Effective Radial Thermal Conductivity of a Parallel Channel

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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Effective Radial Thermal Conductivity of a Parallel Channel Corrugated Metal Structured Adsorbent Pravin B. C. A. Amalraj, Armin D. Ebner, and James A. Ritter* Department of Chemical Engineering, Swearingen Engineering Center, University of South Carolina, Columbia, South Carolina 29208, United States

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S Supporting Information *

ABSTRACT: The effective radial thermal conductivity (keff) of a 2-D analog of a 3-D, parallel channel, corrugated metal, structured adsorbent bed was studied using COMSOL Multiphysics. This 2-D structure consisted of alternating sections of corrugated and flat metal foil sheets, with keff predicted in 1-D perpendicular to the flat metal foil sheet, i.e., the radial direction in a 3-D cylindrical bed. The effect of the thickness of zeolite coating, thickness of metal, type of metal, type of contact between the metal foil sheets (i.e., metal-to-metal, coating-to-coating and metal-to-coating point contacts, and metal-to-metal imbedded contacts), air gap size between the corrugated and flat metal foil sheets, coating on just one or both sides of the metal foil sheets, alignment of the corrugation between sections, and type of stagnant gas medium on keff was studied. In all cases, temperature contour plots revealed the minute region around the point contacts, being mostly stagnant gas medium, manifested a significant resistance to thermal conductivity, with the imbedded contacts minimizing the effect. The parametric study revealed direct metal-to-metal contact had the most positive effect on keff, whether being a point or imbedded contact: keff respectively varied between 0.561 and 0.726 W m−1 K−1 for SS and 6.66 W m−1 K−1 for Al, showing strong dependence on the metal conductivity and weak dependence on the gas medium and all other parameters. When the corrugated and flat metal foil sheets were either coated with zeolite or separated by an air gap, keff was significantly reduced, varying between 0.090 and 0.125 W m−1 K−1 in air for SS or Al; keff also depended strongly on the gas medium but only weakly on the metal conductivity and all other parameters.

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zeolite55 and carbon-zeolite.57 Of special interest to this work are monolithic parallel channel structured adsorbents that are dip-, slip-, wash-, or slurry-coated.31−36 It is interesting that the thermal conductivity k of these kinds of structures varies widely depending on many factors, including temperature and pressure, with numerous studies focused on increasing the value of k for a variety of applications that rely on conductive heat transfer. Structured adsorbents are well suited for improving k with a judicious choice of the support.2 Again, a nonexhaustive review of the literature shows the values of k ranging from 0.25 to >100 W m−1 K−1 for various adsorbent structures.58−66 These include monoliths/ foams comprised of activated carbon-expanded graphite (1−33 W m−1 K−1),58 zeolite-thermally conductive carbon (>100 W m−1 K−1),59 carbon−metal filament parallel passage contactors (0.25 to 1.0 W m−1 K−1),60 carbon (0.25 to 0.93 W m−1 K−1),61 fused silica (1.3 W m−1 K−1),62 silicon carbide (11 W m−1 K−1),63 and cordierite ( MCP contacts > MMP contacts > IMB contacts. In general, the parametric study revealed direct metal-to-metal contact had the most positive effect on keff, whether being a point or imbedded contact: keff showed strong dependence on the metal conductivity and weak dependence on the gas medium and all other parameters. When the corrugated and flat metal foil sheets were either coated with zeolite or uncoated and separated by a gas medium gap, keff was significantly reduced and depended strongly on the gas medium but only weakly on the metal conductivity and all other parameters. In summary, there were only two factors that significantly affected the effective radial thermal conductivity keff of these parallel channel, corrugated metal, structured adsorbent beds. These were the type of metal and the type of gas medium. When there was at least some kind of metal-to-metal contact, whether it was metal-to-metal point contacts with no gas medium gap or imbedded contacts, the only thing that significantly affected keff was the type of metal. When there was no metal-to-metal contact due either to a zeolite layer or a gas medium gap, the only thing that significantly affected keff was the type of gas medium.

Figure 20. Effect of the array alignment (see Figure 4) on the effective thermal conductivity keff (Runs 10 and 24); all other conditions fixed, see Table S3.

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ASSOCIATED CONTENT

S Supporting Information *

Figure 4. The unit cell is shown in Figure 3c. These two alignments represented the extreme cases of how the corrugation might align during the rolling of the structure, with misalignment clearly observed in the photographs in Figure 1. The results correspond to Runs 10 and 24 in Table S3. keff was essentially independent of the alignment of the metal foil sheets, with a value around 0.112 W m−1 K−1. These results showed it does matter how the sheets are rolled up during fabrication.

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.9b03057.

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Tables S1−S3 of model parameters, material properties, and summary of 24 simulations (PDF)

AUTHOR INFORMATION

Corresponding Author

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*E-mail: [email protected].

CONCLUSIONS The effective radial thermal conductivity (keff) of a 2-D analog of a 3-D, parallel channel, corrugated metal, structured adsorbent bed was studied using COMSOL Multiphysics. This 2-D structure consisted of alternating sections of triangular corrugated and flat metal foil sheets, with keff predicted in one direction perpendicular to the flat metal foil sheet, i.e., the radially direction in a 3-D bed. keff was predicted by numerically computing the 1-D temperature gradient along several sections of the corrugated metal structure with insulated boundaries on the upper and lower sides, constant

ORCID

James A. Ritter: 0000-0003-2656-9812 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the DOE National Energy Technology Laboratory under Grant No. DE-FE0007639 and from the NASA Marshall Space Flight Center under Contract No. 81MSFC18C0011. I

DOI: 10.1021/acs.iecr.9b03057 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

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NOMENCLATURE db = depth of the bed, cm keff = effective thermal conductivity, W m−1 K−1 q = heat flux density, W m−2 T = temperature, K Tz=0 = temperature at the left boundary of the bed, K T̅ z=wb = average temperature at the right boundary of the bed, K wb = width of the cross section of the bed, cm z = width, cm

Greek symbols

δa = thickness of adsorbent coating, μm δg = size of gas medium gap between flat and corrugated metal foil sheets, μm δm = thickness of flat or corrugated metal foil sheets, μm ρ = density, kg m−3

Acronyms

A = aligned Al = aluminum CCP = coating-to-coating point MA = misaligned MMP = metal-to-metal point IMB = imbedded SS = stainless steel

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DOI: 10.1021/acs.iecr.9b03057 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.iecr.9b03057 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.iecr.9b03057 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX