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.     

Numerical modeling of heat and mass transfer during forced convection drying of rectangular moist objects

A two-dimensional analysis of heat and mass transfer during drying of a rectangular moist object is performed using an implicit finite difference method, with the convective boundary conditions at all surfaces of the moist object. The variable convective heat and mass transfer coefficients are considered during the drying process. The external flow and temperature fields are first numerically predicted through the Fluent CFD package. From these distributions, the local distributions of the convective heat transfer coefficients are determined, which are then used to predict local distributions of the convective mass transfer coefficients through the analogy between the thermal and concentration boundary layers. Also, the temperature and moisture distributions for different periods of time are obtained using the code developed to determine heat and mass transfer inside the moist material. Furthermore, the influence of the aspect ratio on the heat and mass transfer is studied. It is found that the convective heat transfer coefficient varies from 4.33 to 96.16 W/m² K, while the convective mass transfer coefficient ranges between 9.28 × 10⁻⁷ and 1.94 × 10⁻⁵ m/s at various aspect ratios. The results obtained from the present analysis are compared with the experimental data taken from the literature, and a good agreement is observed.     

Combined heat and moisture convective transport in a partial enclosure with multiple free ports

Combined heat and moisture transport in an enclosure with free ports has been investigated numerically. Enclosed moist air interacts with the surrounding air through these free-vented ports. The governing conservation equations were solved numerically using a control volume-based finite difference technique. Appropriate velocity boundary conditions at each ports are imposed to achieve overall mass conservation across this system. Air, heat and moisture transport structures are visualized respectively by streamlines, heatlines and masslines. Effects of buoyancy ratio, thermal Rayleigh number on convective heat/moisture transfer rate and flow rate across each free-vented port are discussed. Particularly, Numerical results demonstrate that the convective heat and moisture transport patterns and transport rates on horizontal ports greatly depend on properties of porous medium, while the air exchange rate on vertical port is almost unaffected by the buoyancy ratios for most situations.     

Analysis of two‐dimensional heat and moisture transfer during drying of spherical objects

This paper deals with the numerical and analytical modelling of two‐dimensional heat and moisture transfer during drying of a spherical object. Drying is considered to be a process of simultaneous heat and moisture transfer whereby moisture is vapourized by means of a drying fluid (e.g. air), as it passes over a moist object. Numerical modelling of two‐dimensional heat and moisture transfer during drying of a spherical object is carried out using an explicit finite‐difference approach. Temperature and moisture distributions inside the object are determined by using the developed computer code. Moreover, the results predicted from the present model are compared with the experimental data available in the literature and a considerably high agreement is found. Copyright © 2003 John Wiley & Sons, Ltd.     

太阳能辅助热泵干燥粮食的数值模拟研究

粮食的干燥过程实质上是多孔介质热湿耦合传递的过程。基于多孔介质热质传递理论,通过数值模拟的方法,针对利用太阳能辅助热泵干燥粮食时热风随时间变化的情况,采用综合温度和空气绝对湿度作为瞬态边界条件来对干燥过程中粮食内部温度和水分的变化进行模拟研究。模拟结果显示小麦水分在干燥150h后达到安全水分13.6%(干基),而实验结果显示小麦水分在干燥135h后达到安全水分13.6%(干基),二者对比相差不大,并且模拟温度与试验温度吻合较好。     

Two-dimensional heat and moisture transfer analysis of a cylindrical moist object subjected to drying: A finite-difference approach

In this paper a two-dimensional numerical analysis of heat and moisture transfer during drying of a cylindrical object is presented. Drying is a process of simultaneous heat and moisture transfer whereby moisture is vaporized by means of a drying fluid (e.g., air), as it passes over a moist object. The two-dimensional analysis of heat and moisture transfer during drying of a cylindrical object is carried out using an explicit finite-difference approach. Temperature and moisture distributions inside the moist objects are obtained for different time periods and the results predicted from the present analysis are compared with two sets of experimental data available in the literature. A considerably high agreement is found between the predicted and measured values.     

Heat,air and moisture transfer through hollow porous blocks

The combined heat, air and moisture transfer in building hollow elements is of paramount importance in the construction area for accurate energy consumption prediction, thermal comfort evaluation, moisture growth risk assessment and material deterioration analysis. In this way, a mathematical model considering the combined two-dimensional heat, air and moisture transport through unsaturated building hollow bricks is presented. In the brick porous domain, the differential governing equations are based on driving potentials of temperature, moist air pressure and water vapor pressure gradients, while, in the air domain, a lumped approach is considered for modeling the heat and mass transfer through the brick cavity. The discretized algebraic equations are solved using the MTDMA (MultiTriDiagonal-Matrix Algorithm) for the three driving potentials. Comparisons in terms of heat and vapor fluxes at the internal boundary are presented for hollow, massive and insulating brick blocks. Despite most of building energy simulation codes disregard the moisture effect and the transport multidimensional nature, results show those hypotheses may cause great discrepancy on the prediction of hygrothermal building performance.     

