Numerical modelling and parametric study of an air-cooled desiccant coated cross-flow heat exchanger

Journal Pre-proofs Numerical Modelling and Parametric Study of an Air-cooled Desiccant Coated Cross-flow Heat Exchanger Lin Liu, Tao Zeng, Hongyu Huang, Mitsuhiro Kubota, Noriyuki Kobayashi, Zhaohong He, Jun Li, Lisheng Deng, Xing Li, Yuheng Feng, Kai Yan PII: DOI: Reference:

S1359-4311(19)35685-6 https://doi.org/10.1016/j.applthermaleng.2020.114901 ATE 114901

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

14 August 2019 5 December 2019 3 January 2020

Please cite this article as: L. Liu, T. Zeng, H. Huang, M. Kubota, N. Kobayashi, Z. He, J. Li, L. Deng, X. Li, Y. Feng, K. Yan, Numerical Modelling and Parametric Study of an Air-cooled Desiccant Coated Cross-flow Heat Exchanger, Applied Thermal Engineering (2020), doi: https://doi.org/10.1016/j.applthermaleng.2020.114901

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Title: Numerical Modelling and Parametric Study of an Air-cooled Desiccant Coated Cross-flow Heat Exchanger

*Author names and affiliations:

Lin Liu,[a,b] Tao Zeng,[a] Hongyu Huang,*[a] Mitsuhiro Kubota,[c] Noriyuki Kobayashi,[c] Zhaohong He,*[a] Jun Li,[c] Lisheng Deng,[a,d] Xing Li,[a] Yuheng Feng, [d,e] Kai Yan[e]

a

Key Laboratory of Renewable Energy, Guangdong Provincial Key Laboratory of New and

Renewable Energy Research and Development, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, No.2 Nengyuan Rd. Wushan, Tianhe District, Guangzhou 510640, P.R. China b University

c Nagoya

d

of Chinese Academy of Sciences, Beijing 100049, P.R. China

University, Furo-cho, Chikusa-ku, Nagoya-shi, Aichi 464-8603, Japan

Thermal and Environmental Engineering Institute, Tongji University, 1239 Siping Road,

Shanghai 200092, P.R. China e Shanghai

Boiler Works Co Ltd, Minhang, Shanghai 200245, P.R. China

* To whom correspondence should be addressed Corresponding author: 1

Hongyu Huang E-mail: [email protected] Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, No. 2, Nengyuan Rd, Wushan, Tianhe District, Guangzhou 510640, P. R. China

Zhaohong He E-mail: [email protected] Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, No. 2, Nengyuan Rd, Wushan, Tianhe District, Guangzhou 510640, P. R. China

Abstract Air-cooled desiccant coated cross-flow heat exchanger (DCCFHE) system provides a simple and effective approach to improve dehumidification performance by using cooling air to remove the adsorption heat during adsorption process. In this study, a novel numerical model validated by experimental data was established to predict the performance of a conventional silica gel coated cross-flow heat exchanger system. The fin efficiency, as a variable due to the release of adsorption heat, was taken into account in the model. Parametric study for various air velocity and structural parameters was conducted to reveal their effects on the dehumidification performance. Results show that the smaller process air velocity is conducive to improve dehumidification performance, but the performance increases with the increase in cooling air velocity. Compared to the operation case without cooling air, the moisture removal capacity and dehumidification coefficient of performance can obtain about 35% improvement at the cooling air velocity of 1m/s. The results also indicate that thicker desiccant layer thickness and smaller fin pitch improve moisture removal capacity and dehumidification coefficient of performance but result in greater total pressure drop ∆𝑃, while the performance is insensible to fin thickness and fin height. Besides, effect of heat transfer performance in dehumidification and cooling sides on dehumidification performance was also analyzed respectively. It was found that the heat transfer performance in dehumidification side is the dominant factor affecting dehumidification performance. 2

Highlights 

A numerical model was established to predict the performance of DCCFHE system.



Model considered the change in fin efficiency during dehumidification cycle.



Parametric study for various air velocity and structural parameters were conducted.



Cooling air contributes to improve dehumidification performance.



Heat transfer performance in dehumidification side is the dominant factor.

Keywords Numerical modeling; Solid dehumidification; Cross-flow heat exchanger; Desiccant coated heat exchanger; Air conditioning Nomenclature



angle between fin and separator

𝑎

fin pitch (m)

𝜑𝑤

relative humidity of moisture air

𝐴

area (m2)

𝛷

equivalent volume heat source (W/m3)

𝑏

fin height in the direction of z (m)

Superscript

𝐶𝑝

specific heat (J/(kg·K))

′

width and height of air duct with desiccant layer

𝐷𝑎

molecular diffusivity (m2/s)

"

width and height of air duct with halfthickness fin

𝐷ℎ

hydraulic diameter (m)

Subscript

𝐷𝐾

Knudsen diffusivity (m2/s)

1

dehumidification channel

𝐷𝑠

surface diffusivity of absorbed moisture (m2/s)

2

cooling channel

𝑓

mass fraction of active material in desiccant layer 12

interface at the half-thickness separator

ℎ

specific enthalpy (J/kg)

𝑎

moisture air

𝐻ℎ

convection heat transfer coefficient (W/(m2·K))

𝑎𝑑

adsorption process

𝑗𝑚

mass flux at the interface of air and desiccant 𝑎𝑚

ambient

(kg/(m2·s) ) 𝑘

thermal conductivity (W/(m·K))

𝑎𝑝

moisture air in the desiccant pores

𝐾𝑚

convective mass transfer coefficient (m/s)

𝑏

blower

𝐿

geometric size of heat exchanger (m)

𝑐

cooling process

𝑙

fin length in the direction of oblique fin (m)

𝑐𝑠

cross-sectional area of air duct with halfthickness fin

3

𝑚

mass flow (kg/s)

𝑀𝐻2𝑂 molecule mass of water (kg/mol)

𝑑

desiccant

𝑑𝑎

dry air

𝑛

number of channel layer in heat exchanger

𝑑𝑑

dry desiccant

𝑁𝑢

Nusselt number

𝑑𝑚

solid matrix of desiccant (excluding air)

𝑃0

ambient pressure (Pa)

𝑑𝑠

cross section of desiccant layer

𝑃

perimeter (m)

𝑑𝑢𝑐𝑡

one air duct

𝑞

heat flux at the interface of air and solid layer 𝑒𝑓𝑓

effective

(W/m2 ) 𝑄𝑓

heat transfer rate between air and fin surface due 𝑓

fin

to heat conduction (W) 𝑄𝑠𝑡

heat transfer rate between air and fin surface due 𝑓 ― 𝑑

fin and desiccant

to adsorption heat (W) 𝑞𝑠𝑡

adsorption heat (J/kg)

𝐻

constant heat flux condition

𝑅𝑒

Reynolds number

ℎ

convection heat transfer

𝑅𝑣

water vapor gas constant (J/kg·K)

𝑖

operation process including ad, c or r

𝑟𝑝

pore radius of desiccant (m)

𝑖𝑛

inlet

𝑇

temperature (K)

𝑖𝑛𝑓

interface between fin base and separator

𝑡

time (s)

𝛿 ― 𝑖𝑛𝑓

cross section perpendicular to the direction of oblique fin

𝑢

air velocity (m/s)

𝑊

water vapor uptake inside the desiccant layer 𝑚𝑠

𝑚

metal cross section of metal layer

(kg/kg) 𝑌

humidity ratio of moisture air(kg/kg)

Greek symbols

𝑜𝑢𝑡

outlet

𝑝𝑝

previous process

𝛼

ratio between height and width of air duct

𝑟

regeneration

𝛿

thickness (m)

𝑠

solid layer

𝜀

desiccant porosity

𝑠𝑝

separator

𝜂

efficiency

𝑠𝑟

saturation

𝜌

density (kg/m3)

𝑠𝑡

effect of adsorption heat

𝜎

structural void fraction

𝑇

constant wall temperature condition

𝜏𝑎

tortuosity factor for gas diffusion

𝑣

water vapor

𝜏𝑠

tortuosity factor for surface diffusion

𝑣𝑎

vaporization

4

1. Introduction Effective humidity control strategies are essential for decreasing energy consumption of air-conditioning systems. In conventional evaporative cooling systems, the humidity regulation is achieved by lowering the air temperature below its dew point and condensing the moisture at the expense of high electricity requirement. The coupling processing of temperature and humidity may result in a poor air quality and indoor thermal comfort. Moreover, the use of Freon gas as refrigerant brings out noteworthy environmental issues. By comparison, solid desiccant cooling systems driven by low-grade thermal energy provide an efficient and environmentally friendly dehumidification approach to receive energy saving and satisfied indoor thermal environment. Over the past decades, more and more investigation efforts have been devoted to these systems on the basis of numerical simulation, experimental study, thermodynamic analysis and practical application [1-3]. In solid desiccant cooling systems, the desiccant absorbs moisture of process air in adsorption process. Subsequently, a regeneration process is conducted by using heat energy to remove the absorbed moisture and recover adsorption capacity. In the adsorption process, there is a large amount of the release of adsorption heat, which leads to an undesirable temperature rise in the desiccant. In consequence, the dehumidification capacity of the systems is decreased and the process air usually need to be cooled after adsorption process. Several references [3-5] pointed out that the overall performance of the systems can be improved significantly if adsorption heat can be effectively taken away from adsorption process. Recently, a new solid desiccant cooling system with desiccant coated heat exchanger (DCHE) has drawn increasing attention. In DCHE, the desiccant is coated on the surface of metal wall and it is directly cooled by cold fluid at the cooling side of DCHE during adsorption process. The cold fluid helps to effectively eliminate the side effect of adsorption heat. Ge et al. [5] experimentally investigated the dehumidification performance of silica gel and polymer coated DCHE, respectively. Experimental results showed that the cooling water pumping into the DCHEs during adsorption process contributes to improve dehumidification capacity due to the removal of adsorption heat. The results also pointed out that silica gel coated DCHE shows a better dehumidification performance than the polymer one. Kumar and Yadav [6] developed a solar-driven silica gel coated DCHE cooling system. It was found that the system performs well in handling both sensible and latent loads. Oh et al. [7] carried out the performance evaluation for silica gel coated DCHE system under tropical climate conditions. It was reported that the moisture removal capacity enormously depends on inlet air humidity ratio and the

