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

Authors: T. V. S. Sekhar, B. Hema Sundar Raju

Abstract:

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.

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081852

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.