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.     

Two-Dimensional Numerical Analysis of Membrane-Based Heat and Mass Cross-Flow Exchanger

ABSTRACT

A two-dimensional numerical simulation model for a membrane-based heat and mass exchanger was developed. The system model equations were used to determine the coupled heat and moisture transfer from the humid air to the high concentrated liquid desiccant solution (LiCl, lithium chloride) by means of a parallel stack hydrophobic permeable membrane. The two streams of air and liquid desiccant solution were arranged in cross-flow directions. The fourth-order Runge–Kutta method was employed to solve these system model equations in a steady-state condition. This model enables one to predict the latent effectiveness of a membrane-based parallel cross-flow exchanger for dehumidification purpose in response to air to liquid mass flow ratio and the mass transfer unit number.     

Influence of chitosan and porosity on heat and mass transfer in chitosan-treated porous fibrous material

This paper focuses on a theoretical investigation of the coupling mechanism of heat transfer and liquid moisture diffusion in chitosan-treated porous fibrous material. The porous fibrous materials made of cotton with different porosities are modified by chitosan solution with different concentrations. The moisture regain of the chitosan-treated porous fibrous material increases and the contact angle of the chitosan-treated fiber decreases significantly after modification. For comparison, the simultaneous heat and liquid moisture transfer in porous fibrous materials with different porosities modified by chitosan solution with different concentration are discussed. With specification of initial and boundary conditions, the distributions 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 temperature changes in chitosan-treated porous fibrous material are obtained numerically. The comparison with the experimental measurements shows the superiority of the numerical model in resolving the coupled heat and mass transfer in chitosan-treated porous fibrous material. Analysis of the computational and experimental results illustrates that the heat and mass transfer in chitosan-treated porous fibrous material is influenced by chitosan concentration and fabric porosity significantly.     

Experimental and theoretical analysis of air humidification/dehumidification processes using hydrophobic capillary contactors

This paper deals with an experimental and theoretical investigation of air humidification/dehumidification processes carried out in a hollow-fibre membrane contactor.The cross-flow contactor consists of a 1.2 m² total membrane surface of hollow polypropylene capillaries arranged in a staggered array and has a mass transfer area per unit volume of 593 m²/m³.The heat and vapour mass transfer between the liquid phase (water and LiCl saturated solution) and the process air is analysed.During the humidification process, experiments were carried out using three different mass flow rates of water (19, 35, 54 kg/h), while two different mass flow rates of LiCl saturated solution (25, 41 kg/h) were used for air dehumidification. Air flow rates ranging from 30 to 80 m³/h were considered. Variations in the relative humidity of the air and in the temperatures of the air and liquid were measured. Experiments show a high mass transfer efficiency for both humidification and dehumidification.Furthermore, a numerical model to predict heat and mass transfer through the contactor has been developed. Experimental results are in good agreement with theoretical predictions.     

Coupled heat and mass transfer through asymmetric porous membranes with finger-like macrovoids structure

Asymmetric porous membranes with finger-like macrovoids have been extensively used in various processes, either directly as the transfer media or indirectly as the substrate for active layer. Heat and mass transfer through such membranes are the key parameters influencing system performance. However, previous studies on heat and mass transport only treated these membranes as a black box of homogeneous porous media by neglecting their asymmetric nature in structure, which fails to disclose the relations between the membrane structure and system performance. To solve this problem, this study gives a more detailed investigation of the thermal and mass diffusion through these membranes, with the help of scanning electron microscope (SEM) observations of membrane surface and cross-sectional structures. In the model setup, the whole membrane is classified into three layers: a sponge-like porous support layer, a layer of porous media with finger-like macrovoids, and a thin denser skin layer with smaller pores. The model is then incorporated into the analysis of coupled heat and mass transfer in a membrane exchanger for moisture permeations. Results show that the effective diffusivity of the membrane has been dramatically improved due to the existence of more than 70,000 per meter large finger-like voids inside.     

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.     

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.     

Study of heat and moisture transfer in soil with a dry surface layer

Mathematical model for describing simultaneous heat and moisture transfer in the porous soil with a dry surface layer was developed by using the volume-averaging method. Numerical simulation was conducted to investigate water evaporation, transient distributions of temperature and moisture in the porous soil at environmental conditions, which might be useful for agricultural application. In order to validate the mathematical model and numerical method, an experiment was conducted under natural environmental conditions. An additional experiment was conducted in a closed-loop wind tunnel to investigate the temperature effect on soil moisture transport. Theoretical and experimental results indicate that the dry surface layer has an important effect on heat and moisture migration in soil and the influence of temperature on moisture transport in unsaturated soil is significant.     

