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Aerogel-coated Metal Foams for Dehumidification Applications.


Commercial and residential buildings consume one-third of the world's energy. By 2025, buildings worldwide will be the largest consumers of global energy - greater than the transportation and industry sectors combined (ASHRAE 2009). A considerable part of this energy is used to maintain moisture levels for comfort and process control. Different types of solid desiccants, such as a molecular sieve, activated carbon, and silica aerogel etc, employed for humidity control have a microscopic porous structure. When they are used in air conditioning, refrigeration, and cryogenic systems, the system performance is affected by the desiccant characteristics, such as pore size, porosity, and diffusion coefficient. The solid desiccant can be deployed by coating a solid surface (a substrate). The characteristics of the substrate, such as surface area and thermal conductivity affect the moisture removal performance considerably.

One potential candidate for a substrate material is metal foam. Despite manufacturing and implementation issues, these materials hold promise as both heat exchangers and heat sinks (Han et al. 2012, Dia et al. 2012, and Nawaz et al. 2010, 2012). The open porosity, low relative density, high thermal conductivity, large surface area per unit volume, and the ability to enhance fluid mixing can make metal foam thermal management devices efficient, compact, and light-weight. Metal foam heat exchangers are anticipated to have relatively large pressure drop, but they are also expected to have a large heat transfer rate compared to conventional fins. This expectation is reinforced by the complex geometry of the foams, which results in a high degree of boundary layer restarting and wake destruction by mixing. The main advantage of desiccant systems is the separate handling of latent and sensible energy loads, thus improving efficiency by 50% in air cooling and dehumidification (Mazzei et al. 2005). The work reported herein is focused on evaluating the dehumidification performance of aerogel-coated metal foams.


Many mathematical models have been developed to predict the heat and mass transfer behavior in air humidifying/dehumidification applications with solid desiccants. A comprehensive literature review focused on heat and mass transfer modeling in porous media was presented by Ge et al. (2008). They suggested the existing theoretical models of solid desiccant systems can be broadly classified into two categories, which are based on the inclusion of various resistances considered for building the model. The gas-side resistance model considers the heat and mass transfer resistances only in the bulk gas, while solid-side resistances are ignored. Zhang et al. (2003) developed a one-dimensional coupled heat and mass transfer model to design and manufacture a honeycomb rotary desiccant wheel. The mathematical model was validated using experimental data. Sharqawaki and Lior (2008) developed a conjugate, transient, three-dimensional heat and mass transfer model for a humid laminar air stream passing over solid desiccant (silica gel) coating ducts with different cross-sectional geometries: square, circular, and triangular.

Among the gas and solid-side resistance models, most of them consider heat conduction and mass diffusion in one dimension only, but a few consider two dimensional transport. Ruivo et al. (2008) assessed the accuracy of different simplifying assumptions commonly adopted in the modeling of the thermodynamic behavior of porous desiccant media. They proposed simplified numerical methods to predict the behavior of hygroscopic rotors, most of them assuming negligible internal resistances to heat and mass transfer and/or constant properties of the desiccant wall. Sphaier and Worek (2004) developed a dimensionless correlation that accounted for local heat conduction and mass diffusion in solid sorbent materials occurring in either enthalpy exchangers or desiccant wheels. The governing equations were fully normalized using classical dimensionless groups for heat and mass transfer. Simonson and Besant (1997) presented a numerical model of coupled heat and moisture transfer during adsorption and desorption processes occurring in enthalpy wheels. The energy transfer associated with phase change can be up to six times the energy transfer due to advection; therefore, the governing energy equations were developed in a distinct way to include the fact that the energy released during the moisture transfer processes can be delivered to air.

