp. 46-55, 2005.

[16] R. Cortell, Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing, Fluid Dyna. Res., Vol. 37, pp. 231-245, 2005.

[17] R. Cortell, Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet, Phys. Lett. A, Vol. 357, pp. 298-305, 2006.

[18] E. M. A. Elbashbeshy and M. A. Bazid, Heat transfer over a continuously moving plate embedded in a non-Darcian porous medium, Int. J. Heat Mass Transfer, Vol. 43, pp. 3087-3092, 2000.

[19] E. M. A. Elbashbeshy, Heat transfer over an exponentially stretching continuous surface with suction, Arch. Mech., Vol. 53, pp. 643- 651, 2001.

[20] E. M. A. Elbashbeshy and M. A. Bazid, The mixed convection along a vertical plate with variable surface heat flux embedded in porous medium, Appl. Math. Comp., Vol. 125, pp. 317-324, 2002.

[21] E. M. A. Elbashbeshy and M. A. Bazid, Heat transfer over a stretching surface with internal heat generation, Appl. Math. Comput., Vol. 138, pp.239-245, 2003.

[22] H. T. Lin, and Y. P. Shih, Laminar boundary layer heat transfer along static and moving cylinders, J. Chin. Inst. Eng., Vol. 3, pp. 73-79, 1980.

[23] H. T. Lin, and Y. P. Shih, Buoyancy effects on the laminar boundary layer heat transfer along vertically moving cylinders, J. Chin. Inst. Eng., Vol. 4, pp. 47-51, 1981.

[24] A. Ishak and R. Nazar, Laminar boundary layer flow along a stretching cylinder. Euro. J. of Sci. Resc., Vol. 36(1), pp. 22-29, 2009.

[25] L. G. Grubka and K. M. Bobba, Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J. Heat Transfer, Vol. 107, pp. 248-250, 1985.

[26] M. E. Ali, Heat transfer characteristics of a continuous stretching surface, Heat Mass Transfer, Vol. 29, pp. 227-234, 1994.

[27] A. Ishak, Mixed convection boundary layer flow over a vertical cylinder with prescribed surface heat flux, J. Phys. A Math. Theor., Vol. 42, 195501, 2009.

[28] S. Mukhopadhyay, Chemically reactive solute transfer in boundary layer slip flow along a stretching cylinder, Front. Chem. Sci. Eng., Vol. 5(3), pp. 385-391, 2011.