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.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL HEAT AND MOISTURE TRANSFER DURING DRYING OF A RECTANGULAR OBJECT

The present article deals with the numerical modeling of heat and moisture transfer during the drying process of a two-dimensional (2-D) rectangular object subjected to convective boundary conditions. As is common in solids drying, it is assumed that drying takes place as a simultaneous heat and moisture transfer whereby moisture is vaporized by means of a drying fluid (e.g., air), which passes over a moist object. The governing equations representing the drying process in a 2-D rectangular object are discretized using an explicit finite-difference approach, and a computer code is developed to predict the temperature and moisture distributions inside the object. Moreover, the results obtained from the present model are compared with the experimental data available in the literature, and considerably high agreement is found.     

Unsteady heat conduction involving phase changes for an irregular bubble/particle entrapped in a solid during freezing – An extension of the heat-balance integral method

Temperature distributions in the molten layer and solid with distinct properties around a bubble or particle entrapped in the solid during unidirectional solidification are determined by applying a heat-balance integral approximation method. The present model can be used to simulate growth, entrapment or departure of a bubble or particle inclusion in solids encountered in manufacturing and materials processing, MEMS, contact melting processes, drilling, etc. In this work, the proposed heat-balance equations are derived by integrating unsteady elliptic heat diffusion equations and introducing the Stefan boundary condition. Due to the time-dependent irregular shapes of phases, coefficients of assumed quadratic temperature profiles are considered to be functions of longitudinal coordinate and time. Temperature coefficients in distinct regions therefore are determined by solving equations governing temperature coefficients derived from heat-balance equations, imposing boundary conditions, and introducing a fictitious boundary condition. The computed temperature fields show agreement with predictions from the finite-difference method. Since the number of independent variables is reduced by one, this work provides an effective method to solve unsteady elliptic diffusion problems experiencing solid–liquid phase changes in irregular shapes.     

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.     

Spatially and temporally heterothermic kinetic model of hydrogen absorption and desorption in metals with heat transport

Numerical modelling of hydrogen transport is effective for designing and optimizing various energy systems, including hydrogen storage devices, fuel cells, and nuclear fusion reactors. In the present study, we propose and demonstrate a spatiotemporally heterothermic, autonomous kinetic model of hydrogen absorption and desorption in metals for precise simulations. Our bidirectional transport model comprises elementary mass transfer processes of surface adsorption and desorption, subsurface transport, and bulk diffusion. Also implemented are heat generation and conduction stemming from the absorption enthalpy, to determine the evolution of temperature distribution in the metal body, as well as the hydrogen concentration profile. Simulations by our transport model reproduce experimental hydrogen absorption and desorption curves for various temperature levels and metal scales with a single identical set of numerical equations and kinetic parameters, to thus verify the validity of the model.     

Investigation of heat and moisture migration in unsaturated soil under natural boundary conditions

Theoretical and experimental investigations were conducted to determine the heat and moisture migration in unsaturated soil under natural surface boundary conditions. Theoretically, a new model of heat and moisture migration in unsaturated porous media was developed, in which the gradients of volume water content, temperature, and partial vapor pressure were considered as the main driving forces which influence the process of heat and moisture migration in unsaturated soil. A set of coupled, nonlinear, partial differential equations were developed, which are related dynamically to the surface boundary conditions. Heat and moisture migration in sandy soil under solar radiation and air convection were studied experimentally. Temperature, volume water content, and water table evaporation were measured under unsteady conditions. The predictions are in good agreement with experimental data from a fairly sandy soil. © 1999 Scripta Technica, Heat Trans Asian Res, 28(1): 3–17, 1999     

A theoretical study of quasisteady sphericosymmetric combustion of alcohol droplets

A distinct characteristic of alcohol droplet combustion is absorption of moisture, generated as combustion product, during early part of the droplet life. A theoretical model for combustion of alcohol droplets has been developed. The quasisteady sphericosymmetric gas phase equations have been solved analytically while the transient diffusive liquid phase equations have been solved numerically. It is observed that neglecting the effect of moisture absorption in combustion modelling leads to underprediction of droplet life and overprediction of flame temperature and flame stand-off ratio. The results show that for alcohols with boiling points lower than that of water, a significant amount of moisture, generated during combustion is absorbed by the droplet. Absorption of this moisture prolongs droplet life and reduces flame temperature. A similar effect is also observed with increasing initial moisture content in the droplet.     

