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International Heat Transfer Conference 15

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

The Applied Condition of Lumped Parameter Method for Finite Mass Transfer Duration

Jianping Cao
Department of Building Science, Tsinghua University, Beijing 100084, China; Beijing Key Laboratory of Indoor Air Quality Evaluation and Control, Beijing 100084, China

Cong Liu
Department of Building Science, Tsinghua University, Beijing 100084, China

Yinping Zhang
Department of Building Science, Tsinghua University, Beijing 100084, China; Beijing Key Laboratory of Indoor Air Quality Evaluation and Control, Beijing 100084, China

DOI: 10.1615/IHTC15.tdy.008937
pages 7929-7937


KEY WORDS: Thermodynamics, Mass transfer and drying, Lumped parameter method, Finite duration, Applied condition, Semivolatile organic compounds.

Abstract

The lumped parameter method is one of the most convenient ways to address unsteady mass transfer problems. Similar to heat transfer, the classical applied condition of the lumped method in mass transfer has been obtained as that the Biot number (Bim/K = hmL/(DK)) is less than 0.1. It should be called out that if the criterion above is satisfied, the time range within which the lumped parameter method applies is from zero to infinite. However, in practice, the duration of mass transfer process of interest may be finite, instead of infinite. For example, in most cases, the indoor residence time of airborne particles is in the order of one hour. The concerned time duration regarding the mass transfer between particles and gas-phase semivolatile organic compounds is the same as the residence time of particles. During this finite duration, the condition for the lumped parameter method is unclear. In this study, the applied condition of the lumped parameter method for finite mass transfer duration is examined, using mass transfer in a sphere as an example. It has been shown that the applied condition for finite duration is less strict than Bim/K < 0.1. Empirical correlations to calculate critical Bim/K are obtained. Results indicate that for the unsteady mass transfer process of some SVOCs with small mass diffusivity in airborne particles, the lumped parameter method applies during the finite residence time of particles. A similar examination can be conducted for the scenario of mass transfer in plates and cylinders.

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