The reliable evaluation of moisture transfer in porous materials is essential in many engineering applications and dehumidifkation process is one of them. One key aspect is a correct description of moisture flow phenomena and the transport potentials. Baker et al. (2009) investigated the significance of non-isothermal effects on the total moisture transfer through porous building materials. The investigation concluded that the vapor pressure gradient is the critical driving potential for moisture transfer, and thermal diffusion is not significant. Janssen (2011) presented a critical analysis of the investigations supporting the occurrence of thermal diffusion and found that most of the previous studies were flawed. The correct reinterpretation of previous measurements allowed him to conclude that no consistent nor significant thermal diffusion can be observed. This conclusion also agreed with a thermodynamic analysis of the process, which confirmed the existence of thermal diffusion, but also indicated its negligible magnitude. In conclusion it can be stated that thermal diffusion is not significant for moisture transfer in desiccant materials, leaving vapor pressure (concentration gradient) as the sole significant transport potential for the diffusion of water vapor in porous materials.


Determination of Effective Diffusion Coefficient

The vast majority of silica aerogels are prepared using silicon alkoxide precursors. The most common of these are tetramethyl orthosilicate (TMOS, Si [(OC[H.sub.3]).sub.4]) and tetraethyl orthosilicate (TEOS, Si [(OC[H.sub.2]C[H.sub.3]).sub.4]). The following equation explains the formation of a wet gel by TMOS:

Si[(OCH.sub.3]).sub.4 (Liq.)] + 2[H.sub.2][O.sub.(Liq.)] [right arrow] Si[O.sub.2 (Solid)] + 4H0C[H.sup.3 (Liq.)] (1)

The above reaction was conducted in methanol used as solvent. A dip coating process was used to coat the metal foams samples with wet gel, which was later dried by the super-critical drying process. A more detailed description of the sample preparation can be found in Nawaz et al. (2013a, b). Figure la shows the flow diagram of the metal foam coating process. A dynamic vapor sorption (DVS; Surface Measurement Systems) apparatus was used to determine the effective diffusion coefficient for coated aerogel samples. The experimental scheme to evaluate the response of the coated metal foam sample is presented in Figure lb. The sample was exposed to a sudden change in relative humidity and mass variation was recorded with time. The resulting data were used with the solution of the one dimensional transient diffusion equations to calculate the adsorption and desorption diffusion coefficient for coated samples. The uncertainty in the diffusion coefficients was found to be less than 1.5 % based on the uncertainty in the mass measurement.

Determination of Friction Factor-f and Colburn j-Factor

Pressure gradient and heat transfer rate in metal foams depends on the characteristics of the foams, such as pore and ligament size. Based on the experimental results, Nawaz et al. (2010, 2012, and 2013) developed empirical correlations to predict the thermal-hydraulic performance of metal foam heat exchangers. These correlations were based on thermal-hydraulic performance of 5, 10, 20 and 40 PPI metal foams (Figure 2). Through a trial and error process, it was found that the friction factor and Colburn j factor data would collapse to a single curve (equation (2) and (3)), with a goodness of fit suitable for engineering design, if pore diameter was included as a characteristic length. The Reynolds number in equations (2) and (3) is based on the hydraulic diameter:

[mathematical expression not reproducible] (2)

[mathematical expression not reproducible] (3)

When the metal foams are coated with silica aerogels, both the hydraulic diameter and the pore diameter change. Table 2 provides geometric characteristics for different types of foams before and after the coating (Uncertainty=6% of the value). Figure 3 shows the SEM images of a 5 PPI metal foam sample before and after coating with silica aerogel.

The mass transfer coefficient can be determined using the heat and mass transfer analogy.

[mathematical expression not reproducible] (4)

Simultaneous Heat and Mass Transfer Model

In order to determine the dehumidification performance of desiccant coated on foam substrate, a model was developed based on the conservation of energy and species.

The following equations describe the energy balance with appropriate initial and boundary conditions.