5

remarkable improvement in COP can be achieved by lowering regeneration temperature. Besides the experimental findings, numerical modelling of DCHE has also attracted researcher’s interests. Ge et al. [8] established a dynamic one-dimensional model to study the dehumidification characteristics of silica gel coated DCHE system. They pointed out that the operation time is a crucial factor for cooling capacity. The structural parameter analysis indicated that the smaller copper tube external diameter and fin spacing of DCHE could improve dehumidification performance. Ge et al. [9] also developed an integrated system model which combines the sub-numerical models of each components in solar-driven DCHE system. The reported results showed that the system can provide satisfied supply air for indoor space under hot and humid conditions. Recently, Jagirdar et al. [10] developed a two-dimensional model to conduct a series of parametric study for DCHE system. This model takes mass transfer resistance in the desiccant layer and fin efficiency into consideration. Numerical results indicated that the integration of DCHE sub-system with a conventional cooling system can receive 31% energy savings if the low temperature waste heat (323.15 K hot water) is available for regeneration. In these mentioned researches, the fin-tube heat exchanger was mostly employed as a substrate. The water circulation loop was often required in order to provide cooling fluid and regenerative hot water. Additionally, the solid desiccant cooling system with desiccant coated cross-flow heat exchanger (DCCFHE) has also received considerable research attentions. In earlier years, Worek and Lavan [11] used silica gel as desiccant to construct a DCCFHE prototype. In this DCCFHE, the silica gel sheets were adhered on the surface of metal wall at the dehumidification side of cross-flow parallel-plate heat exchanger. The cooling air was introduced into the cooling side of DCCFHE to cool desiccant during adsorption process. The experimental and numerical study in their subsequent works [12-14] revealed that the DCCFHE system has great potential in improving dehumidification performance and reducing regeneration temperature. Yuan et al. [15] experimentally and numerically investigated a new modified DCCFHE. Results demonstrated that the DCCFHE could obtain a better cooling effect and dehumidification performance under the effect of internal cooling air, especially for high humidity conditions. Jeong et al. [16] investigated the minimum driving heat source temperature for four different types of desiccant cooling system based on developed numerical models. They found that the system with the DCCFHE possesses the lowest driving heat source temperature about 306 K. Munz et al. [17] fabricated a SAPO-34 coated DCCFHE for solar-driven desiccant cooling system. They reported that the SAPO-3 system could outperform commonly used silica gel system and it shows a high potential for dehumidification. In our previous study [18, 19], two 6

DCCFHEs were fabricated by coating silica gel and aluminophosphate (AlPO) zeolite on the surface of plate-fin heat exchangers respectively. Experimental study demonstrated that the cooling air effectively enhances the heat and mass transfer as well as promotes the removal of moisture. The results also showed that the AlPO zeolite coated DCCFHE can be driven by using low-temperature heat at 333 K. Noted that the DCCFHE system can directly use air as cooling source to cool desiccant during adsorption process. This system without need for water circulation system is simpler than the one with water coolant. Moreover, the presence of metal fin with high thermal conductivity in the air channels enhances the heat and mass transfer capacity. From the above literatures, the air-cooled DCCFHE system is a quite potential humidity control system for improving dehumidification performance. However, there has been little focus on the optimization analysis of the operating and structural parameters for the key component DCCFHE. It is necessary to conduct a detailed parametric study for performance evaluation and system optimization analysis. Considering that extensive parametric study through experiments are a difficult, time consuming and costly work, the establishment of an accuracy numerical model for predicting the dehumidification characteristics of DCCFHE system is quite indispensable. In this study, a detailed numerical model was developed to simulate the transient heat and mass transfer in an air-cooled desiccant coated cross-flow platefin heat exchanger (DCCFHE). The novelty of this model is to deduce the expression of fin efficiency as a variable due to the release of adsorption heat, while it usually was not considered or set as a fixed value in the reported references. The cooling air with the same humidity ratio and temperature as process air was used as coolant to remove adsorption heat during adsorption process and the effects of air velocity on dehumidification performance of DCCFHE system were discussed. Detailed study for structural parameters was carried out to optimize the DCCFHE. Besides, effect of heat transfer performance in dehumidification and cooling sides of DCCFHE on dehumidification performance were also analyzed respectively.

2. Numerical model 2.1 Geometric analysis The DCCFHE in this study is a plate-fin heat exchanger coated with silica gel on the surface of dehumidification channels as depicted in Fig. 1. In adsorption process, the moisture is removed when process air flows through dehumidification channels. Meanwhile, the cooling air with the same humidity ratio and temperature as the process air is introduced into cooling 7

channels to cool the desiccant. In regeneration process, the regeneration air flows directly into dehumidification channels to desorb the adsorbed moisture. Each channel layer in local region is surrounded by two same other channel layers due to their alternate arrangement. The cross section of each channel layer perpendicular to the direction of air flow is a centrally symmetrical geometry. Thus, there is an idealized plane at the center of each channel layer (The plane is represented by the yellow dotted line at the right side of Fig. 1) through which there is no net heat and mass transfer. This fact supports the subsequent establishment of conservation equations ignoring temperature and moisture gradients in “z” direction of the DCCFHE.

Fig.1 Schematic diagram of air-cooled DCCFHE For the convenience of geometric analysis, the cross sections of adjacent two channel layers are partially described on one plane (“yz” plane) as shown as Fig. 2. There is an idealized adiabatic interface at each half-thickness fin (As shown as the blue dotted lines in the fins), because the two air streams with same states centrosymmetrically flow through both surfaces of each fin. Combining with the analysis of Fig. 1, it can be concluded that the quadrilateral domain (CV1) surrounded by the red solid line in Fig. 2 has no net energy and mass transfer with the adjacent ambience. The CV1 is selected as the analysis domain to develop numerical model. Because the CV1 and CV2 (The domain is surrounded by purple solid line) have the same cross-sectional area for air duct, fin and separator, in order to show the calculation of geometric parameters more clearly, the CV2 is used as analysis object to calculate these parameters of numerical equations as depicted in Eq. (1)-Eq. (6). The cross section of air duct is considered as an isosceles triangular top and a flat base as described in the right side of Fig. 2.

8

Fig.2 Geometric analysis of air channels The geometric parameters are calculated as follow: 𝑎′ =

𝑏′ 𝑏 𝑎;

"

𝑎 =

𝑏" 𝑏 𝑎;

𝑎 2

𝑏′ = 𝑏 ― 𝛿𝑑 ―

2𝛿𝑑 𝑏2 + (2) 𝑎

"

;𝑏 =𝑏+

𝛿𝑠𝑝 2

𝑎 2

+

𝛿𝑓 𝑏2 + (2) 𝑎

(1)

Two elements with the length of 𝛥𝑥 and 𝛥𝑦 (𝛥𝑥 = 𝛥𝑦) at the flow direction form the total control volume 𝐴𝐶𝑉1 × ∆𝑥 in the Fig. 2. The two air streams were considered to fix at one direction (“x” direction) to develop numerical model, even though they seemingly crossed. Fig. 3 shows that the heat and mass transfer processes in the channels with the cross section of 𝐴𝐶𝑉1 on the “xz” plane. It should be mentioned that the subsequent conservation equations are all based on x-direction.

Fig.3 Schematic diagram of heat and mass transfer process during dehumidification cycle For the total control volume formed by 𝐴𝐶𝑉1 × ∆𝑥, the geometric parameters are determined as follow. The cross-sectional area of air duct and the element area of air-solid interfaces for fin and separator: 1

𝑎′ 2

𝐴𝑑𝑢𝑐𝑡1 = 2𝑎′𝑏′; 𝐴𝑓1 = 2∆𝑥 𝑏′2 + ( 2 ) ; 𝐴𝑠𝑝1 = 𝑎′∆𝑥;

9

𝑎 2

1

𝐴𝑑𝑢𝑐𝑡2 = 2𝑎𝑏; 𝐴𝑓2 = 2∆𝑥 𝑏2 + (2) ; 𝐴𝑠𝑝2 = 𝑎∆𝑥; 𝐴𝑠𝑝12 = 𝑎"∆𝑥

(2)

The perimeter of cross section of air duct for fin and separator: 𝑎′ 2

𝑎 2

𝑃𝑓1 = 2 𝑏′2 + ( 2 ) ; 𝑃𝑓2 = 2 𝑏2 + (2) ; 𝑃𝑠𝑝1 = 𝑎′; 𝑃𝑠𝑝2 = 𝑎; 𝑃𝑠𝑝12 = 𝑎"

(3)

The hydraulic diameter of air duct: 4𝐴𝑑𝑢𝑐𝑡1

4𝐴𝑑𝑢𝑐𝑡2

𝐷ℎ1 = 𝑃𝑓1 + 𝑃𝑠𝑝1; 𝐷ℎ2 = 𝑃𝑓2 + 𝑃𝑠𝑝2

(4)

The cross-sectional areas for desiccant layer, metal layer and air duct with half-thickness fin and separator: 1

𝐴𝑑𝑠 = 𝐴𝑑𝑢𝑐𝑡2 ― 𝐴𝑑𝑢𝑐𝑡1; 𝐴𝑚𝑠 = 2 × (𝐴𝑐𝑠 ― 𝐴𝑑𝑢𝑐𝑡2); 𝐴𝑐𝑠 = 2𝑎"𝑏"

(5)

The structural void fraction of air duct: 𝜎1 =

𝐴𝑑𝑢𝑐𝑡1

𝐴𝑑𝑢𝑐𝑡2

𝐴𝑐𝑠

𝐴𝑐𝑠

; 𝜎2 =

(6)

2.2 Assumptions The DCCFHE consists of a series of alternately arranged cooling and dehumidification channel layers. The mass and heat transfer process in DCCFHE are depicted in Fig. 3. In order to simplify the numerical modelling, the following assumptions implicitly involved in this paper should be specifically stated: (1) All governing equations only consider the temperature and moisture gradient in the direction of air flow; (2) Heat conduction and mass diffusion within air streams are small compared to the convective transfer and are neglected; (3) The thermodynamic properties of dry air, adsorbate, desiccant and metal material are assumed to be constant; (4) Since Re < 2300, the air flow is considered as laminar flow. The heat and mass transfer coefficients between the air steams and solid wall are constant along the channel; (5) Since heat transfer Bi is less than or close to 0.1 and the cross-sectional area of an element is relatively small, the temperature gradient along the thickness and height of solid layer (metal wall and desiccant layer) is neglected and the solid layers at the elements 𝛥𝑥 and 𝛥𝑦 are assumed to be at the same temperature 𝑇𝑠1 and 𝑇𝑠2; (6) The DCCFHE is assumed to be infinitely large in the “z” direction, so the boundary effect of the top and bottom of channel layers is neglected. 10

