The problem of simple mathematical models of laminar natural convective flow within a long vertical parallel-plate channels and circular tubes kept at uniformly heated walls is revisited to seek a clear physical understanding of heat transfer mechanisms. A series solution method to analyze the fully developed flow and an integral solution method to analyze the developing flow are used. Chapters 3, 4, and 5 of this dissertation constitute a series of three-paper manuscripts for submission to archival journals. The channels and circular tubes considered here are assumed to be sufficiently long to yield a fully developed flow thermally as well as hydrodynamically before the exit is encountered. In such fully developed flow situation, the fluid mass flow rate naturally induced into the channel due to buoyancy is found to be a function of the wall heating condition. The predicted average Nusselt number as a function of GrPrD/L not only agrees with the existing literature but also is found to be in a functional form comparable to that proposed by Elenbaas (1942 a and b). Our results show that, in spite of being driven by buoyancy (rather than by a pump or a blower), the flow and heat transfer characteristics in the fully developed regime are essentially the same as those of fully developed laminar forced convection in which the flow is externally driven. This observation is confirmed to be valid also in the study (Chapter 5) of laminar natural convection in the developing (entrance) region within a long vertical parallel-plate channel and circular tube. The mass flow rate, which has to remain invariant with axial location even in the entry region, is determined by the flow in the fully developed region. This is the same mechanism involved in forced convection in which the fluid outside the developing boundary layers (i.e. the core flow) is forced to accelerate in the entrance region. The entrance length of channel natural convection is also discovered to be about the same as that in forced convection. / Graduation date: 2001

Graduation date: 1992

Determination of the heat transfer coefficients for natural and mixed convection in horizontal annuli is important for designing double pipe heat exchangers and for energy storage systems. In part one and two of this study, the 2D numerical solution of the laminar natural convection of water in six internally finned horizontal annuli has been obtained. The fins are attached to the external surface of the inner cylinder. Only the symmetrical half of the horizontal annulus with three equally spaced longitudinal divergent solid and porous fins are considered. The parameters of the problem are Rayleigh number, fin height, permeability and porosity of the porous fin, etc. The above parameters are suitably varied to ascertain their effects on fluid flow and heat transfer. The results show that traditional solid fins provide much higher heat transfer rates compared to the porous fins. Part three of this work deals with mixed convective heat transfer (laminar natural and forced convections) of water in a vented annulus. The forced flow conditions are imposed by providing an inlet at the top and an outlet at the bottom. For various parameters of the problem, the average and local Nusselt numbers along the inner cylinder are calculated for water for both aiding and opposing flows. The fourth part of this study deals with numerical modeling of natural convection of nanofluids in a horizontal cylindrical annulus. Simulations are carried out for Cu-water nanofluids. The results, in general, show that nanoparticles systematically decrease the natural convective heat transfer coefficient on the inner cylinder. Practical and useful correlations are provided for calculating average heat transfer rates from the inner cylinder in the form of average equivalent thermal conductivity and average Nusselt number for all of the four cases discussed above. These correlations are new and will be helpful in designing heat exchangers.

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