Effect of an Isothermal Baffle on Pseudosteady-State Natural Convection Inside Spherical Containers

The influence of an isothermal thin baffle on pseudosteady-state natural convection within spherical containers is studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables, whereby the time-dependent, two-dimensional axisymmetric form of the governing continuity, momentum and energy equations are solved. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 10⁴, 10⁵, 10⁶ and 10⁷, baffles with 3 lengths positioned at 5 different locations were investigated. In effect, a parametric study involving 60 cases were performed. The computational results were benchmarked against previous data available in the literature by comparing the heat transfer correlations, temperature distribution and streamline patterns for cases with no baffle. In general, regardless of the presence of an isothermal baffle, fluid that is heated adjacent to the surface of the sphere rises replacing the colder fluid which sinks downward. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid. This behavior can lead to onset of oscillations in the temperature and flow fields. Partly due to the blockage effect of an isothermal thin baffle and also the extra heating afforded by the baffle, multi-cell recirculating vortex structures are observed. The number and strength of these vortices depend on the position and length of the baffle. The additional heat that is brought into the baffle through the isothermal baffle is directly linked to creation of a counter clockwise rotating vortex next to the baffle. This baffle, in turn, directs hot fluid into the center of the sphere and disrupts thermal stratified layers. For the majority of the length and location combinations investigated, the Nusselt number is lower than the case with no baffle, however the time rate of rise of the bulk temperature can be greater for some combinations. The extent of heat transfer modifications depends on the Rayleigh number, length and location of the baffle.