[mathematical expression not reproducible] (5a)

T(x,0) = [T.sub.i] (5b)

T(0,t) = [T.sub.o] (5c)

[K.sub.eff] [[partial derivative]T/[partial derivative]x] (L, t) = -[h.sub.t] [T(L, t) - [T.sub.[infinity]]] (5d)

Equation (5c) presents a isothermal surface condition, while equation (5d) provides a convection boundary condition at the surface of the coating. Similarly, the following set of equations describe the diffusion of moisture in desiccant coating,

[mathematical expression not reproducible] (6a)

C(x,0) = [C.sub.i] (6b)

[[partial derivative]C/[partial derivative]x] (0,t) = 0 (6c)

[D.sub.eff] [[partial derivative]C]/[partial derivative]x] (L,t) = -[h.sub.m][C(L,t) - [C.sub.[infinity]]] (6d)

In equation (6a), [beta] represents the thermal-diffusion coefficient. For most of the dehumidification processes in porous media, this coefficient is very small and can be ignored. Thus, the conservation equations are coupled in one way and can be solved analytically. Equation (6c) presents a boundary condition for impermeable surface and equation (6d) presents the convection boundary condition at the coating surface.

For the given boundary/initial conditions, moisture concentration in the desiccant coating is given by equation (7).

[mathematical expression not reproducible] (7)

[[lambda].sub.n] Ate the eigen values calculated by the following equation (8), [Bi.sub.m] is the mass transfer Biot number.

[mathematical expression not reproducible] (8)

Similarly, the solution for the energy conservation gives the temperature variation in the coating layer,

[mathematical expression not reproducible]

[[mu].sub.m] are the eigen values calculated based on the [Bi.sub.t] (Heat transfer Biot number).

[mathematical expression not reproducible] (10)

The saturation time for the desiccant coating can be found using the following correlation.

[mathematical expression not reproducible] (11)

When the [Bi.sub.m] is large the values of the constants of equation (11) are

[xi], = 1.5708, K = 1.2733


The heat and mass transfer model was used to predict the temperature and moisture concentration distribution in the desiccant (aerogel) coating. Figure 5a presents the moisture concentration at two different times for two thicknesses of desiccant coating. For these simulations the characteristics of a 10 PPI metal foam coated with silica aerogel ([D.sub.eff]=4.87 ([10.sup.-10])) were used. The initial desiccant temperature and the substrate surface temperature were assumed to be 273 K. The air was assumed to be 298 K with 70% relative humidity. The desiccant coating was assumed to be completely dry at the start of process. The heat of adsorption of water vapor in silica aerogel was assumed to be 50 kJ/kmol. For smaller thicknesses (0.5 mm) the concentration became uniform after 500 seconds; however, for larger thicknesses the moisture concentration was found to be changing during the same time period. Figure 5b shows the temperature variation, which continues to change due to the heat of adsorption till the mass concentration becomes uniform in the coating. The heat transfer coefficients for aerogel coated metal foams samples for varying face velocity are compared in Figures 6a and 6b. As shown in the Figures (6a and 6b) when the desiccant coated on the metal foam with smaller pore size, the resulting heat transfer coefficient and mass transfer coefficient are larger relative to those for the foams with larger pore size. However, the resulting pressure gradient is also large (Figure 7a). The saturation time for different types of desiccants coated on the metal foam is presented in Figure 7b. For Sample 1, the coating on the 10 PPI metal foam was manufactured from hydrofluoric acid used as the catalyst in the Sol-Gel process, while for sample 2, the coating was prepared using ammonium hydroxide as the catalyst. As shown in Figure 7b, both diffusivity and the coating thickness affect the saturation time. The experimentally determined desorption diffusion coefficients for both samples were almost twice the value of the adsorption diffusion coefficients (Table 1). Thus, the time required for desorption should be smaller compared to the time required for adsorption process.


A mathematical model was developed to predict the performance of aerogel-coated metal foams. The effect of thermal-diffusion was neglected. The coupled heat and mass conservation equations were solved and the results were used to predict the variation of temperature and concentration in the coated desiccants on the metal foam surface. Due to better thermal diffusivity, the temperature profile became steady in less time than that required for the concentration profile to become steady. Based on the previous studies for bare metal foams, the dehumidification performance of aerogel coated metal foams was predicted. The effect of the type of foam was investigated on the heat and mass transfer coefficients and the pressure gradient. It was found that metal foams with smaller pore sizes when coated with desiccant, provide higher heat and mass transfer coefficients, but the pressure drop per unit length was high as well. The model was used to determine the saturation time for different desiccant types and coating thicknesses. Samples with larger coating thicknesses and small diffusivity took longer to saturate with moisture.


