A Note on Limiting Laminar Nusselt Number in Ducts With Constant Temperature Gradient by Analogy to Thin-Plate Theory

Marco, S. M.; Han, L. S.

doi:10.1115/1.4014446

Cited by 8 publications

(1 citation statement)

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“…In the case of fully developed laminar flow, the Nusselt number is a constant that is fully determined by the geometry of the CFHX [70]. For a uniform heat flux and a rectangular channel the Nusselt number can be calculated as a function of the channel aspect ratio (X) [71]…”

Section: Nusselt Numbermentioning

confidence: 99%

Distributed Joule-Thomson microcooling for optical detectors in space

Derking

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Section: Nusselt Numbermentioning

confidence: 99%

Distributed Joule-Thomson microcooling for optical detectors in space

Derking

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Convective diffusion in a rectangular duct with one catalytic wall—laminar flow—arbitrary reaction order

Solbrig

Gidaspow

1967

AIChE Journal

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In a recent experimental study of reaction rates measured in a rectangular duct with a reaction of arbitrary order occurring on one wall, the results were analyzed in terms of an infinite parallel plate duct. The subject of this paper is the determination of the requirements necessary to treat a rectangular duct as a flat duct in the fully developed laminar flow regime. To this end, the rectangular duct problem is solved numerically. The results obtained show that mixing-cup concentrations, average wall concentrations, and Nusselt numbers for any aspect ratio y (between a square duct and parallel plates) may be estimated from the parallel plate results when a reduced distance is used. These parameters vary only slightly with aspect ratio.If the actual distance instead of this reduced coordinote is used, an aspect ratio of one to ten would be required to obtain results which are accurate to 6%. These conclusions are not valid for a catalytic reactor with four catalytic walls.The rectangular duct geometry is quite common industrially in heat exchangers, catalytic reactors, and fuel cells. The geometry is advantageous in experimental determinations of catalytic reaction rates. For example, a catalyst may be applied uniformly to the catalytic wall and can be examined in detail before the duct is assembled. Deterioration of the catalyst can be checked periodically by disassembly, whereas in a tubular reactor this is generally impossible. In a rectangular duct reactor with one catalytic wall, concentration, velocity, and temperature probes can be inserted in the opposite noncatalytic wall so that catalytic plates of different materials may be used interchangeably in the same reactor.In our recent studies of convective diffusion (10, 11) with a reaction occurring on one wall the results were reported for a parallel plate duct. The subject of this paper is the determination of the necessary requirements which will allow a rectangular duct to be treated as a parallel plate duct in the laminar flow regime. Such information is necessary for proper analysis of reaction rate and diffusion data obtained in a real rectangular duct which approximates a parallel plate reactor. Experimental mass transfer coefficient and reaction rate data obtained in a rectangular duct with one catalytic wall were analyzed by Kulacki and Gidaspow (6) using Solbrig and Gidaspow's ( 1 1 ) parallel plate analysis. One of the consequences of the results reported in this paper is that the data analysis with a parallel plate Reynolds number was justified for the duct with only one catalytic wall. It appears that even a square duct would have been a satisfactory approximation to a parallel plate reactor for analysis of mixing-cup concentrations.The articles reviewed by the authors which pertain to the present discussion may be grouped as follows:1. Completely analytical sohtions which treat on1 region in which the concentration profile is fully B evel-the oped and the boundary conditions are constant flux conditions. 2.Variational solutions which can be ...

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