Numerical Solution of Free-Convection Heat Transfer over a Vertical Cone Embedded in a Non-Newtonian Power-Law Fluid-Saturated Porous Medium with Viscous Dissipation
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
A numerical study of the problem of heat transfer to the non-Newtonian power-law fluid over a vertical cone embedded in a porous medium has been investigated, taking into consideration the viscous dissipation effect. The governing equations describing the problem are transformed into a system of nonlinear ordinary differential equations, which is solved numerically using the Chebyshev spectral method. The effects of the power-law index and the viscous dissipation that is characterized by the local Gebhart number on the temperature profiles and the local Nusselt number are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author would like to thank the reviewers for their valuable comments.
References
Al-Hadhrami, A. K., Elliot, L., and Ingham, D. B. (2002). “Combined free and forced convection in vertical channels of porous media.” Transp. Porous Media, 49(3), 265–289.TPMEEI
Al-Hadhrami, A. K., Elliot, L., and Ingham, D. B. (2003). “A new model for viscous dissipation in porous media across a range of permeability values.” Transp. Porous Media, 53(1), 117–122.TPMEEI
Bejan, A. (1995). Convection Heat Transfer, Wiley, New York.
Chen, H. T., and Chen, C. K. (1987). “Natural-convection of non-Newtonian fluids about a horizontal surface in a porous medium.” J. Energy Resour. Technol., 109(3), 119–123.JERTD2
Chen, H. T., and Chen, C. K. (1988). “Free convection flow of non-Newtonian fluids along a vertical plate embedded in a porous medium.” Trans. ASME: J. Heat TransferJHTRAO, 110(1), 257–259.
Cheng, P., Le, T. T., and Pop, I. (1985). “Natural convection of a Darcian fluid about a cone.” Int. Commun. Heat Mass Transf.IHMTDL, 12(6), 705–717.
Christopher, R. H., and Middleman, S. (1965). “Power-law flow through a packed tube.” Ind. Eng. Chem. Fundam., 4(4), 422–426.IECFA7
Dharmadhikari, R. V., and Kale, D. D. (1985). “Flow of non-Newtonian fluids through porous media.” Chem. Eng. Sci., 40(3), 527–529.CESCAC
El-Gendi, S. E. (1969). “Chebyshev solution of differential, integral and integro-differential equations.” Comput J.CMPJA6, 12(3), 282–287.
Ene, H. I., and Sanchez-Palencia, E. (1982). “On thermal equation for flow in porous media.” Int. J. Eng. Sci., 20(5), 623–630.IJESAN
Groşan, T., Postenlnicu, A., and Pop, I. (2004). “Free convection boundary layer over a vertical cone in a non-newtonian fluid saturated porous medium with internal heat generation.” Technische Mechanik, 24(4), 91–104.
Ingham, D. B., Pop, I., and Cheng, P. (1990). “Combined free and forced convection in a porous medium between two vertical walls with viscous dissipation.” Transp. Porous Media, 5(4), 381–389.TPMEEI
Kumari, M., and Jayanathi, S. (2005). “Uniform lateral mass flux on natural-convection flow over a vertical cone embedded in a porous medium saturated with a non-newtonian fluid.” J. Porous Media, 8(1), 73–84.JPMEFB
Mehta, K. N., and Rao, K. N. (1994). “Buoyancy-induced flow of non-Newtonian fluids in a porous medium past a vertical flat plate with nonuniform surface heat flux.” Int. J. Eng. Sci., 32(2), 297–302.IJESAN
Nakayama, A. (1993). “A similarity solution for free convection from a point heat source embedded in a non-newtonian fluid-saturated porous medium.” Trans. ASME: J. Heat TransferJHTRAO, 115(2), 510–513.
Nakayama, A., and Koyama, H. (1991). “Buoyancy-induced flow of non-newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium.” Appl. Sci. Res., 48(1), 55–70.ASRHAU
Nakayama, A., and Pop, I. (1989). “Free convection over a nonisothermal body in a porous medium with viscous dissipation.” Int. Commun. Heat Mass Transf.IHMTDL, 16(2), 173–180.
Nield, D. A. (2000). “Resolution of a paradox involving viscous dissipation and nonlinear drag in a porous medium.” Transp. Porous Media, 41(3), 349–357.TPMEEI
Nield, D. A. (2002). “Modeling flow in saturated porous media at interfaces.” Transport phenomena in porous media II, Ingham, D. B. and Pop, I., eds., Elsevier Science, Oxford, UK.
Nield, D. A. (2007). “The modeling of viscous dissipation in a saturated porous medium.” J. Heat Transfer, 129(10), 1459–1463.JHTRAO
Nield, D. A., and Bejan, A. (2006). Convection in porous media, 3rd Ed., Springer, New York.
Nield, D. A., Kuznetsov, A. V., and Xiong, M. (2004). “Effects of viscous dissipation and flow work on forced convection in a channel filled by a saturated porous medium.” Transp. Porous Media, 56(3), 351–367.TPMEEI
Pascal, J. P., and Pascal, H. (1997). “Free convection in a non-Newtonian fluid saturated porous medium with lateral mass flux.” Int. J. Non-linear Mech., 32(3), 471–482.IJNMAG
Pop, I., and Ingham, D. B. (2001). Convection heat transfer, mathematical and computational viscous fluids and porous media, Pergamon, Oxford, UK.
Vafai, K. (2005). Handbook of porous media, 2nd Ed., Taylor & Francis, New York.
White, D. A. (1967). “Non-newtonian flow in porous media.” Chem. Eng. Sci., 22(4), 669–672.CESCAC
Yih, K. A. (1998). “Uniform lateral mass flux effect on natural convection of non-newtonian fluids over a cone in porous media.” Int. Commun. Heat Mass Transf.IHMTDL, 25(7), 959–968.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 6 • June 2012
Pages: 555 - 559
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Mar 2, 2010
Accepted: Dec 2, 2011
Published online: Dec 4, 2011
Published in print: Jun 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.