Investigation of the 3D model of coupled heat and liquid moisture transfer in hygroscopic porous fibrous media

This paper focuses on the investigation of the 3D mathematical model to simulate the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media. The flow of the liquid moisture, the water vapor sorption/desorption by fibers and the diffusion of the water vapor are taken into account in this 3D model. Prediction-corrector method is used to solve the 3D governing equations. A series of computational results of the coupled heat and moisture transfer are obtained with the specific initial conditions and boundary conditions. The distribution of the water vapor concentration in the void spaces, the volume fraction of the liquid water in the void spaces, the distribution of the water content in fibers and the changes of the temperature in porous fibrous media are computed. It is shown that the effects of the gravity and capillary actions are significant in hygroscopic porous fibrous media. The comparison with the experimental measurements shows the reasonable agreement between the two. The results illustrate that the 3D model of the coupled heat and liquid moisture transfer in hygroscopic porous fibrous media is satisfactory.     

A fractal model for the coupled heat and mass transfer in porous fibrous media

This paper developed a mathematical model for the coupled heat and mass transfer in porous media based on the fractal characters of the pore size distribution. According to Darcy’s law and Hagen–Poiseuille’s law for liquid flows, the diffusion coefficient of the liquid water, a function of fractal dimension, is obtained theoretically. The liquid flow affected by the surface tension and the gravity, the water vapor sorption/desorption by fibers, the diffusion of the water vapor and the phase changes are all taken into account in this model. With specification of initial and boundary conditions, distributions of water vapor concentration in void spaces, volume fraction of liquid water, distribution of water molecular content in fibers and temperature changes in porous fibrous media are obtained numerically. Effects of porosity of porous fibrous media on heat and mass transfer are analyzed. The theoretical predictions are compared with experimental data and good agreement is observed between the two, indicating that the fractal model is satisfactory.     

保温用天然生物质材料的热湿特性

实验分析一些廉价天然材料(椰壳和花生壳)的导热特性。利用同心球稳态测量方法测量确定椰壳和花生壳的导热系数,以及导热系数随温度的变化规律,同时以硅酸铝纤维材料为标准试样,与天然材料的导热性能进行对比分析。还对这些材料的低温吸湿作了初步测试,分析此类材料作为低温绝热材料的吸湿特性。研究结果表明,所有材料的导热系数均随温度的升高而增大,且增大速率都近似相等。影响天然生物质材料导热性质的因素主要有：纤维或多孔固体材料中的导热、孔隙中空气的对流换热,如果温度足够高的话,还有辐射换热。     

Numerical simulation of the transient heat and liquid moisture transfer through porous textiles with consideration of electric double layer

The liquid water transport coupled with moisture and heat transfer through porous textiles is a complicated process involving simultaneous, coupled heat and mass transfers. The flows in porous textiles are different from the traditional flows transfer in porous media due to the adsorption of moisture by fibers. Based on the Poisson-Boltzmann equation for electric double layers and Navier-Stokes equation for liquid flows, a mathematical model for describing resistance effects of electric double layer (EDL) on the coupled heat and liquid moisture transfer in porous textiles is developed. The resistance effect of the EDL in porous textiles can be measured by a dimensionless number, which is called electric resistance number. It is proportional to the square of the liquid dielectric constant, the solid surface zeta potential and inversely proportional to the liquid dynamic viscosity, electric conductivity and the square of the effective pore size. With specification of initial and boundary conditions, the distributions of the temperature, moisture concentration, and liquid water content in porous textiles have been obtained. The theoretical predictions are compared with experimental data, and good agreement is observed between the two, indicating that the heat and mass transfer process are influenced by the EDL in porous textiles.     

Simultaneous heat and moisture transfer through a composite supported liquid membrane

Composite supported liquid membranes (SLM) are an efficient transfer media to recover heat and moisture from exhaust air due to the high moisture diffusivity in the liquid layer. However, heat transfer has adverse effects on moisture transfer since the water concentration in the LiCl solution decreases at higher temperatures. This study gives a detailed quantitative analysis of these effects. More specifically, simultaneous heat and moisture transfer through a composite supported liquid membrane is modeled. The SLM involved comprises three layers: two hydrophobic porous skin layers and a hydrophilic porous support layer where a layer of LiCl liquid solution is immobilized in the macro and micro pores as the permselective substance. The equations governing the heat mass transport in the microstructures, as well as the transfer of heat and moisture in the air streams adjacent to the membrane, are solved numerically in a coupled way. An experiment has been built to validate the model. The results found that though heat transfer has adverse effects on moisture transfer, in general, the effects on moisture effectiveness are quite limited. The high moisture permeation rates of SLM can be sustained when there is concomitant simultaneous heat transfer.     