Experimental Studies for Convective Drying of Potato

An experimental facility was built at the Indian Institute of Technology Delhi in order to examine the characteristics of convective drying of a moist object. The test facility consists of an inlet section, a divergent and convergent section, a settling chamber, a test section, and an outlet section. Initial moisture content and time-dependent moisture content of a rectangular shaped moist object (4 cm × 2 cm × 2 cm) are measured by this test facility. The potato slice was selected as a sample moist object. Moisture content was measured at different air temperatures of 40, 50, 60, and 70°C with an air velocity of 2 m/sec. The density of potato slice was determined for various drying temperatures. The volume shrinkage during drying decreased almost linearly with moisture content. The percentage air pores and porosity increased gradually with decreasing moisture content and increasing drying air temperature. Volumes of water, air, and solid content of potato were determined at different drying air temperatures. The results are validated with theoretical data.     

Numerical and experimental analysis of moisture transfer for convective drying of some products

Numerical and experimental results of moisture transfer in drying process for apple and potato slices are compared in this study. Experimental results are obtained using a cyclone type dryer. Two-dimensional analysis of heat and moisture transfer during drying of objects is carried out solving heat and mass equations using finite-volume approach. Thus, moisture distributions inside the moist objects are obtained at different time steps. Comparison of results showed that there is a considerably high agreement between experimentally measured data and predicted values. Moist distribution also presented inside the products at different time periods.     

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.     

A simple solution for transient heat transfer during heating of a slab product

A theoretical and experimental study of transient heat transfer in the heating of an individual slab product, subjected to an air flow at a temperature of 50°C and a velocity of 1 m/s, is presented. Experimental temperature measurements at the centre of the slab product were made, and the experimental heat-transfer rates were derived from the temperature data. A simplified analytical technique, using the boundary condition of the third kind in transient heat transfer, was used to predict the theoretical heat transfer rates for two cases, the first considering that the heat transfer coefficient is a convective heat transfer coefficient, and the second considering that heat transfer coefficient is the sum of the convective and radiative heat transfer coefficients. The experimental heat-transfer rates were compared with the predictions for two cases, and a very good agreement was obtained.     

Numerical study of the thermal–hydraulic performance of evaporative natural draft cooling towers

In this paper, the mathematical and physical models governing the flow, mass and heat energy of moist have been set up for an evaporative natural draft cooling tower. The models consider the effect of non-spherical shape of water drops on the flow, heat and mass transfer. Experimental data has been adopted to validate the numerical scheme. Average difference between the measured and the predicted outlet water temperature is 0.26°C. Distributions of the velocity components of the moist air, density, pressure, enthalpy and moisture content, the water temperature and its mass flux have been predicted. The simulation shows that some recirculation exits under the lower edge of the shell, where the air enthalpy, temperature, humidity and moisture content are higher, but the density is lower. The simulation also proves that the main transfer processes take place in the fill region where the percentage of latent heat transfer is predicted as 83%. However, about 90% of the heat energy is transferred via evaporation in the rain region although the total heat transfer rate there is very small compared to the fill region. Hourly performance of a natural draft cooling tower under the meteorological condition of Singapore has also been predicted.     

Laminar fluid flow and mass transfer in a standard field and laboratory emission cell

The field and laboratory emission cell (FLEC) is becoming a standard method of characterizing pollutant emissions from building materials. Based on this method, the material and the inner surface of the FLEC cap form a cone-shaped cavity. The airflow is distributed radially inward over the test surface through a slit in a circular-shaped channel at the perimeter of the chamber. After mass transfer, the air is exhausted through an outlet in the center. Usually, emission rate profiles are obtained using such cells. However, the local convective mass transfer coefficients are now needed. In this study, laminar fluid flow and mass transfer in a standard FLEC are investigated. The velocity field and moisture profiles are obtained by solving Navier-Stokes equations numerically. The whole geometry, including the air inlet and outlet, channel, air slit, and emission space, are included in the numerical modeling domain. The mean convective mass transfer coefficients are calculated and compared with the experimental data. In the test, distilled water is used in the FLEC lower chamber to substitute the emission surface. Mass transfer data are obtained by calculating humidity differences between the inlet and outlet of a gas stream flowing through the FLEC. The study concentrates on assessing the variations of velocity and humidity profiles, as well as convective mass transfer coefficients, in the cell.     

