How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Numerical analysis of free convective flows in partially open enclosure

 Laminar steady state buoyancy induced flows in a two-dimensional, air filled partial open enclosure with a discrete flush mounted iso-flux heat source on one of its walls is investigated numerically. The transport equations for energy and vorticity are solved with the aid of the ADI finite difference scheme on uniform mesh. Because of the specific application of the present study in the air cooling of electronic equipments, results are obtained only for a Prandtl number of 0.71 with an aspect ratio of 1.0 for a range of Rayleigh numbers, Ra (≤10⁵), heat flux parameter, Q and opening parameter, A ₀ using constant properties and Boussinesq approximation by imposing approximate conditions at the opening. Results of flow and temperature patterns, velocity and temperature profiles shows that the outgoing flow is governed by strong characteristics of the cavity condition whereas the incoming flow influenced by outside conditions. It is observed that Rayleigh number considerably affects the flow and thermal fields within the open enclosure when compared with intensity of heat flux and size of the opening. Received on 22 January 2001 / Published online: 29 November 2001