2.3 Governing equations Based on the aforementioned assumptions, the mass and energy conservation equations in the total control volume of 𝐴𝐶𝑉1 × ∆𝑥 can be derived as follows. Mass conservation equation of moisture air: ∂𝑌𝑎1

𝜌𝑎1𝐴𝑑𝑢𝑐𝑡1∆𝑥

∂𝑡

∂𝑌𝑎1

+ 𝜌𝑎1𝐴𝑑𝑢𝑐𝑡1𝑢1∆𝑥

∂𝑥

(7)

= ― 𝑗𝑚(𝐴𝑓1 + 𝐴𝑠𝑝1)

The 𝑗𝑚 is mass flux between the moisture air and desiccant layer, which can be expressed by: (8)

𝑗𝑚 = 𝐾𝑚𝜌𝑎1(𝑌𝑎1 ― 𝑌𝑑) Energy conservation equation of moisture air: ∂𝑇𝑎1

𝜌𝑎1𝐴𝑑𝑢𝑐𝑡1∆𝑥𝐶𝑝,𝑎1

∂𝑡

∂𝑇𝑎1

+ 𝜌𝑎1𝐴𝑑𝑢𝑐𝑡1𝑢1∆𝑥𝐶𝑝,𝑎1

∂𝑥

= ―(𝑞1 + 𝑗𝑚𝑞𝑣𝑎)(𝜂𝑓,𝑠𝑡𝐴𝑓1 + 𝐴𝑠𝑝1)

(9)

The 𝑞1 represents heat flux between the moisture air and desiccant layer, which is given by: 𝑞1 = 𝐻ℎ1(𝑇𝑎1 ― 𝑇𝑠1) (10) The 𝑞𝑣𝑎 is termed the heat of adsorbate transfer at the air-solid interfaces, which is given by [20]: (11)

𝑞𝑣𝑎 = 𝐶𝑝,𝑣(𝑇𝑠1 ― 𝑇𝑎1) Mass conservation equation of desiccant layer:

(

)

∂𝑌𝑑 ∂𝑊𝑑 ∂ 𝐷𝑎∂𝑌𝑑 𝜀𝜌𝑑𝑎𝐴𝑑𝑠∆𝑥 + (1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑𝑠∆𝑥 = 𝜀𝜌𝑑𝑎𝐴𝑑𝑠∆𝑥 ∂𝑡 ∂𝑡 ∂𝑥 𝜏𝑎 ∂𝑥

(

)+𝑗

∂ 𝐷𝑠∂𝑊𝑑 𝜏𝑠 ∂𝑥

+ (1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑𝑠∆𝑥∂𝑥

𝑚(𝐴𝑓1

(12)

+ 𝐴𝑠𝑝1)

Energy conservation equation of solid layer in the total control volume of 𝐴𝐶𝑉1 × ∆𝑥: 1 ∂ 1 (1 ) ∂𝑡 + 𝜌𝑚(2𝐴𝑚𝑠)∆𝑥𝐶𝑝,𝑚 ∂𝑡 = 𝐴𝑑𝑠∆𝑥∂𝑥(𝑘𝑑 ∂𝑥 ) + (2𝐴𝑚𝑠)∆𝑥 ∂𝑇 ∂𝑇 ∂ 1 ∂ ( ) ∂𝑥(𝑘𝑚 ∂𝑥 ) +(2𝐴𝑚𝑠)∆𝑥∂𝑥(𝑘𝑚 ∂𝑥 ) + 𝑞1 𝜂𝑓,𝑠𝑡𝐴𝑓1 + 𝐴𝑠𝑝1 + 𝑞2(𝜂𝑓𝐴𝑓2 + 𝐴𝑠𝑝2) + (1 ― 𝜀)𝑓𝜌𝑑𝑑 ∂𝑇𝑠1

𝜌𝑑𝐴𝑑𝑠∆𝑥𝐶𝑝,𝑑

∂𝑡

+ 𝜌𝑚 2𝐴𝑚𝑠 ∆𝑥𝐶𝑝,𝑚

𝑠1

∂𝑊𝑑

𝐴𝑑𝑠∆𝑥[

∂𝑡

∂𝑇𝑠1

∂𝑇𝑠2

∂𝑇𝑠1

𝑠2

(

)]𝑞

∂ 𝐷𝑠∂𝑊𝑑 𝜏𝑠 ∂𝑥

― ∂𝑥

𝑠𝑡

(13)

The first term at the left side of Eq. (13) represents the energy storage within desiccant layer at the element ∆𝑥, and the second and third terms account for the energy storage within 11

metal layer at the element ∆𝑥 and ∆𝑦 respectively. Correspondingly, the first, second and third terms at the right side of Eq. (13) represent the heat diffusion at the desiccant and metal layer, while the fourth and fifth terms account for the convection heat transfer between air streams and solid layer and the final term accounts for heat generation due to phase change (adsorption heat). The 𝑞2 represents the heat flux between the cooling air and metal wall, which is given by: (14)

𝑞2 = 𝐻ℎ2(𝑇𝑎2 ― 𝑇𝑠2) Energy conservation equation of cooling air: ∂𝑇𝑎2

𝜌𝑎2𝐴𝑑𝑢𝑐𝑡2∆𝑥𝐶𝑝,𝑎2

∂𝑡

∂𝑇𝑎2

+ 𝜌𝑎2𝐴𝑑𝑢𝑐𝑡2𝑢2∆𝑥𝐶𝑝,𝑎2

∂𝑥

(15)

= ― 𝑞2(𝜂𝑓𝐴𝑓2 + 𝐴𝑠𝑝2)

Energy conservation equation of metal layer at the element ∆𝑦:

(1 )

𝜌𝑚 2𝐴𝑚𝑠 ∆𝑥𝐶𝑝,𝑚

∂𝑇𝑠2 ∂𝑡

( 𝐴 )∆𝑥 (𝑘 1 2 𝑚𝑠

=

∂𝑇𝑠2 𝑚 ∂𝑥

∂ ∂𝑥

) + 𝑞2(𝜂𝑓𝐴𝑓2 + 𝐴𝑠𝑝2) + 𝐴𝑠𝑝12𝑞12 (16)

The 𝑞12 represents the heat flux due to heat conduction between the half-thickness metal separators at the elements ∆𝑥 and ∆𝑦, which is given by Fourier law of heat conduction: 𝑞12 = 𝑘𝑚

(𝑇𝑠1 ― 𝑇𝑠2)

(17)

1 2𝛿𝑠𝑝

After simplification and re-arrangement, the governing equations are summarized as follow: ∂𝑌𝑎1

𝜌𝑎1

∂𝑡

∂𝑌𝑎1

+ 𝜌𝑎1𝑢1 ∂𝑇𝑎1

𝜌𝑎1𝐶𝑝,𝑎1

∂𝑡

∂𝑥

=―

𝑗𝑚(𝑃𝑓1 + 𝑃𝑠𝑝1)

∂𝑇𝑎1

+ 𝜌𝑎1𝑢1𝐶𝑝,𝑎1

∂𝑌𝑑

)

𝐴𝑚𝑠 ∂𝑇𝑠1

1

𝑑 𝑝,𝑑

+ 2𝜌𝑚𝐶𝑝,𝑚 𝐴𝑑𝑠

𝑞1(𝜂𝑓,𝑠𝑡𝑃𝑓1 + 𝑃𝑠𝑝1) 𝐴𝑑𝑠

+

∂𝑥

∂𝑊𝑑

𝜀𝜌𝑑𝑎 ∂𝑡 + (1 ― 𝜀)𝑓𝜌𝑑𝑑

(𝜌 𝐶

∂𝑡

(18)

𝐴𝑑𝑢𝑐𝑡1

∂𝑡

=―

(𝑞1 + 𝑗𝑚𝑞𝑣𝑎)(𝜂𝑓,𝑠𝑡𝑃𝑓1 + 𝑃𝑠𝑝1)

∂

+ 2𝜌𝑚𝐶𝑝,𝑚 𝐴𝑑𝑠

𝑞2(𝜂𝑓𝑃𝑓2 + 𝑃𝑠𝑝2)

∂𝑌𝑑

(

)

∂𝑡

∂𝑊𝑑

(

∂

[(

1

)

∂𝑊𝑑 ∂𝑡

∂

(

) ]+ )]𝑞

𝐴𝑚𝑠 ∂𝑇𝑠1

= ∂𝑥 𝑘𝑑 + 2𝑘𝑚 𝐴𝑑𝑠

+ 𝑓𝜌𝑑𝑑[(1 ― 𝜀)

𝐴𝑑𝑠

∂

= 𝜌𝑑𝑎∂𝑥 𝐷𝑎,𝑒𝑓𝑓 ∂𝑥 +𝑓𝜌𝑑𝑑∂𝑥 𝐷𝑠,𝑒𝑓𝑓 ∂𝑥 + 𝐴𝑚𝑠∂𝑇𝑠2

1

(19)

𝐴𝑑𝑢𝑐𝑡1

∂𝑥

𝑗𝑚(𝑃𝑓1 + 𝑃𝑠𝑝1) 𝐴𝑑𝑠

𝐴𝑚𝑠∂𝑇𝑠2 ∂ 1 ∂𝑥(2𝑘𝑚 𝐴𝑑𝑠 ∂𝑥 )

(20)

+

∂𝑊𝑑

― ∂𝑥 𝐷𝑠,𝑒𝑓𝑓 ∂𝑥

𝑠𝑡

(21) ∂𝑇𝑎2

𝜌𝑎2𝐶𝑝,𝑎2

𝜌𝑚𝐶𝑝,𝑚

∂𝑡 ∂𝑇𝑠2 ∂𝑡

∂𝑇𝑎2

+ 𝜌𝑎2𝑢2𝐶𝑝,𝑎2 ∂

(

∂𝑇𝑠2

)

∂𝑥

= ∂𝑥 𝑘𝑚 ∂𝑥 +

=―

𝑞2(𝜂𝑓𝑃𝑓2 + 𝑃𝑠𝑝2)

(22)

