Natural Convection Boundary Layer Flow Past a Sphere with Constant Heat Flux in Viscoelastic Fluid
DOI:
https://doi.org/10.11113/jt.v62.1885Keywords:
Natural convection, boundary layer flow, viscoelastic fluid, sphere, constant heat fluxAbstract
The steady natural convection boundary layer flow of a viscoelastic fluid over a solid sphere with constant heat flux is studied in this paper. The boundary layer equations of viscoelastic fluid are an order higher than those for the Newtonian (viscous) fluid. 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 variables and then solved by using an implicit finite difference scheme known as Keller box method. Numerical results for the velocity and temperature profiles, wall temperature, as well as skin friction are shown graphically for different values of viscoelastic parameters and Prandtl number. It is found that, when the viscoelastic parameter increased, the values of skin friction decreased while the values of wall temperature are increased.References
Tham, L., Nazar, R. and Pop, I. 2011. Mixed Convection Boundary-layer Flow About an Isothermal Solid Sphere in a Nanofluid. Phys. Scr. 84: 025403.
Prhashanna, A. and Chhabra, R. P. 2010. Free Convection in Power-law Fluids from a Heated Sphere. Chemical Engineering Science. 65: 6190–6205.
Chiang, T., Ossin, A., and Tien, C. L. 1964. Laminar Free Convection from a Sphere. J. Heat Transf. 86C: 537–542.
Huang, M. J., and Chen, C. K. 1987. Laminar Free Convection from a Sphere with Blowing and Suction. J. Heat Transf. 109: 529–532.
Nazar, R., Amin, N., Grosan, T., and Pop, I. 2002. Free Convection Boundary Layer on an Isothermal Sphere in a Micropolar Fluids. Int. Commun. Heat Mass Transf. 29(3): 377–386.
Nazar, R., Amin, N., Grosan, T., and Pop, I. 2002. Free Convection Boundary Layer on an Isothermal Sphere with Constant Surface Heat Flux in a Micropolar Fluids. Int. Commun. Heat Mass Transf. 29(8): 1129–1138.
Thomas, R. H., and Walters, K. 1965. The Unsteady Motion of a Sphere in a Elastico-viscous Liquid. Adv. Tech.
Verma, R. L. 1977. Elastico-viscous Boundary-layer Flow on the Surface of Sphere. Dr. Dietrich Steinkopff Verlag, Darmstadt. 16. 510–515.
Carew, E. O. A. and Townsend, P. 1988. Non-newtonian Flow Past a Sphere in a Long Cylindrical Tube. Rheol. Acta. 27: 125–129.
Chang, T. B., Mehmood, A., and Anwar Bég, O. Narahari, M., Islam, M. N., Ameen, F. 2011. Numerical Study of Transient Free Convective Mass Transfer in a Walters-B Viscoelastic Flow with Wall Suction. Commun Nonlinear Sci Numer Simulat. 16: 216–22.
Kasim, A. R. M., Mohammad, N. F., and Shafie. S. 2012. Effect of Heat Generation on Free Convection Boundary Layer Flow of a Viscoe-lastic Fluid Past a Horizontal Circular Cylinder with Constant Surface Heat Flux. AIP Conf. Proc. 1450: 286.
Kasim, A. R. M. and Shafie. S. 2010. Mixed Convection Boundary Layer of a Viscoelastic Fluid Past a Circular Cylinder with Constant Heat Flux. Proceeding on Regional Conference on Applied and Engi-neering Mathematics. 1(20): 124–129.
Kasim, A. R. M., Muhammad N. F., Anwar, I. and Shafie, S. 2013. MHD Effect on Convective Boundary Layer Flow of a Viscoelastic Flu-id Embedded in Porous Medium with Newtonian Heating. Recent Ad-vances In Mathematics.182–189.
Na, T. Y. 1979. Computational Methods in Engineering Boundary Value Problem. New York: Academic Press.
Cebeci, T., Bradshaw, P. 1988. Physical and Computational Aspects of Convective Heat Transfer. New York: Springer.
Salleh, M. Z., Nazar, R., and Pop, I. 2010. Modeling of Free Convec-tion Boundary Layer Flow on a Sphere with Newtonian Heating. Acta Appl. Math. 112: 263–274.
Rajagopal, K. R, Na, T.Y. and Gupta, A. S. 1984. Flow of a Visco-Elastic Fluid Over a Stretching Sheet. Rheol Acta. 23: 213–215.
Subhash, A. and Veena, P. H. 1988. Visco-elastic Fluid Flow And Heat Transfer In A Porous Medium Over A Stretching Sheet. Int. J. of Non-linear Mech. 33: 531–538.
Veena, P. H., Abel, S., Rajagopal, K., and Pravin,V. K. 2006. Heat Transfer in a Visco-elastic Fluid Past a Stretching Sheet with Viscous Dissipation and Internal Heat Generation. Z. angew. Math. 57: 447–463.
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