Authors acknowledge support provided by the Air Conditioning and Refrigeration Center (ACRC), Material Research Labs (MRL), and Department of Food Science and Human Nutrition at University of Illinois at Urbana Champaign. The project is financially supported by the ACRC (an NSF-founded Industry-University Cooperative Research Center) and the ASHRAE Grant-in-aid program.

[C.sub.[infinity]]  Ambient moisture concentration (kmol/[m.sup.3])
[C.sub.0]           Initial moisture concentration (kmol/[m.sup.3])
[c.sub.p]           Specific heat of air (J/kmol-K)
[C.sub.max]         Maximum moisture adsorbed (kmol/[m.sup.3])
[D.sub.eff]         Effective diffusion coefficient ([m.sup.2]/s)
[D.sub.p]           Pore diameter (m)
[D.sub.h]           Hydraulic diameter (m)
G                   Mass flux (kg/[m.sup.2]-sec)
[h.sub.m]           Mass transfer coefficient (m/s)
[h.sub.T]           Heat transfer coefficient (W/[m.sup.2]-K)
[j.sub.Dp]          Heat transfer Colbum j factor
[j.sub.m,Dp]        Mass transfer Colburn j factor
[k.sub.eff]         Effective thermal conductivity of desiccant (W/m-K)
L                   Desiccant coating thickness (m)
Pr                  Prandtl number
[Re.sub.Dh]         Reynold number (based on hydraulic diameter)
Sc                  Schmidt number
[T.sub.i]           Initial temperature of desiccant (K)
[T.sub.o]           Surface temperature of substrate (K)
V                   Face velocity (m/s)
[alpha]             Heat of adsorption (J/kmol)
[beta]              Thermal-diffusion coefficient (kmol/sec-K)
K                   Thermal diffusivity ([m.sup.2]/s)
[rho]               Density of desiccant (kg/[m.sup.3])


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Kashif Nawaz

Student Member ASHRAE

Shelly J. Schmidt, PhD

Anthony M. Jacobi, PhD


Kashif Nawaz is a student majoring in Mechanical Engineering at University of Illinois at Urbana Champaign. Shelly J. Schmidt, PhD is a professor at University of Illinois at Urbana Champaign teaching in the Department of Food Science and Human Nutrition. Anthony M. Jacobi, PhD is a professor at University of Illinois at Urbana Champaign teaching in the Department of Mechanical Science and Engineering.
Table 1. Diffusion Coefficients of Aerogel-coated Metal Foam Samples

          Catalyst used in Sol-Gel  Adsorption diffusion
          process                   coefficient([m.sup.2]/s)

Sample 1  Hydrofluoric acid         8.34 ([10.sup.-10])
Sample 2  Ammonium hydroxide        4.87 ([10.sup.-10])

          Desorption diffusion

Sample 1  1.53 ([10.sup.-9])
Sample 2  9.23 ([10.sup.-10])

Table 2. Geometric Properties of Coated and Uncoated Metal Foams

Type of Foam  Ligament Diameter (mm) Pore Diameter (mm)
              Uncoated  Coated       Uncoated  Coated

 5            0.50      0.58         4.02      3.94
10            0.45      0.52         3.28      3.21
20            0.35      0.39         2.58      2.54
40            0.30      0.22         1.80      1.60

Type of Foam  Surface Area per unit Volume
(PPI)         ([m.sup.2]/[m.sup.3])
              Uncoated  Coated

 5             700       950
10            1000      1350
20            2000      2500
40            2800      3400
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Author:Nawaz, Kashif; Schmidt, Shelly J.; Jacobi, Anthony M.
Publication:ASHRAE Conference Papers
Date:Dec 22, 2014
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