Heat transfer of phase change materials (PCMs) in porous materials

In this paper, the feasibility of using metal foams to enhance the heat transfer capability of phase change materials (PCMs) in low- and high-temperature thermal energy storage systems was assessed. Heat transfer in solid/liquid phase change of porous materials (metal foams and expanded graphite) at low and high temperatures was investigated. Organic commercial paraffin wax and inorganic calcium chloride hydrate were employed as the low-temperature materials, whereas sodium nitrate was used as the high-temperature material in the experiment. Heat transfer characteristics of these PCMs embedded with open-cell metal foams were studied. Composites of paraffin and expanded graphite with a graphite mass ratio of 3%, 6%, and 9% were developed. The heat transfer performances of these composites were tested and compared with metal foams. The results indicate that metal foams have better heat transfer performance due to their continuous inter-connected structures than expanded graphite. However, porous materials can suppress the effects of natural convection in liquid zone, particularly for PCMs with low viscosities, thereby leading to different heat transfer performances at different regimes (solid, solid/liquid, and liquid regions). This implies that porous materials do not always enhance heat transfer in every regime.     

Computational modelling of heat and mass transfer during the high-temperature heat treatment of wood

During the heat treatment process, the heat and mass transfer takes place between the solid and the drying medium, and the moisture evaporation occurs within the solid due to the capillarity action and diffusion. In the current work, the three-dimensional Navier–Stokes equations along with the energy and concentration equations for the fluid coupled with the energy and mass conservation equations for the solid (wood) are solved to study the conjugate heat treatment behaviour. Whitaker’s continuum approach has been used to obtain the equations for the liquid and vapour migration within the solid. Three moisture phases are accounted for: free water, bound water, and water vapour. The model equations are solved numerically by the commercial package FEMLAB for the temperature and moisture content histories under different treatment conditions. The model validation is carried out via a comparison between the predicted values with those obtained experimentally. The comparison of the numerical and experimental results shows good agreement, implying that the proposed numerical algorithm can be used as a useful tool in designing high-temperature wood treatment processes.     

热质渗透壁面饱和多孔介质通道流动与热质传递的数值模拟

利用数值模拟方法研究了多孔介质中存在温度梯度、浓度梯度并具有热质渗透壁面时的受迫对流对传热传质的影响。采用有限容积法在同位网格上离散控制多孔介质内流体流动与热质传递方程守恒方程(即N-S)，对流项采用二阶精度的QUICK格式，扩散项采用中心差分格式。利用SIMPLE算法求解压力和速度耦合问题。利用所发展的程序研究了在不同孔隙率，不同的温度、浓度边界条件下，流场、温度场和浓度场以及Nu和Sh的变化规律。     

Fluid flow and heat mass transfer in membrane parallel-plates channels used for liquid desiccant air dehumidification

Fluid flow and convective heat mass transfer in membrane-formed parallel-plates channels are investigated. The membrane-formed channels are used for liquid desiccant air dehumidification. The liquid desiccant and the air stream are separated by the semi-permeable membrane to prevent liquid droplets from crossing over. The two streams, in a cross-flow arrangement, exchange heat and moisture through the membrane, which only selectively permits the transport of water vapor and heat. The two flows are assumed hydrodynamically fully developed while developing thermally and in concentration. Different from traditional method of assuming a uniform temperature (concentration) or a uniform heat flux (mass flux) boundary condition, the real boundary conditions on membrane surfaces are numerically obtained by simultaneous solution of momentum, energy and concentration equations for the two fluids. Equations are then coupled on membrane surfaces. The naturally formed boundary conditions are then used to calculate the local and mean Nusselt and Sherwood numbers along the channels. Experimental work is performed to validate the results. The different features of the channels in comparison to traditional metal-formed parallel-plates channels are disclosed.     

