Slip flow of an optically thin radiating non-Gray couple stress fluid past a stretching sheet

Document Type : Full Length Research Article

Authors

1 University of Gour Banga, Malda 732 103, WB, India

2 University of Gour Banga, Malda 732 103, India

3 Vidyasagar University, Midnapore 721 102, India

Abstract

This paper addresses the combined effects of couple stresses, thermal radiation, viscous dissipation and slip condition on a free convective flow of a couple stress fluid induced by a vertical stretching sheet. The Cogley- Vincenti-Gilles equilibrium model is employed to include the effects of thermal radiation in the study. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and solved numerically using the Runge-Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and rate of heat transfer. The effects of the pertinent parameters on these quantities are examined. It is found that both the fluid velocity and temperature reduce in the presence of thermal radiation. Increasing values of the couple stress parameter thicken the momentum boundary layer. The slip parameter greatly influences the fluid flow and shear stress on the surface of the stretching sheet.

Keywords

Main Subjects

References

[1].  Stokes, V. K. (1966). Couple stresses in fluid. The Physics of Fluids 9(9), 1709-1715 .
[2].  Stokes, V. K. (1984). Theories of Fluids with Microstructure: An Introduction, Springer Verlag, New York.
[3].  Fischer, E.G. (1976). Extrusion of plastics. Wiley, New York, 1976.
[4].  Sakiadis, B.C.(1961). Boundary layer behaviour on continuous solid surfaces: I boundary layer on a continuous flat surface. AICHE J. 7, 221–5.
[5].  Crane, L.(1970). Flow past a stretching plate. Z. Angew. Math. Phys. 21, 645-7.
[6].  Gupta, P.S., Gupta, A.S. (1977). Heat and mass transfer on a stretching sheet with suction or blowing. Canad. J. Chem. Engg. 55, 744-746.
[7].  Rajagopal, K.R., Na, T.Y., Gupta, A.S.(1984). Flow of viscoelastic fluid due to a stretching sheet. Rheol. Acta. 23, 213-215.
[8].  Siddappa, B., Abel, M. S.(1985). Non- Newtonian flow past a stretching surface, Z. Angew. Math. Phys. 36, 890-892.
[9].  Andersson, H.I.(1992). MHD flow of a viscoelastic fluid past a stretching surface. Acta Mech. 95, 227-230.
[10].    Kumaran, V., Ramanaiah, G.(1996) A note on the flow over a stretching sheet. Acta Mech. 116, 229- 233.
[11].    Wang, C.Y. (2002). Flow due to a stretching boundary with partial slip. An exact solution of the Navier–Stokes equations. Chem. Eng. Sci. 57, 3745–7.
[12].    Cortell, R. (2007). Viscous flow and heat transfer over a nonlinearly stretching sheet. Appl. Math. Comput. 184 (2), 864-873.
[13].    Ariel, P.D., Hayat, T., Asghar, S. (2006). The flow of an elastico-viscous fluid past a stretching sheet with slip. Acta Mech. 187, 29–36.
[14].    Akyildiz, F.T., Bellout, H., Vajravelu, K.(2006). Diffusion of chemically reactive species in a porous medium over a stretching sheet. J. Math. Anal, Appl. 320, 322–39.
[15].    Wang, C.Y.(2009). Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonlinear Anal Real World Appl. 10, 375–80.
[16].    Fang, T., Zhang, J., Yao, S. (2009). Slip MHD viscous flow over a stretching sheet- An exact solution. Comm. Nonlinear Num. Simu. 14, 3731-3737.
[17].    Fang, T., Zhang, J., Yao, S. (2010). Slip MHD viscous flow over a permeable shrinking sheet. Chinese Phys. Lett. 27, 124702.
[18].    Fang, T.G., Zhang, J.(2010). Thermal boundary layers over a shrinking sheet: an analytical solution. Acta Mech. 209, 325–43.