𝐴𝑑𝑢𝑐𝑡2

2𝑞2(𝜂𝑓𝑃𝑓2 + 𝑃𝑠𝑝2) 𝐴𝑚𝑠

+

2𝑞12𝑃𝑠𝑝12 𝐴𝑚𝑠

The effective gas diffusion coefficient, 𝐷𝑎,𝑒𝑓𝑓, is defined below [21]: 12

(23)

𝑇1.685 𝑠1

𝐷𝑎,𝑑 = 1.758 × 10 ―4

𝑃0

; 𝐷𝐾 = 97𝑟𝑝

𝑇𝑠1

𝑀𝐻2𝑂;

𝜀

1

1

𝐷𝑎,𝑒𝑓𝑓 = 𝜏𝑎(𝐷𝑎,𝑑 + 𝐷𝐾)

―1

(24)

The effective surface diffusivity of Ds,eff is defined by [22]: 𝑞𝑠𝑡

𝐷𝑠,𝑒𝑓𝑓 = 1.6 × 10 ―6exp ( ― 0.45𝑅𝑣𝑇 )( 𝑠1

1―𝜀 𝜏𝑠 )

(25) 2.4 Thermophysical properties involved in the equations The thermophysical properties of moisture air and desiccant layer are defined by using the similar equations in Ref. [23]. The density, specific heat and thermal conductivity of moisture air both in dehumidification channel and cooling channel are determined as follow: 𝜌𝑎1 = 𝜌𝑑𝑎(1 + 𝑌𝑎1); 𝐶𝑝,𝑎1 =

𝜌𝑑𝑎𝐶𝑝,𝑑𝑎 + 𝑌𝑎1𝜌𝑑𝑎𝐶𝑝,𝑣 𝜌𝑎1

𝜌𝑎2 = 𝜌𝑑𝑎(1 + 𝑌𝑎2); 𝐶𝑝,𝑎2 =

; 𝑘𝑎1 =

𝜌𝑑𝑎𝐶𝑝,𝑑𝑎 + 𝑌𝑎2𝜌𝑑𝑎𝐶𝑝,𝑣 𝜌𝑎2

𝜌𝑑𝑎𝑘𝑑𝑎 + 𝑌𝑎1𝜌𝑑𝑎𝑘𝑣 𝜌𝑎1

; 𝑘𝑎2 =

;

𝜌𝑑𝑎𝑘𝑑𝑎 + 𝑌𝑎2𝜌𝑑𝑎𝑘𝑣 𝜌𝑎2

(26)

The thermophysical properties of desiccant layer are the function of porosity and they are defined by: 𝜌𝑑 = 𝜀𝜌𝑎𝑝 +(1 ― 𝜀)𝜌𝑑𝑚; 𝜌𝑑𝑚 = 𝜌𝑑𝑑(1 + 𝑓𝑊𝑑); 𝜌𝑎𝑝 = 𝜌𝑑𝑎(1 + 𝑌𝑑); 𝐶𝑝,𝑎𝑝 = 𝐶𝑝,𝑑 =

𝜌𝑑𝑎𝐶𝑝,𝑑𝑎 + 𝑌𝑑𝜌𝑑𝑎𝐶𝑝,𝑣

𝜌𝑑𝑑𝐶𝑝,𝑑𝑑 + 𝜌𝑑𝑑𝑓𝑊𝑑𝐶𝑝,𝑤

𝜌𝑎𝑝

𝜌𝑑𝑚

; 𝐶𝑝,𝑑𝑚 =

;

(1 ― 𝜀)𝜌𝑑𝑚𝐶𝑝,𝑑𝑚 + 𝜀𝜌𝑎𝑝𝐶𝑝,𝑎𝑝

𝜌𝑑𝑎𝑘𝑑𝑎 + 𝑌𝑑𝜌𝑑𝑎𝑘𝑣

𝜌𝑑

𝜌𝑎𝑝

𝑘𝑑𝑚 =

; 𝑘𝑎𝑝 =

;

𝜌𝑑𝑑𝑘𝑑𝑑 + 𝜌𝑑𝑑𝑓𝑊𝑑𝑘𝑤

(1 ― 𝜀)𝜌𝑑𝑚𝑘𝑑𝑚 + 𝜀𝜌𝑎𝑝𝑘𝑎𝑝

𝜌𝑑𝑚

𝜌𝑑

; 𝑘𝑑 =

(27)

The convective heat transfer coefficients can be calculated from the Nusselt number in the isosceles triangular channel [24]. 𝑁𝑢𝑇 = 0.943 × (𝛼5 + 5.3586𝛼4 ― 9.2517𝛼3 + 11.9314𝛼2 ― 9.8035𝛼 + 3.3754)/𝛼5 𝑁𝑢𝐻 = 2.059 × (𝛼5 + 1.2489𝛼4 ― 1.0559𝛼3 + 0.2515𝛼2 + 0.1520𝛼 ― 0.0901)/𝛼5 𝑁𝑢 =

𝑁𝑢𝑇 + 𝑁𝑢𝐻

(28)

2

where α is the ratio between the height and width of air duct. For the dehumidification channel, 𝑏′

𝑏

α = 𝑎′, and for the cooling channel, α = 𝑎. The convective heat and mass transfer coefficients are estimated by:

13

𝐻ℎ =

𝑁𝑢 × 𝑘𝑎 𝐷ℎ

; 𝐾𝑚 =

𝑆ℎ × 𝐷𝑎,𝑎 𝐷ℎ

𝑇1.685 𝑎

; 𝐷𝑎,𝑎 = 1.758 × 10 ―4

𝑃0

(29)

where the 𝑆ℎ is supposed to be equal to 𝑁𝑢 according to the analogy between heat and mass transfer [25]. The adsorption isotherms for silica gel desiccant in Ref. [25] show a good agreement with the experimental data [18], which is selected to calculate the absorbed water content of the desiccant:

{

𝜑𝑤 = (3.4188 × 𝑊𝑑)1.3369 0.622𝜑𝑤𝑃𝑠𝑟

𝑌𝑑 = 𝑃0 ― 𝜑𝑤𝑃𝑠𝑟 𝑃𝑠𝑟 = exp (23.196 ―

(30)

3816.44 𝑇𝑠1 ― 46.13)

The adsorption heat of silica gel, 𝑞𝑠𝑡, is calculated by [26]: 𝑞𝑠𝑡 =

+ 3500) × 1000, 𝑊 < 0.05 {( ― 12400𝑊 (1400𝑊 + 2950) × 1000, 𝑊 ≥ 0.05 𝑑

𝑑

𝑑

𝑑

(31)

2.5 Initial and boundary conditions The initial conditions of adsorption or desorption process are the final states of the previous process due to the periodic operation of DCCFHE system. They are given by: 𝑌(0,𝑥) = 𝑌(𝑡𝑝𝑝,𝑥); 𝑇(0,𝑥) = 𝑇(𝑡𝑝𝑝,𝑥)

(32)

The inlet boundary conditions for the adsorption process: 𝑢1,𝑖𝑛(𝑡𝑎𝑑,0) = 𝑢1,𝑎𝑑,𝑖𝑛; 𝑌𝑎1,𝑖𝑛(𝑡𝑎𝑑,0) = 𝑌𝑎1,𝑎𝑑,𝑖𝑛; 𝑇𝑎1,𝑖𝑛(𝑡𝑎𝑑,0) = 𝑇𝑎1,𝑎𝑑,𝑖𝑛; 𝑢2,𝑖𝑛(𝑡𝑎𝑑,0) = ― 𝑢2,𝑐,𝑖𝑛; 𝑌𝑎2,𝑖𝑛(𝑡𝑎𝑑,0) = 𝑌𝑎2,𝑐,𝑖𝑛; 𝑇𝑎2,𝑖𝑛(𝑡𝑎𝑑,0) = 𝑇𝑎2,𝑐,𝑖𝑛

(33)

The inlet boundary conditions for the regeneration process: 𝑢1,𝑖𝑛(𝑡𝑟,0) = 𝑢1,𝑟,𝑖𝑛; 𝑢2,𝑖𝑛(𝑡𝑟,0) = 0; 𝑌𝑎1,𝑖𝑛(𝑡𝑟,0) = 𝑌𝑎1,𝑟,𝑖𝑛; 𝑇𝑎1,𝑖𝑛(𝑡𝑟,0) = 𝑇𝑎1,𝑟,𝑖𝑛

(34)

2.6 Fin efficiency For the fin efficiency 𝜂𝑓,𝑠𝑡 in the dehumidification channels, the conventional fin efficiency equation cannot be used in the present situation since adsorption heat is generated. The fin efficiency expression needs to be deduced. According to the aforementioned analysis in Fig. 2, there is an adiabatic surface at the half-height of each fin. The following derivation of fin efficiency 𝜂𝑓,𝑠𝑡 is based on the half-height fin as shown in Fig. 4.

14

Fig. 4 Schematic of a half-height fin In this paper, the fin efficiency is defined by the ratio between the heat transfer from fin to air and the heat transfer when the fin is at the temperature of fin-base (separator)，which is same to the definition of fin efficiency in Ref. [10]. 𝑄𝑓 + 𝑄𝑠𝑡,𝑓

∫𝐻ℎ(𝑇𝑓 ― 𝑇𝑎)𝑑𝐴

𝜂𝑓,𝑠𝑡 = ∫𝐻 (𝑇 ℎ

𝑠𝑝

(35)

= 𝐻ℎ𝐴𝑓(𝑇𝑠𝑝 ― 𝑇𝑎) ― 𝑇 )𝑑𝐴 𝑎

where the 𝑄𝑓 is the heat transfer from fin base to air due to heat conduction and 𝑄𝑠𝑡 is the released adsorption heat on the surface of fin. They are calculated by: 𝑑𝑇

𝑑𝑇

𝑄𝑓 = ― 𝑘𝑚𝐴𝑓,𝛿 ― 𝑖𝑛𝑓 𝑑𝑙 ∣𝑙 = 0 = ― 𝑘𝑚𝑠𝑖𝑛2𝐴𝑓,𝑖𝑛𝑓 𝑑𝑧 ∣𝑧 = 0 ∂𝑊𝑑

𝑄𝑠𝑡,𝑓 = 𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓𝑙

(36)

∂𝑡

For the half-height fin without desiccant layer, ignoring the transient term, energy conservation equation can be written as: 𝑑2𝑇 𝑑𝑙2

ℎ

(37)

+ 𝑘𝑚 = 0

where the ℎ is equivalent volume heat source derived from the convective heat transfer on the interfaces between fin and air stream.

ℎ = ―

𝑃𝑓,𝛿 ― 𝑖𝑛𝑓∆𝑙(𝑇 ― 𝑇𝑎) 𝐴𝑓,𝛿 ― 𝑖𝑛𝑓∆𝑙

=―

𝑃𝑓,𝛿 ― 𝑖𝑛𝑓𝐻ℎ(𝑇 ― 𝑇𝑎)

(38)

𝐴𝑓,𝛿 ― 𝑖𝑛𝑓

Substituting Eq. (38) into Eq. (37), the equation can be written as: 𝑑2𝑇 𝑑𝑧

2

―

𝑃𝑓,𝛿 ― 𝑖𝑛𝑓𝐻ℎ(𝑇 ― 𝑇𝑎) 𝑠𝑖𝑛2𝑘𝑚𝐴𝑓,𝛿 ― 𝑖𝑛𝑓

(39)

=0

While for the half-height fin with desiccant layer in Fig. 4, considering the generated adsorption heat, the energy conservation equation in the element ∆𝑙 is:

15

𝑑2𝑇

∂𝑊𝑑

𝑘𝑚 𝑑𝑙2 𝐴𝑓,𝛿 ― 𝑖𝑛𝑓∆𝑙 + ℎ,𝑠𝑡𝐴𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓∆𝑙 + 𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓∆𝑙

∂𝑡

=0

(40)

=0

(41)

The Eq. (40) can be written as follow: 𝑑2𝑇

𝑠𝑖𝑛2𝑘𝑚 𝑑𝑧2 𝐴𝑓,𝑖𝑛𝑓∆𝑧 + ℎ,𝑠𝑡𝐴𝑓 ― 𝑑,𝑖𝑛𝑓∆𝑧 + 𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝑖𝑛𝑓∆𝑧 𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓∆𝑙𝐻ℎ(𝑇 ― 𝑇𝑎)

ℎ,𝑠𝑡 = ―

𝐴𝑓 ― 𝑑,,𝛿 ― 𝑖𝑛𝑓∆𝑙

=―

𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓𝐻ℎ(𝑇 ― 𝑇𝑎) 𝐴𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓

∂𝑊𝑑 ∂𝑡

(42)

Since 𝑘𝑚 ≫ 𝑘𝑑, the heat conduction in the l direction mainly passes through the metal fin, so the heat conduction through the desiccant is neglected in the Eq. (40) and Eq. (41). The third term of Eq. (41) represents the internal heat source generated by adsorption heat. The Eq. (41) is derived as follow: 𝑑2𝑇 𝑑𝑧2

―

𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓𝐻ℎ(𝑇 ― 𝑇𝑎) 𝑠𝑖𝑛2𝑘𝑚𝐴𝑓,𝛿 ― 𝑖𝑛𝑓

+

∂𝑊𝑑 ∂𝑡

𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓 𝑠𝑖𝑛2𝑘𝑚𝐴𝑓,𝛿 ― 𝑖𝑛𝑓

=0

(43)

Eq. (43) also can be expressed as 𝑑2𝑇 𝑑𝑧

2

―

𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓𝐻ℎ(𝑇 ― 𝑇𝑎,𝑎𝑣𝑔) 𝑠𝑖𝑛2𝑘𝑚𝐴𝑓,𝛿 ― 𝑖𝑛𝑓

where 𝑇𝑎,𝑎𝑣𝑔 = 𝑇𝑎 +

(44)

=0 ∂𝑊𝑑 ∂𝑡

𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓 𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓𝐻ℎ

，it is found that the Eq. (44) has the same form as Eq.

(39). Substituting 𝜃 = 𝑇 ― 𝑇𝑎,𝑎𝑣𝑔 into the Eq. (44) can imply 𝑑2𝜃 𝑑𝑧2

= 𝑚2𝜃

(45)

The boundary conditions for equation solving are 𝑇 = 𝑇𝑠𝑝 at z = 0 →𝜃0 = 𝑇𝑠𝑝 ― 𝑇𝑎,𝑎𝑣𝑔; 𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓𝐻ℎ

𝑏 𝑑𝜃

𝑧 = 2, 𝑑𝑧 = 0, where 𝑚 =

.

𝑠𝑖𝑛2𝑘𝑚𝐴𝑓,𝛿 ― 𝑖𝑛𝑓

The Eq. (45) is a second-order linear homogeneous ordinary differential equation, its general solution is 𝜃 = 𝑐1𝑒𝑚𝑧 + 𝑐2𝑒 ―𝑚𝑧

(46)

Combining the boundary conditions, the temperature distribution in the fin can be obtained: 𝜃=

𝑒𝑚𝑧 + 𝑒𝑚𝑏𝑒 ―𝑚𝑧 𝜃0 1 + 𝑒𝑚𝑏

𝑏

=

𝑐ℎ[𝑚(𝑧 ― 2)] 𝜃0 𝑚𝑏 𝑐ℎ( 2 )

(47)

The 𝑄𝑓 is calculated by

16

(𝑚𝑏2 ) 𝜃 ( ―𝑚) 𝑚𝑏 𝑐ℎ( ) 2 𝑠ℎ

𝑑𝜃 𝑄𝑓 = ― 𝑘𝑚𝑠𝑖𝑛2𝐴𝑓,𝑖𝑛𝑓 ∣𝑧 = 0 = ― 𝑘𝑚𝑠𝑖𝑛2𝐴𝑓,𝑖𝑛𝑓 𝑑𝑧

(𝑚𝑏2 ) =

= 𝑚𝑘𝑚𝑠𝑖𝑛2𝐴𝑓,𝑖𝑛𝑓𝜃0𝑡ℎ

0

𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓

(𝑚𝑏2 )

(48)

𝜃0𝑡ℎ

𝑚𝑠𝑖𝑛

Thus, according to Eq. (36), the fin efficiency 𝜂𝑓,𝑠𝑡 can be determined as follow: 𝑄𝑓 + 𝑄𝑠𝑡,𝑓

𝜂𝑓,𝑠𝑡 =

𝐻ℎ𝐴𝑓(𝑇𝑠𝑝 ― 𝑇𝑎)

=

𝑄𝑓 + 𝑄𝑠𝑡,𝑓

𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓 𝑏 (𝑇 ― 𝑇𝑎) 2 𝑠𝑝 𝑠𝑖𝑛 𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓 ∂𝑊𝑑 𝑚𝑏 + 𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓𝑙 𝜃0𝑡ℎ 2 ∂𝑡 𝑚𝑠𝑖𝑛

()

( )

(

= 𝜂𝑓 1 𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓 𝑏 (𝑇 ― 𝑇𝑎) 2 𝑠𝑝 𝑠𝑖𝑛 ∂𝑊𝑑 ∂𝑊𝑑 𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓 𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓 ∂𝑡 ∂𝑡 ― + 𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓(𝑇𝑠𝑝 ― 𝑇𝑎) 𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓(𝑇𝑠𝑝 ― 𝑇𝑎)

=

()

)

= 𝜂𝑓 +(1 ― 𝜂𝑓) where 𝜂𝑓 =

(𝑚𝑏2 )

𝑡ℎ

𝑚𝑏 2

∂𝑊𝑑 ∂𝑡

𝑞𝑠𝑡(1 ― 𝜀)𝑓𝜌𝑑𝑑𝐴𝑑,𝛿 ― 𝑖𝑛𝑓

(49)

𝐻ℎ𝑃𝑓 ― 𝑑,𝛿 ― 𝑖𝑛𝑓(𝑇𝑠𝑝 ― 𝑇𝑎)

. In this study, the 𝑇𝑠𝑝 =

𝑇𝑠1 + 𝑇𝑠2 2

. It can be found from Eq. (49) that when

there is no desiccant layer on the fin surface, Eq. (49) degenerates into 𝜂𝑓,𝑠𝑡 = 𝜂𝑓 =

(𝑚𝑏2 )

𝑡ℎ

𝑚𝑏 2

, which

is the same form to the conventional expression for fin efficiency without desiccant layer. Due to the presence of the desiccant, the adsorption or desorption heat during dehumidification cycle would cause the change of fin efficiency, so the 𝜂𝑓,𝑠𝑡 is an apparent fin efficiency rather than conventional fin efficiency. 2.7 Pressure drop The friction loss as well as contraction at the inlet and expansion at the outlet of air duct result in the pressure drop of air stream. The pressure drop in each duct of the DCCFHC can be calculated as follow [24]: 𝐺2𝑎

(

∆𝑃𝑖 = 2𝑔𝜌𝑎,𝑖𝑛[1 ― 𝜎2 + 𝐾𝑐𝑜 +2

𝜌𝑎,𝑖𝑛

𝜌𝑎,𝑜𝑢𝑡

)

4𝐿

𝜌𝑎,𝑖𝑛

(𝜌1)𝑎𝑣𝑔 ― (1 ― 𝜎2 ― 𝐾𝑒𝑥)𝜌

― 1 +𝐹𝐷ℎ𝜌𝑎,𝑖𝑛

𝑎,𝑜𝑢𝑡

](50)

17

1

1

1

1

where (𝜌)𝑎𝑣𝑔 = 2(𝜌𝑎,𝑖𝑛 + 𝜌𝑎,𝑜𝑢𝑡). Considering the difference of air density between inlet and outlet states is small, thus 𝜌𝑎,𝑖𝑛 = 𝜌𝑎,𝑜𝑢𝑡 = 𝜌𝑎 is used to calculate the pressure drop. 𝐺𝑎 = 𝜌𝑎𝑢 is the mass velocity and 𝑔 = 1 is the proportionality constant in the Newton’s second law of motion. Contraction and expansion coefficients 𝐾𝑐𝑜 and 𝐾𝑒𝑥 are obtained by the curve fitted equations in the chart given by Shah and Sekulic for the laminar flow in the triangular tube [24]. 𝐾𝑐𝑜 = ―0.42598𝜎2 +0.02332𝜎 + 1.26445𝐾𝑒𝑥 = 1.01464𝜎2 ―2.87075𝜎 + 1.00524 (51) For the isosceles triangular channel, the friction coefficient is evaluated by the following correlation [24]: 𝐹=

12(𝛼3 + 0.2592𝛼2 ― 0.2046𝛼 + 0.0552)

(52)

𝛼3𝑅𝑒

The total pressure drop in one dehumidification cycle is calculated by: (53)

∆𝑃 = ∆𝑃1,𝑎𝑑 +∆𝑃2,𝑐 +∆𝑃1,𝑟 2.8 Model validation

The present model is validated against the experimental results of two silica gel coated DCCFHEs in our previous study [18]. Fig. 5 illustrates the schematic diagram of the experimental DCCFHE system which consists of temperature/humidity controlled room, blower, ultrasonic flow meter (Aichi tokei denki Co., Ltd, TRX80D-C/4P, Accuracy: ±2.5%RS), hygrometer (Vaisala, HUMICAP HMT-333, Accuracy: ±0.2 K, ±1%RH), air heater and DCCFHE with two air ducts made of polycarbonate. The whole system was placed in a room where the temperature can be adjusted and kept constant. The temperature/humidity controlled room can provide the air with required temperature and humidity. Rectification plates were installed at positions 125 mm and 250 mm of air duct in the front of the DCCFHE in order to introduce sufficiently developed air stream. Three K-type sheath thermocouples were installed 30 mm away from each of inlet and outlet of DCCFHE.

18

Fig.5 Schematic diagram of experimental system The dehumidification performance of the DCCFHEs with different thickness of desiccant layer (0.0794 mm and 0.148 mm) was experimentally investigated under wide range of operating conditions (volume flow rate of process air ranging from 9.2 m3/h to 36.8 m3/h, volume flow rate of cooling air from 0 m3/h to 46.1 m3/h ). The DCCFHEs are composed of 11 channel layers (six of them are cooling channel layer). The moisture is removed when process air flows through the dehumidification channels in adsorption process. Meanwhile, the cooling air is introduced into the cooling channels to take away the adsorption heat. In regeneration process, the regeneration air flows (volume flow rate is 36.8 m3/h) directly into dehumidification channels to desorb the adsorbed moisture. The inlet air velocities of dehumidification channel and cooling channel are calculated as follow: 𝑢1 =

(𝑛1 + 𝑛2) × 𝑚𝑎1

(𝑛1 + 𝑛2) × 𝑚𝑎2

𝑛1𝜌𝑎1𝜎1𝐿𝑦𝐿𝑧

𝑛2𝜌𝑎2𝜎2𝐿𝑥𝐿𝑧

; 𝑢2 =

(54)

The numerical model was established in the finite element based solver Comsol Mutiphysics 5.4. The total number of grids is 940. The partial-differential equation interfaces were applied to establish the description of Eqs. (18)-(23), and the model was solved through direct solver/PARDISO solver (Sparse matrix algorithm). The time stepping approach is implicit, backward finite difference in transient solver with maximum time step less than 1 s.

19

In the validation process, the relative deviations between experimental and numerical results were calculated every ten seconds. The simulated input parameters are listed in Table 1. It can be observed that the predicted data in terms of transient outlet humidity ratio and temperature shows a good agreement with the experimental results as depicted in Fig. 6. The deviations between the simulated data and experimental results are less than 5 % for outlet temperature and less than 20 % for outlet humidity ratio. The relatively large deviations are always concentrated in the initial period of the adsorption process due to state switching and response time of instrument. The hygrometer tends to require a larger response time compared to thermocouple, which results in that the accurate measurement of humidity ratio is much harder than that of temperature. In addition, the residual heat in the experimental system after regeneration produces the decrease in relative humidity of process air, which reduces the adsorption rate of desiccant. These facts are responsible for the larger humidity deviation. It should be mentioned that the aforementioned assumptions in simplifying the governing equations may result in some negative effects on the prediction accuracy of model. Nevertheless, the model still shows a reliable accuracy, which can be adopted to predict the dynamic dehumidification performance of DCCFHE system.

Table 1. Input parameters for model validation Desiccant and metal properties 𝜌𝑑𝑑

554 (kg/m3)

𝐶𝑝,𝑑𝑑 921 (J/kg/K)

𝑓

0.8

𝜀

0.3

𝑘𝑑𝑑 0.11 (W/m/K)

𝑟𝑝

2.5nm

𝜏𝑎

3.0

𝜏𝑠

3.0

𝐶𝑝,𝑚

921.1 (J/kg/K)

𝑘𝑚

238(W/m/K)

𝜌𝑚

2670(kg/m3)

Adsorbate properties 𝐶𝑝,𝑑𝑎

1007 (J/kg/K)

𝐶𝑝,𝑤 4180 (J/kg/K)

𝑘𝑣

0.0196 (W/m/K)

𝐶𝑝,𝑣

1872 (J/kg/K)

𝑘𝑑𝑎 0.0263 (W/m/K)

𝑘𝑤

0.613 (W/m/K)

𝜌𝑑𝑎

1.1614 (kg/m3)

20

Geometrical parameters of DCCFHE 𝐿𝑥

94 (mm)

𝐿𝑧

101 (mm)

𝑏

8 (mm)

𝐿𝑦

94 (mm)

𝑎

2.5 (mm)

𝛿𝑓

0.1 (mm)

𝛿𝑠𝑝

1.1 (mm)

𝛿𝑑

0.0794, 0.148 (mm)

𝑇𝑎1,𝑎𝑑,𝑖𝑛 = 𝑇𝑎2,𝑐,𝑖𝑛

303.15 (K)

𝑇𝑎1,𝑟,𝑖𝑛353.15 (K)

𝑌𝑎1,𝑎𝑑,𝑖𝑛 = 𝑌𝑎2,𝑐,𝑖𝑛

0.016 (kg/kg)

𝑌𝑎1,𝑟,𝑖𝑛0.016 (kg/kg)

Operating parameters

21

𝑡𝑎𝑑 = 𝑡𝑟

480 (s)

Fig. 6 Comparison between experimental results and numerical data for transient outlet humidity ratio and temperature

3. Results and discussion The established numerical model was used to investigate the dehumidification performance of DCCFHE system under various operating and structural parameters listed in Table 2. One parameter is varied at one time to investigate its effect while all other parameters remain the same as the baseline values of Table 2. During regeneration process, regeneration air flows directly into the dehumidification channels to desorb the adsorbed moisture. The regeneration air velocity is fixed at 1 m/s. In this study, a full regeneration process was firstly simulated and then the final states of regeneration equilibrium were taken as the initial conditions of the first dehumidification cycle. So each study case has the same initial conditions. Four dehumidification cycles were calculated and it was found the cycle characteristics can be steady after the second cycle. It should be mentioned that all the described results were obtained under steady cycle (the third dehumidification cycle), except the results of transient variations in outlet humidity ratio and temperature. Similarly, effect of heat transfer performance in dehumidification and cooling sides on dehumidification performance were analyzed respectively.

Table 2. Various operating and structural parameters Parameters

Baseline values

Parametric variations

𝑢1

1 (m/s)

1-5 (m/s)

𝑢2

4 (m/s)

0-5 (m/s)

𝛿𝑑

0.2 (mm)

0.05-0.25 (mm)

𝛿𝑓

0.1 (mm)

0.1-0.3 (mm)

𝑎 (fin pitch)

2.5 (mm)

1.5-3.5 (mm)

𝑏 (fin height)

8 (mm)

6-10 (mm)

22

3.1 Evaluation indices The moisture removal capacity DD and dehumidification coefficient of performance DCOP as two different evaluation indices were adopted to analyze the performance of the DCCFHE system. Moisture removal capacity DD is defined as the absolute dehumidification capacity of the DCCFHE: (55)

𝐷𝐷 = 𝑌𝑎1,𝑖𝑛 ― 𝑌𝑎1,𝑜𝑢𝑡

where the 𝑌𝑎1,𝑖𝑛 is the inlet humidity ratio of process air and the 𝑌𝑎1,𝑜𝑢𝑡 is the time-average value of outlet humidity ratio of process air. The auxiliary blower is needed to drive the air flow in the air channels and its power consumption is evaluated as 𝐴𝐵𝑃 =

𝑚𝑎∆𝑃𝑖

(56)

𝜌 𝑎𝜂 𝑏

The blower efficiency 𝜂𝑏 is assumed to be 0.35 based on its typical performance in practical application [27]. The dehumidification coefficient of performance, DCOP, describes the ratio between the thermal power related to the air dehumidification and the energy consumption in one dehumidification cycle. 𝑚𝑎1,𝑎𝑑 × 𝐷𝐷 × ∆ℎ𝑣𝑠

𝐷𝐶𝑂𝑃 = 𝑚𝑎1,𝑟(ℎ𝑎1,𝑖𝑛,𝑟 ― ℎ𝑎1,𝑎𝑚) + 𝐴𝐵𝑃1,𝑎𝑑 + 𝐴𝐵𝑃2,𝑐 + 𝐴𝐵𝑃1,𝑟

(57)

It is worth pointing out that the power consumed by auxiliary blower is usually much less than the regenerative heat energy. The latent heat of vaporization of water, ∆ℎ𝑣𝑎, is calculated by the following equation [28]: ∆ℎ𝑣𝑎 = ―0.614342 × 10 ―4(𝑇𝑎1,𝑖𝑛 ― 273.15)3 +0.158927 × 10 ―2(𝑇𝑎1,𝑖𝑛 ― 273.15)2 (58) ―0.236418 × 10(𝑇𝑎1,𝑖𝑛 ― 273.15) +0.250079 × 104 Enthalpy of moisture air is determined by [10]: ℎ𝑎 = 103 × [1.006𝑇𝑎 + 𝑌𝑎(2501 + 1.86𝑇𝑎)]

(59)

3.2 Parametric study 3.2.1 Effect of process air velocity Effect of process air velocity on the transient outlet humidity ratio and temperature of the DCCFHE system was simulated and plotted in Fig. 7(a) and (b), respectively. In adsorption process, the outlet humidity ratio decreases quickly at the initial period, and then it generally increases with time until approaching the inlet humidity ratio due to the increasing desiccant