Heat and mass transfer in a cross-flow membrane-based enthalpy exchanger under naturally formed boundary conditions

Heat and mass transfer mechanisms in a cross-flow parallel plate membrane-based enthalpy exchanger for heat and moisture recovery from exhaust air streams are investigated. The flow is assumed laminar and hydrodynamically fully developed, but developing in thermal and concentration boundaries. Contrary to the traditional methods to assume a uniform temperature (concentration) or a uniform heat flux (mass flux) boundary condition, in this study, the real boundary conditions on the exchanger surfaces are obtained by the numerical solution of the coupled equations that govern the transfer of momentum, thermal energy, and moisture in the two cross-flow air streams and through the membrane. The naturally formed heat and mass boundary conditions are then used to calculate the local and mean Nusselt and Sherwood numbers along the cross-flow passages, in the developing region and thereafter. A comparison was made with those results under uniform temperature (concentration) and uniform heat flux (mass flux) boundary conditions, for rectangular ducts of various aspect ratios. An experiment is done to verify the prediction of outlet moisture content.     

Steady-state heat conduction analysis of solids with small open-ended tubular holes by BFM

In this work, the boundary face method (BFM) is applied to implement steady-state heat conduction analysis of solids containing a large number of open-ended tubular shaped holes of small diameters. A new meshing scheme is used to discretize the boundary integral equations (BIE) such that the holes can be modeled by a small number of surface elements while keeps the exact geometry, resulting in substantial savings in both modeling effort and computational cost. In the scheme, each tubular pipe surface is represented with a number of curvilinear tube elements similar to the ‘hole element’ proposed by P.K. Banerjee. To model the end faces that are intersected by the tubular holes, a special triangular element with negative parts is proposed. These elements are defined in the parametric space of the surface, and the exact geometry data can be directly available from CAD models of the solids. Numerical examples show that current implementation is very efficient in modeling of solids with many holes of arbitrary shape. The temperature and flux on the pipe surfaces or inside solids are obtained with high accuracy, even the local thermal concentration on and near the holes can be captured.     

太阳辐照下湿份分层土壤中热湿传输的数值模拟

考虑温度对土壤湿分迁移的影响，建立描述存在干饱和层时的土壤热湿传递的数学模型，并就自然环境和恒定太阳辐照下两种情况进行数值模拟，获得不同环境条件下土壤中温度和湿分分布以及水分蒸发的动态特性，分析干饱和土壤层对土壤热湿迁移与水分蒸发以及温度对土壤湿分传输的影响。     

Effect of chemical reaction and heat generation or absorption on double-diffusive convection from a vertical truncated cone in porous media with variable viscosity

This work is focused on the study of combined heat and mass transfer on double-diffusive convection near a vertical truncated cone in a fluid-saturated porous medium in the presence of a first-order chemical reaction and heat generation or absorption with variable viscosity. The viscosity of the fluid is assumed to be an inverse linear function of the temperature. A boundary layer analysis is employed to derive the non-dimensional non-similar governing equations. The governing equations for this investigation are formulated and solved numerically using the fourth-order Runge–Kutta integration scheme with Newton–Raphson shooting technique. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. A parametric study illustrating the influence of chemical reaction parameter, heat generation or absorption parameter, viscosity-variation parameter, buoyancy ratio and Lewis number on the fluid velocity, temperature, concentration as well as Nusselt number and Sherwood number is conducted. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.     

Attic radiant barrier systems: A sensitivity analysis of performance parameters

During the past seven years, the Florida Solar Energy Center (FSEC) has conducted extensive experimental research on radiant barrier systems (RBS). This paper presents recent research on the development of mathematical attic models and results from a sensitivity analysis of RBS performance parameters. Two levels of modelling capability have been developed. A very simplified model based on ASHRAE procedures is used to study the sensitivity of RBS performance parameters, and a very detailed finite-element model is used to study highly complex phenomena, including moisture adsorption and desorption in attics. The speed of the simple model allows a large range of attic parameters to be studied quickly, and the finite-element model provides a detailed understanding of combined heat and moisture transport in attics. This paper concentrates on the sensitivity analysis of attic RBS performance parameters using the simplified model. The development of the model is described, and results of the analyses are presented and discussed. Results from the finite-element model are also presented and compared with measurements from a test attic to illustrate the effects of moisture adsorption and desorption in common attics. The simplified steady-state model shows excellent agreement with measured steady-state data when thermal stratification of the attic air is modelled. Results of the sensitivity analysis using this model show that the radiant barrier surface emittance and the attic ventilation inlet air temperature are the most sensitive performance parameters for attic radiant barrier systems. The detailed, finite-element model shows that moisture sorption phenomena can have significant effects in attics. The daily temperature extremes in attics are significant, and they induce a moisture flux at the surfaces of the materials bounding the air zone(s). If this moisture flux is not accounted for in detail (i.e. with fully coupled heat and moisture transport equations) inaccurate surface temperature predictions are likely to occur.     

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.     

