Graduate Thesis Or Dissertation
 

Laminar natural convection within long vertical uniformly heated parallel-plate channels and circular tubes

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  • 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.
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