Internal natural convective heat transfer from a thin walled, vertical cylinder with an exposed vertical surface is investigated numerically. The top and bottom end faces are assumed isothermal. This setup approximates the vertical wellbore of a christmas tree for simulating cool-down of subsea oil and gas equipment during shutdown operations. The primary objective of this study is to determine the cooling rate of the interior fluid and the onset of fluid rotation caused by the two non-adiabatic surfaces as a function of Biot (Bi) at the vertical cylindrical wall. The flow is assumed to be three-dimensional, non-steady, and transitional with constant fluid properties except for the density variation with temperature. This latter effect gives rise to the buoyancy forces; being treated by using the Boussinesq approach. The solution is obtained by numerically solving the governing equations; these equations were written in terms of dimensionless variables. The solution is obtained using a commercial finite element method based-code, COMSOL Multiphysics. The specific application that motivated this investigation involved a range of Prandtl numbers (Pr) from 0.7, to 168. The results for these cases are presented herein. In addition, a range of other governing parameters has been considered. From the numerical results for small and moderate values of Rayleigh number, it is observed that steady state solutions (i.e. temperature and velocity) are stratified at the source temperature region regardless of the Biot number.

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