Mathematical modelling and experimental investigation of tropical fruits drying

A mathematical model has been developed to solve the heat and mass transfer equations for convective drying of tropical fruits. The model takes into account shrinkage of material and moisture content and shrinkage dependant effective diffusivity. Heat and mass transfer equations for the dryer, termed as equipment model, have also been developed to determine the changes of drying potential of the drying medium during drying. The material model is capable of predicting the instantaneous temperature and moisture distribution inside the material. The equipment model, on the other hand, describes the transfer process in the tunnel dryer and predicts the instantaneous temperature and humidity ratio of air at any location of the tunnel. Thus, the model is capable of predicting the dynamic behaviour of the dryer. The predicted results were compared with experimental data for the drying of banana slices dried in a solar dryer. Experimental results validated the model developed.     

Frost deposition in a parallel plate channel under laminar flow conditions

The subject of this paper is a theoretical and experimental study of frost formation on cooled parallel plates in laminar forced convection. In the experiments time variation of the frost layer thickness was measured at several locations downstream along the test section which was positioned in an open-loop wind tunnel. The parameters varied were air velocity (Reynolds number), air temperature, air humidity ratio, and plate temperature. The process was simulated numerically using a two-dimensional transient model based on the conservation equations of mass, momentum, energy, and species. The physical domain of interest was divided into two subdomains, one for the moist air stream between the plates (gaseous phase), and one for the frost layer (solid phase). The two sets of governing equations were coupled by boundary conditions at the moving interface which required an iterative solution strategy. With this approach, the local distribution of temperature and porosity in the frost layer, which is nearly impossible to obtain in the experiments, could be predicted at any time. The results of the total heat and mass transfer rates as well as the development of the local and average frost thicknesses were compared with the experimental findings.     

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.     

MHD flow over an inclined radiating plate with the temperature‐dependent thermal conductivity,variable reactive index,and heat generation

We study the effects of higher‐order chemical reaction and heat generation on coupled heat and mass transfer by MHD mixed convection from a permeable radiating inclined plate with the thermal convective boundary condition. The governing boundary layer equations are formulated and transformed into a set of similarity equations using dimensionless similarity variables developed by Lie group analysis. The resulting equations are then solved numerically using Maple 13 which uses a fourth–fifth order Runge–Kutta–Fehlberg algorithm for solving nonlinear boundary value problems. A representative set of numerical results are displayed graphically and discussed to show some interesting aspects of the parameters: convective heat transfer (γ), the angle of inclination (α), generation order of chemical reaction (n), reaction rate (λ), the Prandtl number (Pr), and the Schmidt number (Sc) on the dimensionless axial velocity, the temperature, and the concentration profiles. Also effects of pertinent parameters on the skin friction factor, the rate of heat, and the rate of mass transfer are obtained and displayed in tabular form. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20409     

Etude experimentale du transfert simultane de chaleur et de masse au cours du sechage par contact sous vide d'un bois resineux

An experimental study of the conjugate heat and mass transfer during the vacuum contact drying of softwood is described.The experimental results show that the drying rate is increased by means of a convective movement induced by a total pressure gradient in the gaseous phase at high free moisture content.An analysis of temperature and moisture distributions distinguishes three stages during drying (excluding the thermal transient regime): 1st stage: the wood temperature does not change in time but the drying rate decreases continuously. 2nd stage: the wood temperature increases quickly. 3rd stage: the moisture equilibrium is reached asymptotically.The previous results suggest a moisture migration mechanism for softwood drying.     

Cross–diffusion effects on mixed convection from an exponentially stretching surface in non–Darcy porous medium

The Soret and Dufour effects on mixed convection flow and heat and mass transfers from an exponentially stretching surface in a quiescent fluid–saturated non–Darcy porous medium is studied. Stretching velocity, wall temperature, and wall concentration are assumed to have specific exponential function forms. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations and then solved numerically using an implicit finite difference scheme known as the Keller–box method. The present results are found to be in excellent agreement with previously published work on various special cases of the problem. The influence of buoyancy, Soret and Dufour numbers, and Darcy and non–Darcy parameters on the convective transport in the boundary layer region is analyzed. Also, the numerical values of the skin friction, heat, and mass transfer coefficients for different values of governing parameters are also tabulated. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21032