Consideration of Heat Transfer Enhancement Mechanism of Nano- and Micro-Scale Porous Layer via Flow Visualization

A convective heat transfer enhancement using nano- and micro-scale porous layer surface was discovered by the authors in 2004. Heat transfer experiments, analytical considerations, and flow visualization near the porous layer were performed to grasp the heat transfer enhancement mechanism. The heat transfer experiments revealed the porous layers were able to enhance heat transfer by 20–25% in net energy compared to the bare plate, independent of substrate materials. In order to understand the mechanism, one-dimensional unsteady heat conduction analysis was performed for a liquid column in the pore. It was found that the temperature recovery of the porous layer was incapable of catching up with the very fast fluctuation, so that the porous layer might be a thermal resistance when the main flow was strongly turbulent. The vestige visualized by the tracer particles of around 0.85 μm in diameter showed a fluid behavior like “squirt” from the porous layer. From the observation of the porous layer surface, the porous layer has some micro-scale bubbles inside its own pore-connecting structure in spite of the good wetting feature. These bubbles could be a main contributor to this heat transfer enhancement. To discuss this postulation, observations of bubble behavior in a microchannel have been carried out.     

Heat and mass transfer for liquid film evaporation along a vertical plate covered with a thin porous layer

The purpose of this work is to evaluate the heat and mass enhancement of liquid film evaporation by covering a porous layer on the plate. Liquid and gas streams are approached by two coupled laminar boundary layers incorporated with non-Darcian modes. The numerical solution is obtained by utilizing a fully implicit finite difference method and examined in detail for the effects of porosity ε, porous layer thickness δ, ambient relative humidity ϕ and Lewis number Le on the average heat and mass transfer performance. It is shown that the heat and mass transfer performance may be enhanced by the presence of a porous layer. Both the average Nusselt and Sherwood numbers are increased with the decrease of ε, δ and ϕ. In addition, the influence of ε on the heat and mass transfer is significantly increased as δ is increased.     

Coupled heat and mass transfer in a counter flow hollow fiber membrane module for air humidification

Hollow fiber membrane based air humidification offers great advantages over the traditional methods because the liquid water droplets are prevented from mixing with the process air, while water vapor can permeate through the membranes effectively. The novelty in this research is that the coupled heat and moisture transport in a hollow fiber membrane module for air humidification is investigated, both numerically and experimentally. The air stream and the water stream flow in a counter flow arrangement. It is found that the membranes play a key role in humidification performances. For sensible heat transfer, both the liquid side and the membrane side resistance can be neglected, while the total heat transfer coefficients are determined by the air side heat transfer coefficients. In contrast, in mass transfer, only the liquid side resistance can be neglected, while the total mass transfer coefficients are co-determined by membrane properties and the air side convective mass transfer coefficients.     

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.     

Simultaneous heat and mass transport in paper sheets during moisture sorption from humid air

A model of simultaneous heat and mass transfer through a porous material is presented to explain transient moisture sorption by paper sheets from humid air. There are three primary resistances to moisture transport: (1) diffusion through an external boundary layer; (2) diffusion through the pore system and, (3) diffusion from the pore system into the fibers. It is found that diffusion through the fiber phase perpendicular to the plane of the sheet is not significant for the moisture content range considered here. The mass transport model is able to predict the results of transverse moisture gradient experiments which show that moisture content gradients in paper are not as large as previously thought during transient periods. The model shows that the sigmoidal temperature response of paper to a linear change of relative humidity is due to non-linearities of the moisture content isotherm and heat of sorption.     

Two-dimensional hygrothermal transfer in porous building materials

A two-dimensional mathematical model for evaluating the simultaneous heat and moisture migration in porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The numerical solution was based on the control volume finite difference technique with fully implicit scheme in time. Two validation experiments were developed in this study. The evolution of transient moisture distributions in both one-dimensional and two-dimensional cases was measured. A comparison between experimental results and those obtained by the numerical model proves that they are fully consistent with each other. The model can be easily integrated into a whole building heat, air and moisture transfer model. Another main advantage of the present numerical method lies in the fact that the required moisture transport properties are comparatively simple and easy to determine.     

Thermal-fluid transports in a five-layer membrane-electrode assembly of a PEM fuel cell

Thermal-fluid transport phenomena in a membrane-electrode assembly (MEA) of a polymer electrolyte membrane (PEM) fuel cell attached to interdigitated gas distributors are studied numerically. The MEA consists of two porous catalyst layers, two porous gas diffusion layers, and an impermeable PEM. In the catalyst layers, the overpotential heating by the electrochemical reaction under thermal equilibrium conditions produces heat that is removed by the fluids as well as the solid matrices. In the diffusion layers, the difference in the heat conductivities between the solid matrices and the fluids causes a thermal non-equilibrium in the porous medium. A two-equation approach is used to resolve the temperature difference between the solid matrices and the fluids. The effects of the porous Reynolds number, interfacial heat transfer coefficient, and overpotential heating are examined. It is found that the local maximum temperature occurs inside the cathodic catalyst layer. In addition, the temperature difference between the solid matrices and the fluids in the diffusion layers decreases with increasing the non-dimensional interfacial heat transfer coefficient. The present results have provided comprehensive heat transfer information that is helpful in understanding of the mechanisms responsible for thermal pathways in a PEM fuel cell.     