[19].    Arnold, J.C., Asir, A.A.,Somasundaram, S., Christopher, T. (2010). Heat transfer in a visco-elastic boundary layer flow over a stretching sheet. Int. J. Heat Mass Transfer 53, 1112–8.
[20].    Shantha, G., Shanker, B. (2010). Free convection flow of a conducting couple stress fluid in a porous medium. Int. J. Numer. Methods Heat Fluid Flow 20, 250-264.
[21].    Srinivasacharya, D., Kaladhar, K. (2012). Mixed convection flow of couple stress fluid in a non-darcy porous medium with Soret and Dufour effects. J. Appl. Sci. Eng 15, 415 -422.
[22].    Nandeppanavar, M.M., Vajravelu, K., Abel, M.S., Siddalingappa, M. N.(2012). Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition. Int. J. Therm. Sci. 58, 143–50.
[23].    Singh, G., Makinde, O.D. (2013). MHD slip flow of viscous fluid over an isothermal reactive stretching sheet. ANNALS of Faculty Engineering Hunedoara – Int. J. Engn. Tome XI, 41-46.
[24].    Hayat, T., Mustafa, M., Iqbal, Z., Alsaedi, A. (2013). Stagnation-point flow of couple stress fluid with melting heat transfer. Appl. Math. Mech.-Eng. Ed 34, 167-176.
[25].    Turkyilmazoglu, M. (2014). Exact solutions for two-dimensional laminar flow over a continuously stretching or shrinking sheet in an electrically conducting quiescent couple stress fluid. Int.J. Heat Mass Transfer 72, 1-8.
[26].    Siddheshwar, P.G., Sekhar, G.N., A. S. Chethan, A.S. (2014). MHD Flow and heat transfer of an exponential stretching sheet in a Boussinesq-Stokes suspension. J. Appl. Fluid Mech. 7(1), 169-176.
[27].    Salem, A. M., Ismail, G. Fathy, R. (2014). Hydromagnetic flow of Cu- water nanofluid past a moving wedge with viscous dissipation. Chin. Phys. B 23(4), 044402.
[28].    Zhu, J., Zheng, L., Zheng, L., Zhang, X. (2015). Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction. Appl. Math. Mech. - Engl. Ed., 36(9), 1131-1146.
[29].    Sheikholeslami, M., Rashidi, M.M. , Ganji, D.D. (2015). Numerical investigation of magnetic nanofluid forced convective heat transfer in existence of variable magnetic field using two phase model. J. Molecular Liquids 212, 117-126.
[30].    Sheikholeslami, M., Rashidi, M.M., Ganji, D.D. (2015). Effect of non-uniform magnetic field on forced convection heat transfer of Fe3O4- water nanofluid. Comput. Methods Appl. Mech. Engrg. 294, 299-312
[31].    Kandelousi, M. S. (2014). Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition. The European Phys. J. Plus, 129- 248.
[32].    Sheikholeslami, M., Ganji, D.D.(2015). Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM. Comput. Methods Appl. Mech. Eng. 283, 651-663.
[33].    Sheikholeslamia, M., Ganji, D. D., Javed, M. Y., Ellahi, R. (2015). Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model. J. Magnetism and Magnetic Materials 374, 36-43.
[34].    Sheikholeslami, M., Vajravelu, K., Rashidi, M. M. (2016). Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field. Int. J. Heat and Mass Transfer 92, 339-348
[35].    A.C. Cogley, W.C. Vincentine, S.E. Gilles, A differential approximation for radiative transfer in a non-gray gas near equilibrium, AIAA Journal 6 (1968) 551-555.
[36].    R. Grief, I. S. Habib, J. C. Lin, Laminar convection of a radiating gas in a vertical channel, J. Fluid Mech. 46 (1970) 513-520.
[37].    T. Y. Na, Computational Method in Engineering Boundary Value Problems. Academic Press, New York, 197

Files

History

  • Receive Date: 01 January 2016
  • Revise Date: 03 April 2016
  • Accept Date: 22 May 2016

Share

How to cite

Statistics