The method of matched asymptotic expansions, which has been used in previous studies of steady natural convection flow, is extended here to transient natural conve ction flows at high Prandtl number (11). Expansion solutions, valid for large 0', arc 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 0', the time to steady state is shown to increase proportional to 0' 1 / 2 โข The temperature and velocity overshoot, which occurs during the transient at moderate 0', is shown to disappear as 0' -+ cc, Uniformly valid expansions for the velocity and temperature profiles near the surface are found to be in good agreement with the calculated solution ofthe full governing equations for 0' as low as 16.For large 0', a simple relation for the propagation of the leading edge effect is also obtained which is consistent with the results of past studies for 11 = 10 and 0'= 100.
Greek symbols {3, coefficient of thermal expansion; * Note that j2 erfc(z) = ~[(1 +2z 2 ) erfc(z)-JIt z e-z ' ].