Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder

Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Authors:

• T. V. S. Sekhar
• B. Hema Sundar Raju

Keywords:

• Higher order compact scheme
• Navier-Stokes equations
• Energy equation
• Natural convection
• Boussinesq's approximation and Mean Nusselt number.

References:

[1] T. Fujii, M. Fujii and T. Honda, "Theoretical and experimental study on
free convection around horizontal wire," J Soc Mech Engrs, vol. 48,
pp. 1312-20, 1982.
[2] M .M. Gupta, "High accuracy solutions of incompressible Navier-Stokes
equations," J. Comput. Phys, vol. 93, pp. 343-59, 1991.
[3] M. Li, T .Tang and B. Fornberg, "A compact fourth-order finite
difference scheme for the steady incompressible Navier-Stokes
equations," Int J Num Meth Fluids, vol. 20, pp. 1137-51, 1995.
[4] W. F. Spotz, and G. F. Carey, "Higher order compact scheme for the
steady stream-function vorticity equations," Int J Num Meth Engg, vol.
38, pp. 3497-3512, 1995.
[5] A. Dipankar, and K. Sengupta, "Flow past a circular cylinder in the
vicinity of a plane wall," J Fluids and Structures, vol. 20, pp. 403-23,
2005.
[6] S. R. K. Iyengar, and R. P. Manohar, "High order difference methods for
heat equation in polar cylindrical coordinates," J Comput Phys, vol. 72,
pp. 425-38, 1988.
[7] M. K. Jain, R. K. Jain, and M. Krishna, "A fourth-order difference
scheme for quasilinear Poisson equation in polar coordinates," Commun
Num Meth Engg, vol. 10, pp. 791-97, 1994.
[8] M. C. Lai, "A simple compact fourth-order Poisson solver on polar
geometry," J Comp Phys, vol. 182, pp. 337-45, 2002.
[9] T. Saitoh, T. Sajiki, and K. Maruhara, "Bench mark solutions to natural
convection heat transfer problem around a horizontal cicular cylinder,"
Int j Heat and Mass Transfer, vol. 36, pp. 1251-1259, 1993.
[10] W. R. Briley, "A numerical study of laminar seperation bubbles using
Navier-stokes equations," J Fluid Mech, vol. 47, pp. 713-36, 1971.
[11] F. Geoola, and A. R. H. Cornish, " Numerical solution of steady-state
free convective heat transfer from a solid sphere," Int J Heat Mass
Transfer, vol. 24, pp. 1369-79, 1981.