Conjugate numerical analysis of flow and heat transfer with phase change in a miniature flat plate CPL evaporator

Two-dimensional numerical model for the global evaporator of miniature flat plate capillary pumped loop (CPL) is developed to describe heat and mass transfer with phase change in the porous wick, liquid flow and heat transfer in the compensation cavity and heat transfer in the vapor grooves and metallic wall. The governing equations for different zones are solved as a conjugate problem. The side wall effect heat transfer limit is introduced to estimate the heat transport capability of evaporator. The influences of liquid subcooling, wick material, metallic wall material and non-uniform heat flux on the evaporator performance are discussed in detail.     

Investigation on heat and mass transfer in 3D woven fibrous material

A 3D mathematical model is developed to describe coupled heat and mass transfer in woven fibrous materials with consideration of its geometrical characters. The liquid water diffusion tensor is derived by matrix transformation. The finite volume method is used to discrete the governing equations, and the obtained linear discrete equations are solved by iteratively utilizing the TDMA (Tri-Diagonal Matrix Algorithm). A high order and absolutely stable difference scheme for water vapor diffusing in fiber is developed. The processes of liquid water transfer in the yarns, water vapor in both inter-yarn and intra-yarn, and their interaction with heat transfer are illustrated by a series of 3D or 4D diagrams. The effects of porosity of the yarn ε and the fabric count on heat and mass transfer are also discussed. The predictions of temperature changes on the fabric surface are compared with experimental measurements, good agreement is observed between the two.     

Effects of Non-Darcian and Inlet Conditions on the Forced Convection Along a Vertical Plate With Film Evaporation

The present study analyzes theoretically the non-Darcian effects and inlet conditions of forced convection flow with liquid film evaporation in a porous medium. The physical scheme includes a liquid–air streams combined system; the liquid film falls down along the plate and is exposed to a cocurrent forced moist air stream. The axial momentum, energy, and concentration equations for the air and water flows are developed based on the steady two-dimensional (2-D) laminar boundary layer model. The non-Darcian convective, boundary, and inertia effects are considered to describe the momentum characteristics of a porous medium. The paper clearly describes the temperature and mass concentration variations at the liquid–air interface and provides the heat and mass transfer distributions along the heated plate. Then, the paper further evaluates the non-Darcian effects and inlet conditions on the heat transfer and evaporating rate of liquid film evaporation. The numerical results show that latent heat transfer plays the dominant heat transfer role. Carrying out a parametric analysis indicates that higher air Reynolds number, higher wetted wall temperature, and lower moist air relative humidity will produce a better evaporating rate and heat transfer rate. In addition, a non-Darcy model should be adopted in the present study. The maximum error for predictions of heat and mass transfer performance will be 21% when the Darcy model is used.     

Heat and moisture transfer in fibrous thermal insulation with tight boundaries and a dynamical boundary temperature

Prefabricated, lightweight building elements are widely used in the building construction sector. Such elements consist of fibrous thermal insulation encapsulated between two metal sheets. Under various circumstances, moisture can appear in the insulation matrix. Since the temperature of the boundary metal sheets changes dynamically with meteorological conditions, heat and mass transfer between boundaries appear in this case. This paper presents a transient model of the heat and mass transfer, including the sorption and condensation processes. A numerical model considers the dynamical changing of the boundary temperatures. A parametric study considering different amplitudes of temperature change, different moisture masses and different thicknesses of the insulation matrix was made. It was found that a relatively small mass of water in the insulation matrix can result in a significantly increased average heat flux during a periodic cycle. The numerical code was verified with experiments, which showed good agreement with the numerics.     

An experimental study on moisture transport through a porous plate with micro pores

An experiment was carried out to examine heat and mass transfer between constant-temperature water and dry air through a porous plate having extremely small pores. The effects of the thermal conductivity in the porous plate on moisture transport were investigated. The controlling factor for moisture transport was found to be the thermal resistance inside the porous plate having a low-thermal-conductivity and the heat transfer at the surface of the porous plate having a high-thermal-conductivity.     

An analytical method to calculate the coupled heat and moisture transfer in building materials

A dynamic model for evaluating the transient thermal and moisture transfer behavior in porous building materials was presented. Both heat and moisture transfer were simultaneously considered and their interactions were modeled. An analytical method has been proposed to calculate the coupled heat and moisture transfer process in building materials. The coupled system was first subjected to Laplace transformation, and then the equations were solved by introducing the Transfer Function Method. The transient temperature and moisture content distribution across the material can thus be easily obtained form the solutions. The results were compared with the experimental data and other analytical solutions available in the literature; a good agreement was obtained.     

