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.     

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.     

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.     

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.     

Transpiration drying of porous hygroscopic materials

The phenomenon of transpiration drying of porous hygroscopic bodies has been investigated, both experimentally and theoretically, to understand the process of heat and mass transfer involved in the drying.The experiments consist of measuring the drying rates of thin sheets of paper dried by passing dry air through the sheets. The time history of drying was measured, under different air flow conditions and for different paper thicknesses, by a gravimetric method. The drying rates were deduced from these data and correlated against flow variables. Characteristic constant and falling drying rates were observed.A two region theoretical analysis of the problem is made. In the first phase, a bulk analysis of the constant drying regime is worked out. This analysis provides a means of properly defining the heat- and mass-transfer coefficients. The analysis is extended to include a specific internal evaporative mechanism within the fibrous body. Analytical and numerical solutions in the form of an evaporative coefficient have been obtained. In the second phase of the analysis, the falling drying rate regime is accounted for by the fact that the vapor pressure inside the body decreases with decreasing moisture content. A numerical solution to the transient mass-energy equation is obtained (incorporating the effects of solid matrix conduction and fiber shrinkage) to predict the drying rate as a function of time. The results agree well with observed data.Based on the analytical and experimental results correlations are given to predict the time to dry from a given initial moisture content to a specific final moisture content.     

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.     

Thermal analysis in fluidized bed drying of moist particles

This paper deals with thermal modeling of the fluidized bed drying of wet particles to study heat and mass transfer aspects and drying thermal efficiencies. The model is then validated with the literature experimental data obtained for corn. A parametric investigation is undertaken to study the effects of the inlet air temperature, the air velocity and the initial moisture content of the material (i.e. corn) on the process thermal efficiency. The results show that the thermal efficiencies of the fluidized bed drying decrease sharply with decreasing moisture content of corn and hence increasing drying time, and apparently become the lowest at the end of the drying process. This clearly indicates that the moisture transfer from the material depends strongly on the air temperature, air velocity and the moisture content of material. A good agreement is obtained between the model predictions and the available experimental results.     

A modelling study for moisture diffusivities and moisture transfer coefficients in drying of solid objects

This article presents an effective analytical model for determining the moisture diffusivities and moisture transfer coefficients for solid objects (namely, infinite slab, infinite cylinder, sphere; and also for irregularly shaped objects, by using a shape factor) subject to drying applications in a medium. The unsteady-state moisture diffusion analysis is used on the basis of two important criteria: 0·1 <Bi < 100 and Bi > 100. The drying coefficients and lag factors were employed. The analytical models are then verified using available experimental data taken from the literature. The results show that the method presented here can be used to determine the moisture diffusion coefficients and moisture transfer coefficients for such solid objects in a simple and accurate manner for a variety of drying applications.     

Numerical and experimental validation of thermo-hygro-mechanical behaviour of wood during drying process

This research aims at developing a new approach able to simulate 3-D heat and moisture transfer coupled with the mechanical behaviour of a wood during drying process. From the moisture content and temperature profiles, a 3-D formulation and a relevant constitutive model are used to calculate the stress/strain evolution within the board due to shrinkage and external mechanical loading. This allows a fast, comprehensive and realistic model to be implemented. The mechanical model takes into account the hydrous, thermal, mechano-sorptive and elastic deformations, as well as the changes of wood properties, caused by these processes, e.g. porosity, permeability, stress–strain relation, etc. The mathematical model describing simultaneous unsteady heat and moisture transfer between a gas phase and a solid phase during heat treatment has been developed. The conservation equations for the wood sample are obtained using diffusion equation and the 3-D incompressible Navier–Stokes equations have been solved for the flow field. The constitutive equations are discussed in some detail. ANSYS-CFX10 commercial code was used to solve the hygro-thermal problem and FESh++ for the mechanical behaviour. Experimental results obtained regarding temperature, moisture content and deformation profiles during industrial drying of black spruce wood are compared with the numerical results. Satisfactory agreement is obtained over a range of drying air temperatures.     