23

saturation. The outlet temperature also shows a large decrease in initial period of adsorption process as the residual heat of previous regeneration process was removed. After that, the outlet temperature slowly decreases until it approaches the inlet temperature since the adsorption heat is effectively taken away by the cooling air. As the air velocity increases, the minimum of outlet humidity ratio shows an increasing trend and the time to reach the corresponding minimum is getting shorter and shorter. This is mainly attributed to the faster desiccant saturation and shorter residence time of process air in the dehumidification channels. The shorter residence time is also conducive to decrease the outlet temperature of process air as shown in Fig. 7(b). In regeneration process, Fig. 7(a) and (b) indicate that the curves of outlet humidity ratio and temperature almost coincide under different process air velocity. This is because the regeneration process encounters the same operating conditions. The absorbed water in desiccant was quickly desorbed by the hot and dry regeneration air in the initial period of regeneration process, so the outlet humidity ratio reaches a very high value in a short time and then gradually decreases to near the inlet humidity ratio. Correspondingly, as the heat consumption for desorption and sensible heating decreases, the outlet temperature generally increases with time but is lower than the inlet regeneration temperature at the end of regeneration process. According to the standards of thermal comfort zones proposed by the ASHRAE [29], assuming that the indoor space need to be maintained at the temperature of 298 K and relative humidity of 50%, then the absolute humidity ratio of supply air should be lower than 0.01 kg/kg. It can be found from Fig. 7(a) that the effective dehumidification time (which has been defined in Ref. [23]) decreases with the increase in air velocity. In particular, the outlet humidity ratio can no longer meet the demand of indoor space when the air velocity exceeds 2 m/s. The calculated average outlet humidity ratio and temperature of adsorption process under different process air velocity were depicted in Fig. 7(c). The high air velocity decreases the average outlet temperature, while it increases the average outlet humidity ratio. Accordingly, the significant decrease in moisture removal capacity DD is observed as depicted in Fig. 7(d). It is also found that as the air velocity increases from 1m/s to 5m/s, the total pressure drop ∆𝑃 almost linearly grows from 77.1 to 152.6 Pa. It is remarkable that the DCOP is approximately stable at 0.19 owing to the fact that the increase in mass flow compensates the fall in DD.

24

25

Fig. 7. Effect of process air velocity on (a) transient outlet humidity ratio during successive dehumidification cycle; (b) transient outlet temperature during successive dehumidification cycle; (c) average outlet humidity ratio and temperature of adsorption process; (d) DD, DCOP and ∆𝑃 3.2.2 Effect of cooling air velocity Since the air in dehumidification channels periodically alternates between process air and regeneration air, the initial states of each adsorption or desorption process are thus the final states of the previous process. When the desorption process is completed, there is a large amount of residual heat in the desiccant and metal layer, which not only causes a decrease in adsorption capacity of desiccant, but also hinders the removal of adsorption heat in time. As 26

shown in Fig. 8(a) and (b), for the case without cooling air (0 m/s), the outlet humidity ratio slowly increases after a slight decrease during adsorption process. The minimum of outlet absolute humidity ratio is higher than 0.01kg/kg, which cannot satisfy the requirement of target outlet humidity. Correspondingly, the outlet temperature shows a moderate decrease in the adsorption process due to the side effect of the residual heat and adsorption heat. On the contrary, when the cooling air is introduced into the cooling channels, the outlet humidity ratio of process air receives a rapid decrease at the initial period of adsorption process until it reaches the corresponding minimum and then quickly increases to near the inlet humidity ratio. All of these minima can be lower than the target outlet humidity and they decrease with the increase in cooling air velocity. The cooling air also contributes to decrease the outlet temperature of process air. The higher the cooling air velocity, the faster the outlet temperature drops in the adsorption process due to the removal of residual heat and adsorption heat. During regeneration process, Fig. 8(a) and (b) show that the case without cooling air has lower outlet humidity ratio and higher outlet temperature than these cases with cooling air. This is because the more residual heat and adsorption heat reduce the water uptake in adsorption process and the heat consumption for desorption and sensible heating in regeneration process. The higher cooling air velocity enhances the heat transfer between the dehumidification and cooling sides, resulting in a better cooling effect for the desiccant. Consequently, the adsorption capacity of desiccant is promoted. Fig. 8(c) shows that the average outlet humidity ratio and temperature of adsorption process decrease with the increase in cooling air velocity. As the air velocity increases from 0m/s to 5m/s, the average outlet temperature of process air shows a large decrease from about 323 K to 308 K. This is of great significant for desiccant cooling system, because it greatly reduces the sensible heat load at the subsequent air temperature regulation. The higher cooling air velocity, the larger adsorption rate, which allows the desiccant to reach adsorption saturation with a faster rate. As a result, the transient outlet humidity ratio increases at a faster rate to even exceed these of values at lower cooling air velocity as depicted in Fig. 8(a). So Fig. 8(c) shows that the average outlet humidity ratio is just slightly reduced as the cooling air velocity increases. Fig. 8(d) depicts the variations of DD, DCOP and ∆𝑃 under different cooling air velocity. It is found that a marked improvement of DD and DCOP can be achieved by simply passing cooling air. The DD and DCOP obtain about 35% improvement at the cooling air velocity of 1m/s compared to that of case without cooling air. However, as the air velocity increases from 1m/s to 5m/s, the increment of DD and DCOP decreases. It should be noted that the increase in DD and DCOP is small even with air velocity of 4 m/s or more. This fact illustrates that the 27

improvement of dehumidification capacity is also limited by the desiccant adsorption capacity and heat transfer performance of the DCCFHE. The cooling of desiccant has been well achieved when the cooling air velocity reaches 4 m/s. It is unnecessary to further increase the velocity. Furthermore, the increase in air velocity will lead to the increase in total pressure drop ∆𝑃.

28

Fig. 8. Effect of cooling air velocity on (a) transient outlet humidity ratio during successive dehumidification cycle; (b) transient outlet temperature during successive dehumidification cycle; (c) average outlet humidity ratio and temperature of adsorption process; (d) DD, DCOP and ∆𝑃 3.2.3 Effect of desiccant layer thickness Effect of desiccant layer thickness on average outlet humidity ratio and temperature of adsorption process are shown in Fig. 9(a). The greater the thickness, the smaller the hydraulic diameter and cross section of air duct, which allows for a more complete dehumidification of process air due to the greater adsorption capacity and the smaller air mass flow. The average outlet humidity ratio decreases almost linearly as the thickness increases. The average outlet 29

temperature increases with increase in adsorption capacity since the greater dehumidification leads to more release of adsorption heat. Fig. 9(b) describes the variations of DD, DCOP and ∆𝑃 with the increase in the thickness of desiccant layer. It is observed that the DD and DCOP increases from about 0.9 g/kg to 5.2 g/kg and 0.04 to 0.24 respectively as the desiccant thickness increases from 0.05 mm to 0.25 mm. The greater thickness, the smaller available cross section for air flow and the greater pressure drop∆𝑃 , which in turn affects the DCOP. Nevertheless, the advantage of thicker desiccant layer far outweighs the drawback of greater pressure drop ∆𝑃, so the DCOP shows a steep increase.

30

Fig. 9. Effect of desiccant layer thickness on (a) average outlet humidity ratio and temperature of adsorption process; (b) DD, DCOP and ∆𝑃 3.2.4 Effect of fin structure The fin thickness 𝛿𝑓, fin pitch 𝑎 and fin height 𝑏 are critical structural parameters for DCCFHE, it is of great significance to investigate their effects on dehumidification performance of DCCFHE system. Fig. 10(a) shows that both average outlet humidity ratio and temperature gently increase with the increase in fin thickness. The thicker fin implies higher metal heat capacity, which results in greater heat consumption and more residual heat during regeneration process. This fact could decrease the dehumidification performance of DCCFHE system. It can be observed from Fig. 10(b) that the DD and DCOP slightly decrease with the increase in fin thickness. Since the cross section of air flow does not change and the change in structural void fraction of air duct is small, the ∆𝑃 keeps an almost constant value about 80 Pa.

31

Fig. 10. Effect of fin thickness on (a) average outlet humidity ratio and temperature of adsorption process; (b) DD, DCOP and ∆𝑃 Fig. 11(a) depicts that both the average outlet humidity ratio and temperature increase as the fin pitch become greater. The greater fin pitch, the greater heat and mass transfer distance in the air channels, which could increase the heat and mass transfer resistances. Such a fact that the dehumidification capacity is reduced and the cooling effect of cooling air is also weakened during adsorption process. More specifically, small fin pitch is in favor for the improvement of dehumidification performance. Fig. 11(b) shows that the DD and DCOP increases from about 2.9 g/kg to 6.5 g/kg and 0.14 to 0.29 respectively as fin pitch decreases from 3.5 mm to 1.5 mm. This can be attributed to the improved heat and mass transfer performance and the fact that more fins and desiccant can be included in the DCCFHE under the case of smaller fin pitch. However, the smaller fin pitch implies the greater air flow resistance and the air channels tend to be blocked. As shown in Fig. 11(b), the total pressure drop ∆𝑃 increases from about 45 Pa to 205 Pa as fin pitch decreases from 3.5 mm to 1.5 mm, therefore a tradeoff should be considered.

32

Fig. 11. Effect of fin pitch on (a) average outlet humidity ratio and temperature of adsorption process; (b) DD, DCOP and ∆𝑃 With the increase of fin height, the transfer coefficients at the air-solid interfaces increase according to the Eq. (28) and (29). And when the inlet air velocity keeps constant, the greater fin height, the greater process air mass flow, which allows more adsorption heat and residual heat to be taken away by process air during adsorption process. However, as the analysis for the fin pitch, the greater fin height, the greater mass transfer distance in the air channels, which results in the decrease in mass transfer capacity. Both the average outlet humidity ratio and temperature slightly increases with the increase in fin height as depicted in Fig. 12(a). Accordingly, the DD and DCOP reduce slightly as shown in Fig. 12(b). It is worth mentioning 33

that the greater fin height contributes to decrease the total pressure drop ∆𝑃 due to lower friction coefficient in Eq. (52).

