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Research Papers: Heat and Mass Transfer

Intraparticle Mass Transfer in Adsorption Heat Pumps: Limitations of the Linear Driving Force Approximation

[+] Author and Article Information
Alexander Raymond

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

Srinivas Garimella1

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405sgarimella@gatech.edu

1

Corresponding author.

J. Heat Transfer 133(4), 042001 (Jan 06, 2011) (13 pages) doi:10.1115/1.4001310 History: Received June 19, 2009; Revised January 12, 2010; Published January 06, 2011; Online January 06, 2011

Adsorption heat pumps and chillers (ADHPCs) can utilize solar or waste heat to provide space conditioning, process heating or cooling, or energy storage. In these devices, intraparticle diffusion is shown to present a significant mass transfer resistance compared with interparticle permeation. Therefore, accurate modeling of intraparticle adsorbate mass transfer is essential for the accurate prediction of overall ADHPC performance. The linear driving force (LDF) approximation is often used to model intraparticle mass transfer in place of more detailed equations because of its computational simplicity. This paper directly compares the adsorbate contents predicted using the LDF and Fickian diffusion (FD) equations for cylindrical and spherical geometries. These geometries are typical of adsorbents commonly used in adsorption refrigeration such as cylindrical activated carbon fibers (ACFs) and spherical silica gel particles. In addition to the conventional LDF approximation, an empirical LDF approximation proposed by El-Sharkawy (2006, “A Study on the Kinetics of Ethanol-Activated Carbon Fiber: Theory and Experiments,” Int. J. Heat Mass Transfer, 49(17–18), pp. 3104–3110) for ACF-ethanol (cylindrical geometry) is compared with the FD solution. By analyzing the relative error of the LDF approximation compared with the FD solution for an isothermal step-change boundary condition, the conditions under which the LDF approximation agrees with the FD equation are evaluated. It is shown that for a given working pair, agreement between the LDF and FD equations is affected by diffusivity, particle radius, half-cycle time, initial adsorbate content, and equilibrium adsorbate content. A step change in surface adsorbate content for an isothermal particle is shown to be the boundary condition that yields the maximum LDF error, and therefore provides a conservative bound for the LDF error under nonisothermal conditions. The trends exhibited by the ACF-ethanol and silica gel-water working pairs are generalized through dimensionless time and dimensionless driving adsorbate content, and LDF error is mapped using these two variables. This map may be used to determine ranges of applicability of the LDF approximation in an ADHPC model.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 5

Dimensionless adsorbate content versus dimensionless cycle time for the (a) FD, conventional LDF and empirical LDF equations in cylindrical coordinates and (b) FD and LDF equations in spherical coordinates

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Figure 6

Relative errors of the conventional LDF and empirical LDF compared with the exact FD solution for ACF (A-20)-ethanol (a) at 95°C and (b) at 60°C desorbing adsorbent temperature

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Figure 8

LDF error versus desorption temperature during adsorption and desorption (a) for cylindrical activated carbon fiber-ethanol by the conventional geometric parameter (F0=8) and (b) for spherical silica gel-water (F0=15)

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Figure 9

Absolute value of relative LDF error versus dimensionless time and dimensionless driving adsorbate content for cylindrical fibers during (a) adsorption and (b) desorption

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Figure 10

Absolute value of relative LDF error versus dimensionless time and dimensionless driving adsorbate content for spherical particles during (a) adsorption and (b) desorption

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Figure 11

Conditions for 5%, 10%, and 15% relative LDF error during adsorption and desorption in (a) cylindrical fibers and (b) spherical particles

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Figure 1

One-dimensional interparticle mass transfer through adsorbent particles replenishing refrigerant for intraparticle diffusion within each adsorbent particle

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Figure 2

Refrigerant pressure versus dimensionless position at discrete times for ACF (A-20)-ethanol and silica gel-water

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Figure 3

Adsorbate content histories predicted using real and ideal thermal conductivities and temperature histories for (a) ACF-ethanol and (b) silica gel-water

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Figure 4

Comparison of the solution to one-dimensional and two-dimensional FD solutions for cylindrical fibers with X equal to 5 and 20

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Figure 7

Relative LDF errors for silica gel-water (a) at 95°C and (b) at 60°C desorbing adsorbent temperature

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