Analysis of transient natural convection flow at high Prandtl number using a matched asymptotic expansion technique

The method of matched asymptotic expansions, which has been used in previous studies of steady natural convection flow, is extended here to transient natural convection flows at high Prandtl number (sigma). Expansion solutions, valid for large sigma, are presented for the transient natural convection flow near a vertical surface which undergoes a step change in temperature. Throughout the transient, the flow is found to have the same dual-layer structure which is characteristic of the steady flow at high Prandtl number. For large sigma, the time to steady state is shown to increase proportional to sigma exp 1/2. The temperature and velocity overshoot, which occurs during the transient at moderate sigma, is shown to disappear as sigma approaches infinity. Uniformly valid expansions for the velocity and temperature profiles near the surface are found to be in good agreement with the calculated solution of the full governing equations for sigma as low as 16.