Mathematical model of a smoldering log

A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one-dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts are obtained in terms of the smolder temperatures. An appropriate smolder transfer number is defined. Heat transfer by conduction, convection, and radiation inside the porous matrix of the log is considered, as are convection and radiation around the log and inside the boundary layer adjacent to the smoldering end. Solutions for the problem without circumferential heat losses and for a single front of drying and pyrolysis are also presented. The effects of variations of several parameters, such as moisture content, log diameter, pyrolysis temperature, heat of char oxidation, heat of pyrolysis, porosity, fuel density, and char density, are evaluated. The theoretical burning rates are in good agreement with available experimental data.     

Moisture transfer models for slabs drying

This paper deals with an experimental and theoretical investigation of drying of moist slabs. Experimental part includes the measurement of the moisture content distributions of eggplant slices with 5 mm thickness and 35 mm diameter during drying at the temperatures of 55 °C, 65 °C, and 75 °C and the velocities of 1.0 and 1.5 m/s, respectively. Four drying models are used to determine drying process parameters (e.g., drying coefficient, lag factor, and half-drying time) and moisture transfer parameters (e.g., moisture diffusivity and moisture transfer coefficient), and to calculate moisture content distributions. The calculated values are then compared with the experimental moisture data during the drying of eggplant slices at different drying air temperatures and flow velocities. An excellent agreement is obtained between the calculations and experimental measurements for the cases considered. Also, the experimental drying times are determined and compared with the ones obtained through four different drying models. The results show that all four models are capable of estimating the drying parameters and moisture content distributions. The experimental drying data and model findings are expected to be useful to drying industry.     

Modelling of heat and mass transfer in a tunnel dryer

This work presents a numerical model for heat and mass transfer of granular products in a fixed-bed tunnel dryer. The drying process is simulated under real operating conditions based on a thin layer model and experimental drying kinetics. A simplified heat and mass transfer numerical model is developed based on the governing equations and the drying rate of a thin layer bed of granular products.The obtained system of non-linear partial differential equations is numerically solved by a finite volume method. The turbulent airflow and granular bed convection coefficient as well as the effective conductivity are estimated using the turbulent airflow over flat-plate correlations. Simulations are compared with experimental data from drying of grapes in a thin layer model.In order to study the effects of the air inlet conditions on the relative moisture content and the drying time and therefore to optimise the tunnel dryer operation, the influences of different parameters essentially the air flow characteristics and the fixed-bed dryer length are examined. The numerical code allows establishing the drying front propagation for several operating conditions.     

Mathematical modeling of convective drying: Lumped temperature and spatially distributed moisture in slab

The present study describes the modeling and simulation of the drying process. The model considers fundamentals of the drying process and takes internal resistance to moisture into account. The main connotation of this study regards the possibility of employing a new analytical method for simultaneous heat and mass transfer. The proposed model considers the evaporative heat transfer at the surface of product. The validation of the model is made with a set of numerical and experimental results reported in the literature for carrot sliced in slab form. The results reveal that there is nearly perfect match between the temperature and moisture obtained by the analytical model and the numerical solution.     

FINITE-ELEMENT SIMULATION AND VALIDATION OF STEPWISE DRYING OF BANANAS

A two-dimensional finite-element formulation and solution of a set of transient coupled heat and diffusive moisture transfer equations is presented. The solution procedure developed uses an alpha family of approximation for stepping in time for the solution of the coupled set of equations applied to simulate the stepwise convective drying behavior of banana slices. The model tested was validated with experimental data from different sources for stepwise drying of banana using a heat pump dryer (HPD) as well as continuous batch drying in both Cartesian and cylindrical coordinate systems. The maximum deviation of moisture content between experimental and simulation results was 0.05% wet basis (% w.b.). Good agreement of the simulated results with experimental data for stepwise as well as continuous convective drying of banana samples indicates the validity of the procedure and its incorporation in the optimization of drying processes.     

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].     

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.     

Development of a new moisture transfer (Bi-Re) correlation for food drying applications

In this paper, newly developed Biot-Reynolds (Bi-Re) correlation to determine the moisture transfer parameters is presented. Development of the new correlation is based on the experimental data taken from various sources in the literature. Moisture diffusivity and moisture transfer coefficient are calculated using the previously developed model. The moisture distribution profiles are then obtained for regular objects such as slab, cylinder and sphere. The results obtained from the present study are compared with the experimental data and a correlation available in the literature. It is found that they are in good agreement. Hence, it is believed that the developed correlation is of great significance for design and practicing engineers working in the drying industries.     

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.