Pseudosteady-State Natural Convection Inside Spheres

Abstract

Natural convection heat transfer to water contained within five different sized spheres was studied. Pseudosteady-state was maintained by keeping the driving force for convection constant, i.e., the temperature outside the sphere was increased steadily so that the temperature difference between the outside and the center remained constant. Flow visualization was used to determine flow patterns within the spheres. Laminar flow was found to exist below Rayleigh numbers of about 107. The flow patterns along with the position of the circulation centers are presented and compared with recent numerical solutions. The overall heat transfer in the laminar region was fitted by least squares and the following correlation obtained: Nu=0.80Ra0.30

Multi-mode heat transfer analysis during freezing of an encapsulated storage medium

“…Multiple physical assumptions have been considered in the mathematical model and attention will now be turned to discuss their applicability. Experimental observations on the freezing of a low temperature PCM [23] and the natural convection heat transfer to a fluid contained in spherical containers [33] suggest that both the phase change process and the buoyancy induced fluid motion can be modeled as axisymmetric. It was also reported by Chow and Akins [33] that for Rayleigh numbers below , laminar flow was found to exist.…”

Convective Motion and Heat Transfer in a Slowly Rotating Fluid Quasi-Sphere With Uniform Heat Source and Axial Gravity

“…It is interesting to mention that Pepper and Heinrich [18] remark that very little work exists in the literature on thermally driven motion of a fluid contained within a spherical enclosure. Anguiano-Orozco and Avila [5] present a review of the most relevant findings on the subject performed by others investigators, and show that at high Rayleigh numbers Ra, the flow becomes three-dimensional with erratic motion [10].…”

“…The goal of these studies has been to have a better insight into the physics of different heat transfer phenomena appearing in nuclear reactors, such as (i) the cooling of the lower plenum of light water reactors pressure vessels, (ii) the thermal behavior of pressurized water reactors vessel lower head, and (iii) the post accident heat removal in liquid metal fast breeder reactors [6][7][8]. Few papers dealing with the subject of nonrotating, terrestrial axial gravity fleld, nonsteady natural convection in heat-generating fluids enclosed in spherical containers (a situation which commonly appear in processes such as fermentation and certain exothermic chemical reactions) have been published in the literature [9][10][11][12][13][14][15][16]. Heinrich and Pepper [17] and Pepper and Heinrich [18], investigated numerically (by using a finite element model to solve in a Cartesian coordinate system the nonsteady, three-dimensional, incompressible fluid flow equations), the stability of the flow, driven by a terrestrial axial gravity field, within a spherical enclosure subjected to differential heating and cooling on the surface.…”