Three dimensional numerical modeling of simultaneous heat and moisture transfer in a moist object subjected to convective drying

The drying behavior of a moist object subjected to convective drying is analyzed numerically by solving heat and moisture transfer equations. A 3-D numerical model is developed for the prediction of transient temperature and moisture distribution in a rectangular shaped moist object during the convective drying process. The heat transfer coefficients at the surfaces of the moist object are calculated with an in-house computational fluid dynamics (CFD) code. The mass transfer coefficients are then obtained from the analogy between the thermal and concentration boundary layer. Both these transfer coefficients are used for the convective boundary conditions while solving the simultaneous heat and mass transfer governing equations for the moist object. The finite volume method (FVM) with fully implicit scheme is used for discretization of the transient heat and moisture transfer governing equations. The coupling between the CFD and simultaneous heat and moisture transfer model is assumed to be one way. The effect of velocity and temperature of the drying air on the moist object are analyzed. The optimized drying time is predicted for different air inlet velocity, temperature and moisture content. The drying rate can be increased by increasing the air flow velocity. Approximately, 40% of drying time is saved while increasing the air temperature from 313 to 353 K. The importance of the inclusion of variable surface transfer coefficients with the heat and mass transfer model is justified.     

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.     

Transient behavior of run-around heat and moisture exchanger system. Part І: Model formulation and verification

In Part І, a numerical model for coupled heat and moisture transfer in a run-around heat and moisture exchanger with a liquid desiccant coupling fluid is developed. The numerical model is two dimensional, transient and is formulated using the finite difference method with an implicit time discretization. The results from the numerical model for the case of only heat transfer for a single heat exchanger are compared to an available analytical solution and good agreement is obtained. For the simultaneous heat and moisture transfer in the run-around membrane energy exchanger (RAMEE), a comparison between numerical model results and experimental measurements obtained from laboratory testing for both sensible and latent effectiveness showed satisfactory agreement at different operating conditions. Part II of this paper applies the model for a range of initial conditions [32].     

Thermal management in PEMFCs: The respective effects of porous media in the gas flow channel

This study aims to evaluate the convective heat transfer enhancement of the proton exchange membrane fuel cells (PEMFC) numerically. As the higher heat transfer surfaces lead to higher heat transfer rates, a flat plate porous layer is utilized in the gas flow channel (GFC). This enhancement in heat transfer stems from the corresponding modification in the temperature and velocity profiles. The influencing parameters on these profiles are the thickness, permeability, and porosity of the GFC porous layer. After performing the simulations, the results indicate that convective heat transfer has a direct relationship with GFC porous layer's thickness and permeability. However, lower values of porosity lead to the higher Nusselt numbers. Previous investigations have also mentioned the positive impact of the microporous layer (MPL) on the water management of these fuel cells. Therefore, six different sizes of MPL and the gas diffusion layer (GDL) are utilized to evaluate their impacts on the thermal management. Results indicate that although these sizes have negligible effects on the heat transfer, Nu increases by enhancing the total size of MPL and GDL. The results also show that thicker MPLs lead to higher heat transfer rates. The evaluation of the friction factor also indicates the adverse effect of the GFC porous layer, although this undesirable effect is negligible. Finally, all the simulated values are utilized to train an artificial neural network (ANN) model with high precision. This ANN model can produce more data for sensitivity analysis and presenting respective 3D diagrams of the influencing parameters on heat transfer.     

Thermodynamic analysis of a counter flow adiabatic dehumidifier with different liquid desiccant materials

Liquid desiccant systems have been proposed as energy saving alternatives to the conventional vapor compression systems for handling the latent load. This paper presents the results from a study of the performance of a counter flow liquid desiccant dehumidifier. A heat and mass transfer theoretical model of an adiabatic packed column has been developed, based on the Runge-Kutta fixed step method, to predict the performance of the device under various operating conditions. Good agreement was found between experimental tests and the theoretical model, with the maximum deviation being ±2.9% in air outlet temperature, ±15.9% in air outlet humidity ratio and ±2.8% in solution outlet temperature. Following the model validation, the rate and the efficiency of the dehumidification process were assessed under the effects of variables, such as air temperature and humidity, desiccant temperature and humidity and air and desiccant flow rates. The three most commonly used liquid desiccant solutions, namely LiCl, LiBr and CaCl₂ were evaluated against each other. The results show that high absorber efficiency and system efficiency could be achieved under humid conditions, low air mass flow rates and LiCl as the desiccant solution.