The effects of viscous dissipation with transient laminar free convection from a nonisothermal vertical cone at a wall surface temperature varying as a power function of the distance from the apex are considered. The fluid is assumed to be viscous and incompressible. The nondimensional governing equations of the flow are unsteady, coupled, and nonlinear partial differential equations, which are solved with the use of an efficient, accurate, and unconditionally stable finite difference scheme of the Crank–Nicolson type. The velocity and temperature profiles are obtained and analyzed to reveal the effect of viscous dissipation at various values of the Prandtl number and the exponent in the power law variation of the surface temperature. The local as well as average skin friction and Nusselt number are presented and analyzed. The present results are compared with available ones from the literature and are found to be in good agreement.
Similar content being viewed by others
References
B. Gebhart, Effects of viscous dissipation in natural convection, J. Fluid Mech., 14, 225–232 (1962).
H. J. Merk and J. A. Prins, Thermal convection laminar boundary layer — I, Appl. Sci. Res., 4, 11–24 (1953).
H. J. Merk and J. A. Prins, Thermal convection laminar boundary layer — II, Appl. Sci. Res., 4, 195–206 (1954).
W. H. Braun, S. Ostrach, and J. E. Heighway, Free convection similarity flows about two-dimensional and axisymmetric bodies with closed lower ends, Int. J. Heat Mass Transf., 2, 121–135 (1961).
R. G. Hering and R. J. Grosh, Laminar free convection from a non-isothermal cone, Int. J. Heat Mass Transf., 5, 1059–1068 (1962).
R. G. Hering, Laminar free convection from a non-isothermal cone at low Prandtl number, Int. J. Heat Mass Transf., 8, 1333–1337 (1965).
H. K. Kuiken, Axisymmetric free convection boundary layer flow past slender bodies, Int. J. Heat Mass Transf., 11, 1141–1153 (1968).
E. M. Sparrow, L. De Mello, and F. Guinle, Deviations from classical free convection boundary layer theory at low Prandtl numbers, Int. J. Heat Mass Transf., 11, 1403–1406 (1968).
S. Roy, Free convection from a vertical cone at high Prandtl numbers, Trans. ASME J. Heat Transf., 96, 115–117 (1974).
M. Alamgir, Overall heat transfer from vertical cones in laminar free convection: an approximate method, ASME J. Heat Transf., 101, 174–176 (1979).
T. Y. Na and J. P. Chiou, Laminar natural convection over a slender vertical frustum of a cone, Wärme Stoffubertragung, 12, 83–87 (1979).
T. Y. Na and J. P. Chiou, Laminar natural convection over a frustum of a cone, Appl. Sci. Res., 35, 409–421 (1979).
R. S. R. Gorla and A. Robert Startman, Natural convection boundary layer flow of water at 4°C past slender cones, Int. Commun. Heat Mass Transf., 13, 403–411 (1986).
H. S. Takhar and V. M. Soundalgekar, Combined convection past a vertical semi-infinite plate with viscous dissipation, Mech. Res. Commun., 14, Nos. 5/6, 307–315 (1987).
T. Watanabe, Free convection boundary layer flow with uniform suction or injection over a cone, Acta Mech., 87, 1–9 (1991).
I. Pop and H. S. Takhar, Compressibility effects in laminar free convection from a vertical cone, Appl. Sci. Res., 48, 71–82 (1991).
J. K. Vajravelu and J. Nayfeh, Hydromagnetic convection at a cone and wedge, Int. Commun. Heat Mass Transf., 19, 701–710 (1992).
I. Pop and T. Y. Na, Natural convection over vertical wavy frustum of a cone, Int. J. Nonlinear Mech., 34, 925–934 (1999).
M. A. Hossain and S. C. Paul, Free convection from a vertical permeable circular cone with non-uniform surface temperature, Acta Mech., 151, 103–114 (2001).
A. A. Afify, The effect of radiation on free convective flow and mass transfer past a vertical isothermal cone surface with chemical reaction in the presence of a transverse magnetic field, Can. J. Phys., 82, 447–458 (2004).
Md. M. Alam, M. A. Alim, and Md. K. Chowdhury, Free convection from a vertical permeable circular cone with pressure work and non-uniform surface temperature, Nonlinear Anal. Model. Control, 12, No. 1, 21–32 (2007).
C. Y. Cheng, Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature, Int. Commun. Heat Mass Transf., 38, 429–433 (2011).
Bapuji Pullepu, K. Ekambavanan, and A. J. Chamkha, Unsteady laminar natural convection flow past an isothermal vertical cone, Int. J. Heat Technol., 25, No. 2, 17–27 (2007).
Bapuji Pullepu, K. Ekambavanan, and I. Pop, Finite difference analysis of laminar free convection flow past a nonisothermal vertical cone, Heat Mass Transf., 44, No. 5, 517–526 ( 2007).
Bapuji Pullepu, K. Ekambavanan, and A. J. Chamkha, Laminar natural convection from a non-isothermal vertical cone, Nonlinear Anal. Model. Control, 13, No. 1, 47–60 (2007).
Bapuji Pullepu, A. J. Chamkha, and I. Pop, Unsteady laminar free convection flow past a non-isothermal vertical cone in the presence of a magnetic field, Chem. Eng. Commun., 199, No. 3, 354–367 (2012).
E. Thandapani, A. R. Ragavan, and G. Palani, Finite-difference solution of unsteady natural convection flow past a nonis 408–421 (2012).
I. Pop, T. Grosan, and M. Kumari, Mixed convection along a vertical cone for fluids of any Prandtl number: case of constant wall temperature, Int. J. Numer. Meth. Heat Fluid Flow, 13, No. 7, 815–829 (2003).
J. Zueco Jordan, Numerical study of an unsteady free convective magnetohydrodynamic flow of a dissipative fluid along a vertical plate subject to a constant heat flux, Int. J. Eng. Sci., 44, 1380–1393 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 87, No. 4, pp. 929–938, July–August, 2014.
Rights and permissions
About this article
Cite this article
Pullepu, B., Sambath, P. Free Convection Flow of Dissipative Fluid from Nonisothermal Vertical Cone. J Eng Phys Thermophy 87, 962–972 (2014). https://doi.org/10.1007/s10891-014-1094-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-014-1094-1