Gas-Particle Heat Transfer Coefficients in Packed Beds at Low Reynolds Numbers

“…The model for the description of the heat transfer in a packed bed has been developed independently by Brodkey (1964) and Kim (1965) and by Barile (1966) and has been presented in detail by Littman et al (1968). These latter authors solved the complete set of equations for sinusoidal gas temperature inputs.…”

Section: Scopementioning

confidence: 99%

“…This simplified the analysis considerably since only two parameters had to be fitted. More recently Littman and Sliva (1970) obtained data at low Reynolds numbers for which the dispersion literature data were not available; consequently, although considerably more complex, they did fit all three parameters.…”

Section: Scopementioning

confidence: 99%

“…The numerical solution is not simple since it involves a system of eight linear, complex-coefficient, algebraic equations in eight unknowns. A solution was achieved by Littman et al (1968) by a numerical matrix inversion method which consisted of an adaptation to complex matrices of the Gauss-Jordan method with pivotal selection.…”

Section: Conclusion and Sign I Ficancementioning

confidence: 99%

“…In the range of our experiments the latter experimental observation was also valid (Kim, 1965). Only in the low Reynolds number range of the results of Littman and Sliva (1970) does the approximation fail, and the complete solution should be used.…”

Section: Conclusion and Sign I Ficancementioning

confidence: 99%

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A mathematical model for heat transfer in a packed bed and a simplified solution thereof

1972

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first necessary to investigate the heat transfer characteristics of the packed bed system and to consider all the effective modes of transfer of heat that are known or suspected to occur. It is well known that the heat transfer coefficient from the particle to the gas phase cannot be established without assuming some mathematical model for the process. The coefficient depends upon the model assumed. In any adequate model there will usually be several adjustable parameters that describe the pysical attributes of the system. Unfortunately, models that are

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Prediction of breakthrough curves in packed beds: I. Applicability of single parameter models

Jeffreson

1972

AIChE Journal

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Applicability of Single Parameter ModelsConditions under which simplified, single parameter models may be used to predict breakthrough curves in linear, packed bed adsorbers and thermal regenerators are examined with reference, in particular, to earlier conditions proposed by Handley and Heggs and by Babcock and co-workers. I t is found that for high values of heat capacity ratio the Schumann model provides a satisfactory description of packed bed dynamics where fluids axial dispersion and solids conduction effects are lumped into a single parameter the curve spread parameter u*.For low values of heat capocity ratio, the equivalent conductivity model of Babcock and co-workers should provide a more accurate description. The value of the Biot number Bi was found to provide the sole criterion for estimating the relative importance of the internal solids conduction. Empirical correlations are presented which allow rapid estimates of breakthrough curves to be mode from the curve spread parameter and which facilitate analysis of experimental data from breakthrough curve experiments.The prediction of breakthrough curves in linear, packedbed adsorbers and thermal regenerators has been the subject of many theoretical and experimental investigations since Schumann's work (19) in 1929. This interest arises fundamentally because of the economic importance of fixed bed-fluid transfer processes and because of the resultant need to rapidly and accurately design related equipment.Design procedures for well insulated thermal regenerators or adsorbers in which particle internal conductivities may be regarded as infinite have been well developed and were summarized by McAdams (21 ) . Such procedures depend on the Schumann model which makes the assumption amongst others that axial conduction or dispersion in the fluid phase is of negligible importance. The addition of a term for fluid phase axial dispersion (5, 7 ) to the Schumann equation greatly complicates the mathematical solution of the equations and raises the question of whether it is necessary to devise a completely new set of design procedures.In this paper the conditions under which the Schumann solution may be extended to cover the cases of finite particle conductivity and axial fluids dispersion are considered. It has also been necessary to examine critically the conditions proposed earlier by Handley and Heggs (9) and by Babcock and co-workers (2, 3 ) .It is shown that for most cases of practical importance the well-established design procedures referred to above may continue to be used, subject to the satisfaction of a number of simple criteria. At the same time, one of the objects of this paper is to make the task of the design engineer easier by presenting empirical correlations of points on a breakthrough curve against nondimensional groups commonly used in chemical engineering. The use of these groups simplifies the tasks of design and analysis and facilitates translation of the results from heat to mass transfer.The application of complex mathematical "models" to...

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Gas-Particle Heat Transfer Coefficients in Packed Beds at Low Reynolds Numbers

Cited by 79 publications

References 9 publications

Solution of Packed Bed Heat-Exchanger Models by Orthogonal Collocation Using Piecewise Cubic Hermite Functions

Solution of Packed Bed Heat-Exchanger Models by Orthogonal Collocation Using Piecewise Cubic Hermite Functions

A mathematical model for heat transfer in a packed bed and a simplified solution thereof

Prediction of breakthrough curves in packed beds: I. Applicability of single parameter models

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