Transient multi-dimensional natural convection heat transfer from horizontal circular cylinders

Abstract

The transient natural convection from a horizontal circular cylinder located in an unbounded fluid medium of confined by an outer cylinder was investigated both numerically and experimentally for a step change of surface boundary condition. Two-dimensional model was adopted for the external flow case and to solve the stream-function vorticity from of the NavierStokes and energy equations, the Euler explicit finite difference scheme was used for the transport equation and a noniterative direct elliptic solver for the Poisson equation. An overshoot in the heat transfer as well as in the thermal layer thickness was calculated associated with the conductionconvection transition whose magnitude was influenced by the Pr and Ra numbers, The onset time of convection was nearly proportional to $Ra^{-1/2}$ in the range $10^3\leqRa\leq10^6$ for Pr=0.7 or 7.0. In order to validate the numerical result, an experiment was also conducted from which Schlieren pictures were obtained. They showed good qualitative agreements for the different stages of the plume development. In an enclosure made by horizontal concentric cylinders, the unsteady three-dimensional natural convection was explored numerically. For the purpose the algorithm by Soh and Goodrich was extended to three-dimensional time-space domain and to higher dimensional vector space of dependent variables including the thermal energy term. In this algorithm the governing equations were approximated by Crank-Nicolson scheme and the pseudo-time and the artificial compressibility were introduced to a continuous auxiliary system which was solved until a convergence is achieved between the real time steps. for a fixed Prandtl number 0.7, two cases were solved with the present algorithm. Whether the ultimate mode is a steady stable flow or not depends upon the diameter ratio and the Grash of number. Comparison with the two-dimensional counterpart and the previous studies showed good agreements one another for stable flow mod...