MIXED CONVECTION ADJACENT TO A SUDDENLY HEATED HORIZONTAL CIRCULAR-CYLINDER EMBEDDED IN A POROUS-MEDIUM

The mixed convection caused when a horizontal circular cylinder is sud denly heated is investigated in the situation when the initial flow pa st the cylinder is uniform and its direction either upwards or downwar ds. An analytical series solution, which is valid at small times, is o btained using the matched asymptotic expansions technique. A numerical solution, which is valid at all times and for any values of the Rayle igh and Peclet numbers, is also obtained using a fully implicit finite -difference method. Three different regimes, when either the free or f orced convection is dominant or when they have the same order of magni tude, are considered. In the free convection dominated regime, two vor tices develop near the sides of the cylinder in both situations of an upward or downward external flow. Comparisons between the analytical a nd numerical results at small times, as well as a detailed discussion of the evolution of the numerical solution are presented. The numerica l results obtained far large Rayleigh, Ra, and Peclet, Pe, numbers sho w that a thermal boundary-layer forms adjacent to the cylinder for any value of the ratio Ra/Pe. The steady state boundary-layer analysis, s imilar to that performed by Cheng and Merkin, is analysed in compariso n to the numerical solution obtained for large values of Ra and Pe at very large times.