Natural convection in a shallow cavity

Abstract

We present numerical solutions of natural convection in a shallow enclosure heated from a side. As a result of hydrodynamic instability transverse cells appear in the flow if the Prandtl number is sufficiently small. Both conducting and insulated top and bottom boundaries were considered. For fluids of small Prandtl number the differences in the flow patterns in these two cases are slight, the strength of the circulation in the cells being somewhat weaker when the boundaries are insulated. This is a result of a more stable flow in this case, caused by the kinetic energy being more vigorously expended in the work against the buoyant forces. Insulated boundaries allow the temperature field to adjust more freely in the end regions leading to crowding of the isotherms there and consequently to larger heat transfer than when the boundaries are conducting.

Numerical solutions for the flow near the end of a shallow laterally heated cavity

“…Generally, the results obtained here are consistent with those obtained earlier in [8] and also with numerical simulations of the full cavity flow by Drummond and Korpela [26].…”

“…where A is given by (26). In Figure 12 the right-hand side of (35) with c given by (33) is compared with the computed values of the left-hand side for each Rayleigh number.…”

Entropy generation in Marangoni convection flow of heated fluid in an open ended cavity

“…However, like other implicit methods, the stability requirement for vorticity at implicit wall boundaries imposes a restriction, say Dt on the time step, in a form similar to that of explicit schemes. For uniform mesh size h, Dt is given by (see [1]):…”

“…The basic examples of such studies are given in [1][2][3]. However, in the presence of a free top surface, the temperature gradient of the surface tension at the free surface may also induce the flow, called the thermocapillary flow or Marangoni convection.…”

Natural convection flow of micropolar fluid in a rectangular cavity heated from below with cold sidewalls

“…The study of thermally induced flow in rectangular domains is considered to be of fundamental importance in this respect, and has been investigated by many authors both for Newtonian and micropolar fluids with a variety of boundary conditions. Some of the basic studies of Newtonian fluids in this regard include the work of Drummond and Korpela [1] and Ostrach [2]. Korpela [1] conducted a detailed natural convection study in a shallow cavity.…”