Mixed Convection Flow of Viscoelastic Fluid over a Sphere under Convective Boundary Condition Embedded in Porous Medium

Abstract:

The investigation on mixed convection boundary layer of a viscoelastic fluid over a sphere which is embedded in porous medium under convective boundary condition is carried out in this paper. The boundary layer equations of viscoelastic fluid are an order higher than Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. Hence, the augmentation on extra boundary conditions is needed in order to solve this problem. The governing partial differential equations are first transformed into non-dimensional forms and then solved numerically using the Keller-box method by augmenting extra boundary conditions at infinity. The numerical results obtained for limiting case are comparing with related outcomes in order to validate the present results. Results on the effects of the viscoelastic parameter in the presence of porosity and mixed convection on the skin friction and heat transfer as well as velocity and temperature profile have been discussed.

• Periodical: Defect and Diffusion Forum (Volume 362)
• Pages: 67-75
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.362.67
• Online since: April 2015
• Authors: Abdul Rahman Mohd Kasim*, Lim Yeou Jiann, N.A. Rawi, A. Ali, Sharidan Shafie
• Keywords: Boundary Layer Flow, Mixed Convection, Numerical Method, Sphere, Viscoelastic Fluids

References

[1] R.H. Thomas, K. Walters, Rheologica Acta, Vol. 5, No. 1, pp.23-27, (1966).

[2] R.L. Verma, Rhelogica Acta, Vol. 16, No. 5, pp.510-515, (1977).

[3] R. Cortell, International Journal of Non-Linear Mechanics, Vol. 43, No. 8, pp.772-778, (2008).

[4] M. Z. Salleh, R. Nazar, I. Pop, Arch. Mech. 62, 4, 283-303, (2010).

[5] A. R. M. Kasim, M. A. Admon, and S. Sharidan, World Academy of Science, Engineering and Technology, Vol. 51, pp.492-499, (2011).

[6] P.D. Ariel, International Journal for Numerical Methods in Fluids, Vol. 14, No. 7, pp.757-774, (1992).

[7] P.D. Ariel, International Journal of Engineering Science, Vol. 33, No. 11, pp.1679-1687, (1995).

[8] A.R.M. Kasim, N.F. Mohammad, and S. Shafie, AIP Conference Proceedings, Vol. 1450, pp.286-292, (2012).

[9] A.R.M. Kasim, and S. Shafie, Proceedings of the 1st Regional Conference on Applied and Engineering Mathematics, Vol. 1, No. 20, pp.124-129, (2010).

[10] X. L. Luo, Journal of Non-Newtonian Fluid Mechanics, Vol. 63, No. 2-3, pp.121-140, (1996).

[11] R.G. Owens, and T.N. Phillips, International Journal for Numerical Methods in Engineering, Vol. 39, No. 9, pp.1517-1534, (1996).

[12] P.D. Ariel, International Journal of Engineering Science, Vol. 39, No. 5, pp.529-533, (2001).

[13] P.D. Ariel, International Journal of Engineering Science, Vol. 40, No. 2, pp.145-162, (2002).

[14] C. Kurtcebe, and M. Z. Erim, International Journal of Heat and Mass Transfer, Vol. 48, No. 23-24, pp.5072-5077, (2005).

DOI: 10.1016/j.ijheatmasstransfer.2005.05.028

[15] J.A. Shercliff, A Textbook of Magnetohydrodynamics, Pergamon Press, (1965).

[16] S. Abel, K.V. Prasad, and A. Mahaboob, International Journal of Thermal Sciences, Vol. 44, No. 5, pp.465-476, (2005).

[17] R. Cortell, Physics Letters A, Vol. 357, No. 4-5, pp.298-305, (2006).

[18] A.M. Salem, Physics Letters A, Vol. 369, No. 4, pp.315-322, (2007).

[19] M.M. Nandeppanavar, M.S. Abel, and K. Vajravelu, International Journal of Heat and Mass Transfer, Vol. 53, No. 21-22, pp.4707-4713, (2010).

DOI: 10.1016/j.ijheatmasstransfer.2010.06.021

[20] T. Cebeci, and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer, (1984).

[21] M. Z. Salleh, R. Nazar, and I. Pop, Archives of Mechanics, Vol. 62, No. 4, pp.283-303, (2010).