Effects of pore size distribution and fiber diameter on the coupled heat and liquid moisture transfer in porous textiles

The pore size distribution and the fiber diameter on the coupled heat and liquid moisture transfer in porous textiles are investigated to reveal the mechanisms of the coupling effects. This paper focuses on a theoretical investigation of the coupling mechanism of heat transfer and liquid moisture diffusion in porous textiles by using an improved mathematical model. In this model, the pore size distribution is assumed to be a cubic-polynomial distribution, which is close to the experimental measurements [Text. Res. J. 56 (1) (1986) 35]. The liquid diffusion behavior in porous textiles can be described as a diffusion equation. The improved diffusion coefficient can be expressed as:

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. For comparison, two types of pore distribution and the fiber diameter in the porous textiles are discussed. With specification of initial and boundary conditions, the distributions of the temperature, moisture concentration, and liquid water content in the porous textiles can be numerically computed. The comparison with the experimental measurements shows the superiority of this new model in resolving the coupled heat and liquid moisture transfer in porous textiles. The results illustrate that the heat transfer process is influenced by the pore size distribution and fiber diameter of the porous textiles.     

Melting of frozen, porous media contained in a horizontal or a vertical, cylindrical capsule

Melting of ice in porous media has been investigated experimentally and analytically for a horizontal and vertical cylindrical capsule. Quantitative results of the temperature distribution and solid-liquid interface motion and shape were obtained for inward melting with different size and types of spherical beads used as the porous media. Predictions from an analysis which considers conduction as the only mode of heat transfer in both the solid and liquid were compared to experimental data to show where natural convection becomes significant. It was found that the melting rate was augmented by natural convection in the liquid. For large differences in the thermal conductivity of the phase-change material and porous medium (e.g. water and aluminum), the effective thermal conductivity of the system was not predicted accurately by the model used, resulting in a further discrepancy between data and predictions. Moreover, the assumption of local temperature equilibrium between the void constituent and the porous medium becomes invalid for a water-aluminum bead system.     

Modeling heat and moisture transfer through fibrous insulation with phase change and mobile condensates

This paper reports on a transient model of coupled heat and moisture transfer through fibrous insulation, which for the first time takes into account of evaporation and mobile condensates. The model successfully explained the experimental observations of Farnworth [Tex. Res. J. 56 (1986) 653], and the numerical results of the model were found to be in good agreement with the experimental results of a drying test. Based on this model, numerical simulation was carried out to better understand the effect of various material and environmental parameters on the heat and moisture transfer. It was found that the initial water content and thickness of the fibrous insulation together with the environmental temperature are the three most important factors influencing the heat flux.     

Pool boiling heat transfer on copper foam covers with water as working fluid

Pool boiling heat transfer with porous media as the enhanced structure is attractive due to its simple geometry and easy operation. However, the available studies focus on low porous porosities. Metallic foams provide large porous porosities that have been less studied in the literature. In this paper a set of copper foam pieces were welded on the plain copper surface to form the copper foam covers for the pool boiling heat transfer enhancement. Water was used as the working fluid. Enhancement of pool boiling heat transfer compared with plain surface depends on the increased bubble nucleation sites, extended heat transfer area, and resistance for vapor release to the pool liquid. Effects of pores per inch (ppi) of foam covers, foam cover thickness, and pool liquid temperatures are examined. It is found that temperatures at the Onset of Nucleate Boiling (ONB) are significantly decreased on copper foam covers compared with on plain surfaces. Heat transfer coefficients of foam covers are two to three times of the plain surface. A large ppi value provides large bubble nucleation sites and heat transfer area to enhance heat transfer, but generates large vapor release resistance to deteriorate heat transfer. Therefore an optimal ppi value exists, which is 60 ppi in this paper. Generally small ppi value needs large foam cover thickness, and large ppi value needs small foam cover thickness, to maximally enhance heat transfer. Effect of pool liquid temperature on the heat transfer enhancement depends on the ppi value. For small ppi value such as 30 ppi, lower pool liquid temperature can dissipate higher heat flux at the same wall superheat. However, the heat transfer performance is insensitive to the pool liquid temperatures when large ppi values such as 90 ppi are used.