Hygrothermal Field Considering Nonlinear Coupling Between Heat and Binary Moisture Diffusion in Porous Media

The hygrothermal field in porous media exposed to heat and moisture considering nonlinear coupling was studied. Dissolved and gaseous phases with different diffusivities were used to model the moisture in solids and voids, respectively. Heat generated by the transformation of gaseous moisture into dissolved moisture was considered along with the transformation from dissolved moisture into gaseous moisture due to a change in temperature. The balance between dissolved and gaseous moistures is determined by the chemical equilibrium. A system of nonlinear coupling diffusion equations was derived, and a steady field for an infinite strip was demonstrated.     

Numerical simulation of fluid bed drying based on two-fluid model and experimental validation

A mathematical model for batch drying based on the Eulerian “two-fluid models” was developed. The two-dimensional, axis-symmetrical cylindrical equations for both phases were solved numerically. The governing equations were discretized using a finite volume method with local grid refinement near the wall and inlet port. The effects of parameters such as inlet gas velocity and inlet gas temperature on the moisture content, temperature of solid and gas at the outlet are shown. This data from the model was compared with that obtained from experiments with a fluidized bed and found to be in reasonably good agreement.     

自然环境下湿分分层土壤中热湿迁移规律的研究

建立描述存在干饱和层时的土壤热湿传递的数学模型并进行数值模拟，获得自然环境下土壤中温度、湿分分布以及水分蒸发的动态特性，分析干饱和土壤层对土壤热湿迁移及水分蒸发的影响。数值模拟获得实验支持。     

Numerical Research on the Influence of Deborah Number on Flow and Heat Transfer of Maxwell Fluid in a Tube with Laminar Pulsating Flow

The flow and heat transfer characteristics of Maxwell fluid in a pipe under pulsating pressure gradient were studied. The governing equations were made dimensionless. The Rubin boundary condition was adopted. The flow field was solved theoretically and the temperature field was obtained using finite volume method. A general model suitable for various fluctuating characteristics and physical parameters was established. The Deborah number(De) was used to characterize the fluidity of the fluid. The influence of De on flow and temperature fields was evaluated. The Nusselt number and start-up process of Maxwell fluid were studied. Results showed that the influence of De on flow field was greater than that on temperature field. The effect of De on Nusselt number was irregular and related to the oscillation parameters. The over-shooting amplitude and oscillation time of axis center velocity in start-up flow grow larger with De.     

Exact solution of coupled heat and mass transfer with double moving interfaces in a porous half-space. Part 3: Effect of surface pressure and permeability on rates of sublimation and desorption

Coupled heat and mass transfer with double moving interfaces, taking place in a porous half-space, is defined, and exact solutions for the temperature and moisture distributions, as well as the positions of two moving fronts, are obtained. As in Part 2 of the paper, the interest is focused on the case of moderate vacuum environment pressure, where the moisture transfer is due to the result of the vapour concentration and pressure gradients. The temperature of sublimation is assumed to be unknown, whereas the temperature of desorption is still assumed to be known, and the pressure of desorption is determined by a linear assumption among pressures of sublimation, desorption and surface. The Clapeyron equation is incorporated on the sublimation front to close the equation system. The effects of the surface pressure and the permeability on the sublimation and desorption are analysed. Conclusions are drawn on the basis of the results.     

Material properties and empirical rate equations for hydrogen sorption reactions in 2 LiNH2–1.1 MgH2–0.1 LiBH4–3 wt.% ZrCoH3

2 LiNH₂–1.1 MgH₂–0.1 LiBH₄–3 wt.% ZrCoH₃ is a solid state hydrogen storage material with a hydrogen storage capacity of up to 5.3 wt.%. As the material shows sufficiently high desorption rates at temperatures below 200 °C, it is used for a prototype solid state hydrogen storage tank with a hydrogen capacity of 2 kWh_el that is coupled to a high temperature proton exchange membrane fuel cell. In order to design an appropriate prototype reactor, model equations for the rate of hydrogen sorption reactions are required. Therefore in the present study, several material properties, like bulk density and thermodynamic data, are measured. Furthermore, isothermal absorption and desorption experiments are performed in a temperature and pressure range that is in the focus of the coupling system. Using experimental data, two-step model equations have been fitted for the hydrogen absorption and desorption reactions. These empirical model equations are able to capture the experimentally measured reaction rates and can be used for model validation of the design simulations.     

The influence of radiation absorption on solar pond stability

This paper presents a study of the gravitational stability of a salty layer of a fluid subject to an adverse temperature gradient as a result of heat absorption. This is intended to model solar ponds where an artificial gradient of salt concentration in water is used to prevent convective motions induced by the absorption of solar radiation. The stability of the Boussinesq approximation of the Navier-Stokes equations is analysed for perturbations of a certain kind imposed on the stationary solution. The marginal states for the onset of convection are obtained using a Galerkin method based on a weak formulation of the governing equations. The analysis considers solar energy absorption in the layer and assumes prescribed heat flux values as boundary conditions for the temperature equation. Results are compared with those obtained earlier by different authors for a layer of fluid, heated from below, with linear profiles of both salt concentration and temperature.