Natural Convection Boundary Layer Flow of a Viscoelastic Fluid on Solid Sphere with Newtonian Heating

Authors: A.R.M. Kasim, N.F. Mohammad, Aurangzaib, S. Sharidan

Abstract:

The present paper considers the steady free convection boundary layer flow of a viscoelastic fluid on solid sphere with Newtonian heating. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. Thus, the augmentation an extra boundary condition is needed to perform the numerical computational. The governing boundary layer equations are first transformed into non-dimensional form by using special dimensionless group and then solved by using an implicit finite difference scheme. The results are displayed graphically to illustrate the influence of viscoelastic K and Prandtl Number Pr parameters on skin friction, heat transfer, velocity profiles and temperature profiles. Present results are compared with the published papers and are found to concur very well.

Keywords: boundary layer flow, Newtonian heating, sphere, viscoelastic fluid.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328964

References:

[1] L. Tham, R. Nazar, and I. Pop, "Mixed convection boundary-layer flow about an isothermal solid sphere in a nanofluid," Phys. Scr., vol. 84, 2011.
[2] T. Chiang, A. Ossin, and C. L. Tien, "Laminar free convection from a sphere," J. Heat Trans., vol. 86C, pp. 537-542, 1964.
[3] M. J. Huang, and C. L. Chen, "Laminar free convection from a sphere with blowing and suction," J. Heat Transf., vol. 109, pp. 529- 532 ,1987.
[4] R. Nazar, N. Amin, T. Grosan, and I. Pop, "Free convection boundary layer on an isothermal sphere in a micropolar fluids," Int. Commun. Heat Mass Transf., vol. 29, no. 3, pp.377-386, 2002.
[5] R. Nazar, N. Amin, T. Grosan, and I. Pop, "Free convection boundary layer on an isothermal sphere with constant surface heat flux in a micropolar fluids," Int. Commun. Heat Mass Transf., vol. 29, no. 8, pp. 1129-1138, 2002.
[6] M. M. Molla, and M. A. Hossain, "Effects of chemical reaction, heat and mass diffusion in natural convection flow from and isothermal sphere with temperature dependent viscosity," Int. J. Comput.-Aided Eng. Softw., vol. 23, pp. 840-857, 2006.
[7] C. Y. Cheng, "Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration," Int. Commun. Heat Mass Transf., vol. 35, pp. 750-755, 2008.
[8] J. H. Merkin, "Natural Convection Boundary-layer Flow on a Vertical Surface with Newtonian Heating," Int. J. Heat Fluid Flow, vol. 15, pp. 392-398, 1994.
[9] M. Z. Salleh, R. Nazar, and I. Pop, "Mixed convection boundary layer flow about a solid sphere with Newtonian heating," Arch. Mech., vol. 62, pp. 283-303, 2010.
[10] M. Z. Salleh, R. Nazar, and I. Pop, "Modeling of free convection boundary layer flow on a sphere with Newtonian heating," Acta Appl. Math., vol. 112, pp. 263-274, 2010.
[11] J. H. Merkin, R. Nazar, and I. Pop, "The development of forced convection heat transfer near a forward stagnation point with Newtonian heating," J. Eng.Math., 2011.
[12] R. H. Thomas, and K. Walters, "The unsteady motion of a sphere in a elastico-viscous liquid," Adv. Tech., 1965.
[13] R. L. Verma, "Elastico-viscous boundary-layer flow on the surface of sphere," Dr. Dietrich Steinkopff Verlag Darmstadt., vol. 16, pp. 510- 515, 1977.
[14] E. O. A. Carew and P. Townsend, "Non-Newtonian flow past a sphere in a long cylindrical tube," Rheol. Acta, vol. 27, pp. 125-129, 1988.
[15] T. B. Chang, A. Mehmood, O. Anwar Bég, M. Narahari, M. N. Islam, and F. Ameen, " Numerical study of transient free convective mass transfer in a Walters-B viscoelastic flow with wall suction," Commun. Nonlinear Sci. Numer. Simulat., vol. 16, pp. 216-225, 2011.
[16] A. R. M. Kasim, M. A. Admon, and S.Sharidan, "Free convection boundary layer flow of a viscoelastic fluid in the presence of heat generation," World Academy of Sci. Eng. Tech., vol. 75, pp. 492-499, 2011.
[17] T. Y. Na, Computational Methods in Engineering Boundary Value Problem. New York: Academic Press, 1979.
[18] T. Cebeci, and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer. New York: Springer, 1988.