Fig. 12. Effect of fin height on (a) average outlet humidity ratio and temperature of adsorption process; (b) DD, DCOP and ∆𝑃 3.2.5 Effect of heat transfer performance in dehumidification and cooling sides In order to investigate the effect of heat transfer performance in dehumidification and cooling sides on the dehumidification performance, the Nu defined by Eq. (28) in dehumidification and cooling sides are artificially changed to 0.5-2.5 times of the baseline Nu calculated from the baseline values in Table 2 respectively. A Nu in one side is varied at one

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time to investigate its effect while that of another side remains the baseline Nu. The air mass flows in dehumidification and cooling sides keep the same. (The corresponding inlet air velocities in the dehumidification and cooling sides are 1.83 m/s and 1 m/s, respectively). Fig. 13(a) shows the variations in average outlet humidity ratio and temperature with the multiple change of Nu in adsorption process. For the dehumidification side, the increase in Nu1 enhances the heat and mass transfer between process air and DCCFHE, so the moisture in process air is better absorbed and more residual heat and adsorption heat are taken away by process air. The average outlet humidity ratio decreases, while the average outlet temperature increases. For the cooling side, the more residual heat and adsorption heat could be removed by cooling air due to the enhanced heat transfer performance with the increase of Nu2, which improves the adsorption capacity of desiccant. Both outlet average humidity ratio and temperature decrease. It is worth noting that although the increase in Nu2 can reduce the average outlet temperature, its effect on the average outlet humidity is not obvious when the multiple change of Nu2 is greater than 1. The same trend is also observed in Fig. 13(b) for the variations in the DD and DCOP. This fact indicates that the main reason for restricting the adsorption performance at these cases is no longer the thermal side effect of the adsorption heat, but the heat and mass transfer performance on the dehumidification side. Fig. 13(b) also demonstrates that the heat transfer performance in dehumidification side is the dominant factor affecting dehumidification performance. Both DD and DCOP can receive an obvious increase with the increase in the multiple change of Nu1.

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Fig. 13 Effect of the multiple change of Nu in dehumidification and cooling sides on (a) average outlet humidity ratio and temperature of adsorption process; (b) DD and DCOP 4. Conclusions A novel transient numerical model was developed in this study to predict the dehumidification performance of an air-cooled cross-flow desiccant coated heat exchanger (DCCFHE) system. The model considered the fin efficiency of desiccant coated heat exchanger and it was well verified by comparing with experimental results. Parametric study was conducted to investigate the effects of several major operating and structural parameters on dehumidification performance. Effect of heat transfer performance in dehumidification and cooling sides on dehumidification performance was also analyzed respectively. The main findings can be summarized as: (1) The smaller process air velocity is conducive to improve dehumidification performance. With the decrease in process air velocity, the minimum transient outlet humidity ratio of process air decreases and the effective dehumidification time increases. In particular, the minimum transient outlet humidity ratio can no longer reach the target outlet humidity ratio when the air velocity exceeds 2 m/s. The smaller process air velocity, the larger DD and smaller pressure drop ∆𝑃. (2) The cooling air contributes to eliminate the side effect of adsorption heat and improve the dehumidification performance. With the increase in cooling air velocity, the minimum transient outlet humidity ratio of process air decreases and the effective dehumidification time increases. Compared to the operation case without cooling air, the DD and DCOP obtain about 36

35% improvement at the cooling air velocity of 1m/s. It should be noted that the increase in DD and DCOP is small after the air velocity reaches 4 m/s. (3) Dehumidification performance shows a near linear rise with the increase in desiccant layer thickness, but the larger thickness results in the smaller available cross section for air flow and the total pressure drop ∆𝑃 increases. (4) Dehumidification performance is not sensitive to fin thickness and fin height, while it is quite sensitive to fin pitch. The smaller fin pitch, the lower average outlet humidity ratio and temperature of process air as well as the larger DD and DCOP. However, the total pressure drop ∆𝑃 increases greatly. (5) The heat transfer performance in the dehumidification side is the dominant factor affecting dehumidification performance. Although the increase of Nu2 in the cooling side can reduce the average outlet temperature of process air, the variation in dehumidification performance is very small when the multiple change in Nu2 is greater than 1. On the contrary, both DD and DCOP can receive an obvious increase with the increase in the multiple change of Nu1 in the dehumidification side.

Conflict of Interest None declared.

Acknowledgements This work was supported by the Science and Technology Program of Guangzhou, China (No. 2016201604030014); Shanghai Rising-Star Program, China (No. 17QC1401000) The authors thank for the support of scholarship from China Scholarship Council (CSC.201804910599)

References [1]

D. La, Y. J. Dai, Y. Li, R. Z. Wang, T. S. Ge, Technical development of rotary desiccant

dehumidification and air conditioning: A review, Renewable & Sustainable Energy Reviews. 14(1)(2010) 130-147. [2]

N. Enteria, K. Mizutani, The role of the thermally activated desiccant cooling technologies in the

issue of energy and environment, Renewable & Sustainable Energy Reviews. 15(4)(2011) 2095-2122.

37

[3]

P. Vivekh, M. Kumja, D. T. Bui, K. J. Chua, Recent developments in solid desiccant coated heat

exchangers – A review, Applied Energy. 229(2018) 778-803. [4]

D. La, Y. Dai, Y. Li, T. Ge, R. Wang, Case study and theoretical analysis of a solar driven two-stage

rotary desiccant cooling system assisted by vapor compression air-conditioning, Solar Energy. 85(11)(2011) 2997-3009. [5]

T. S. Ge, Y. J. Dai, R. Z. Wang, Z. Z. Peng, Experimental comparison and analysis on silica gel and

polymer coated fin-tube heat exchangers, Energy. 35(7)(2010) 2893-2900. [6]

A. Kumar, A. Yadav, Experimental investigation of solar driven desiccant air conditioning system

based on silica gel coated heat exchanger, International Journal of Refrigeration. 69(2016) 51-63. [7]

S. J. Oh, K. C. Ng, W. Chun, K. J. E. Chua, Evaluation of a dehumidifier with adsorbent coated heat

exchangers for tropical climate operations, Energy. 137(2017) 441-448. [8]

T. S. Ge, Y. J. Dai, R. Z. Wang, Performance study of silica gel coated fin-tube heat exchanger

cooling system based on a developed mathematical model, Energy Conversion and Management. 52(6)(2011) 2329-2338. [9]

T. S. Ge, Y. J. Dai, Y. Li, R. Z. Wang, Simulation investigation on solar powered desiccant coated

heat exchanger cooling system, Applied Energy. 93(2012) 532-540. [10]

M. Jagirdar, P. S. Lee, Mathematical modeling and performance evaluation of a desiccant coated

fin-tube heat exchanger, Applied Energy. 212(2018) 401-415. [11]

W. M. Worek, Z. Lavan, Performance of a Cross-Cooled Desiccant Dehumidifier Prototype, Journal

of Solar Energy Engineering. 104(3)(1982) 187-196. [12]

V. C. Mei, Z. Lavan, Performance of Cross-Cooled Desiccant Dehumidifiers, Journal of Solar

Energy Engineering. 105(3)(1983) 300-304. [13]

S. Dini, W. M. Worek, Sorption equilibrium of a solid desiccant felt and the effect of sorption

properties on a cooled-bed desiccant cooling system, Journal of Heat Recovery Systems. 6(2)(1986) 151167. [14]

P. Majumdar, W. M. Worek, Performance of an open-cycle desiccant cooling system using advanced

desiccant matrices, Heat Recovery Systems and CHP. 9(4)(1989) 299-311. [15]

W. Yuan, Z. Yi, X. Liu, X. Yuan, Study of a new modified cross-cooled compact solid desiccant

dehumidifier, Applied Thermal Engineering. 28(17)(2008) 2257-2266. [16]

J. Jeong, S. Yamaguchi, K. Saito, S. Kawai, Performance analysis of desiccant dehumidification

systems driven by low-grade heat source, International Journal of Refrigeration. 34(4)(2011) 928-945. [17]

G. M. Munz, C. Bongs, A. Morgenstern, et al., First results of a coated heat exchanger for the use in

dehumidification and cooling processes, Applied Thermal Engineering. 61(2)(2013) 878-883. [18]

M. Kubota, S. Shibata, H. Matsuda, Water Adsorption Characteristics of Desiccant Humidity

Controlling System with Cross-flow Type Heat Exchanger Adsorber (In Japanese), Transactions of the Japan Society of Refrigerating and Air Conditioning Engineers. 30(3)(2013) 213-220. [19]

M. Kubota, N. Hanaoka, H. Matsuda, A. Kodama, Dehumidification behavior of cross-flow heat

exchanger type adsorber coated with aluminophosphate zeolite for desiccant humidity control system, Applied Thermal Engineering. 122(2017) 618-625.

38

[20]

L. A. Sphaier, W. M. Worek, Analysis of heat and mass transfer in porous sorbents used in rotary

regenerators, International Journal of Heat & Mass Transfer. 47(14)(2004) 3415-3430. [21]

L. Z. Zhang, J. L. Niu, Performance comparisons of desiccant wheels for air dehumidification and

enthalpy recovery, Applied Thermal Engineering. 22(12)(2002) 1347-1367. [22]

K.J. Sladek, E.R. Gilliland, R.F. Baddour, Diffusion on surface. 2. Correlation of diffusivities of

physically and chemically adsorbed species, Ind. Eng. Chem. Fundam. 13 (2) (1974) 100–105. [23]

L. Liu, Y. Bai, Z. He, et al., Numerical investigation of mass transfer characteristics for the desiccant-

coated dehumidification wheel in a dehumidification process, Applied Thermal Engineering. (2019) 113944. [24]

R. K. Shah, D. P. Sekulic. Fundamentals of heat exchanger design: John Wiley & Sons; 2003.

[25]

D. Cheng, E. A. J. F. Peters, J. A. M. Kuipers, Numerical modelling of flow and coupled mass and

heat transfer in an adsorption process, Chemical Engineering Science. 152(2016) 413-425. [26]

M. A. Mandegari, S. Farzad, G. Angrisani, H. Pahlavanzadeh, Study of purge angle effects on the

desiccant wheel performance, Energy Conversion & Management. 137(2017) 12-20. [27]

F. Wang, H. Yoshida, M. Miyata, Total Energy Consumption Model of Fan Subsystem Suitable for

Continuous Commissioning, ASHRAE Transactions. 110(1)(2004). [28]

T. Ge, F. Ziegler, R. Wang, A mathematical model for predicting the performance of a compound

desiccant wheel (A model of compound desiccant wheel), Applied Thermal Engineering. 30(8-9)(2010) 1005-1015. [29]

A. H. F. ASHRAE, American society of heating, refrigerating and air-conditioning engineers, Inc

Atlanta. (1997).

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Highlights 

A numerical model was established to predict the performance of DCCFHE system.



Model considered the change in fin efficiency during dehumidification cycle.



Parametric study for various air velocity and structural parameters were conducted.



Cooling air contributes to improve dehumidification performance.



Heat transfer performance in dehumidification side is the dominant factor.

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