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.     

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.     

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.     

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.     

A model of through-air drying of tufted textile materials

A transient two-dimensional mathematical model is developed to simulate the through-air drying process for tufted textile materials. The heat and mass transfer in a cylindrical porous medium and the air flowing around it are analyzed separately. First, thermal and mass circuits are used to analyze the simultaneous heat and mass transfer within the porous medium. Then, the equations of the conservation of mass and energy are written for the drying medium. The resulting system of three non-linear differential equations is numerically solved by an implicit finite difference method. The numerical solutions are compared with experimental drying results obtained using magnetic resonance imaging (MRI) and a laboratory through-air dryer (LTAD).     

Numerical study of the interaction among a pair of blunt plates subject to convective drying – A conjugate approach

The effect of the relative positioning of a pair of porous blunt plates, subject to convective drying, on heat/mass transfer phenomena is investigated numerically based on a combination of a flow-heat transfer simulation with a suitable drying model. The air flow is assumed incompressible, two-dimensional, laminar, confined in a channel and parallel to the plates. The finite volume method is used and the computed temporal and spatial variations of flow parameters, moisture content and temperature for different arrangements are analyzed. Several configurations are studied: Side-by-Side, Staggered and in-Tandem arrangements, in an attempt to find the optimum relative positioning which results in the highest reduction of the mean moisture content of the plates, as well as in a more uniform drying. It was found that the Side-by-Side arrangement shows the best overall drying behaviour among all arrangements considered, owing to the enhancement of heat/mass transfer caused by the blockage effect. The analysis of the parameters affecting the transport rates and the uniformity of drying as well as the discussion of the development of unfavorable aerodynamic or thermal effects due to the interaction of product units, may be valuable in optimizing the arrangement of the products in the dryer.     

Modeling of heat transfer and energy analysis of potato slices and cylinders during solar drying

In the present work, a method based on energy balance considering the effects of heat capacity of the food product, radiative heat transfer from food product to the drying chamber and solar radiation absorbed in the product during drying is proposed for determination of convective heat transfer coefficient, h_c. A natural convection mixed-mode solar dryer is used for performing the experiments on potato cylinders and slices of same thickness of 0.01 m with respective length and diameter of 0.05 m. The present investigation indicates that the cylindrical samples exhibit higher values of h_c and faster drying rate compared to those of slices, as expected. The h_c values for each sample shape are correlated by an equation of the form Nu = C(Ra)ⁿ. Laplace transform is applied to solve the proposed heat transfer diffusion model considering the effect of moisture transfer rate to predict the transient sample temperature. The model is validated through a close agreement between calculated and experimental results of transient sample temperature. Results of energy analysis reveal that for both the sample geometries, decreasing product moisture content during drying resulted in significant reduction in specific energy consumption. For almost similar drying conditions, a considerable amount of reduction in specific energy consumption is achieved for cylinders, as expected.     

Heat and mass transfer during drying of a bed of shrinking particles – Simulation for carrot cubes dried in a spout-fluidized-bed drier

The purpose of the present study was to develop a model to describe the heat and mass transfer during the drying of carrot cubes in a spout-fluidized-bed drier. The model took into account the non-homogeneous shrinkage of the material. The Arbitrary Lagrange–Eulerian (ALE) formulation was applied to enter the problem with moving boundaries. Three phases of drying were distinguished according to the behavior of changes in percent local error of estimation: an initial phase of warming up the material – characterized by a low level of error of moisture content prediction, a second phase – characterized by an increase in the error of moisture content prediction and a phase of decreasing error. A simple test of the sensitivity of the model to the changes in heat transfer coefficient was performed in order to improve the ability of the model to predict the changes in moisture content and temperature of dried carrots. The predicted changes in both the moisture content and the temperature of carrot cubes during drying in a spout-fluidized-bed drier indicate that the model can be successfully applied to describe moisture content, temperature and deformation of dried particles in cases when the very high accuracy of moisture content and temperature prediction is not a crucial element of investigation of the drying process.     

Effects of pore size distribution and pore-architecture assembly on drying characteristics of pore networks

Simulation of isothermal drying using two-dimensional networks comprised of interconnected cylindrical pores is presented. Transport of moisture inside pore segments was described by Fick’s law. The results have shown that the shielding of large pores by the smaller pores in the stochastic pore network, which is supposed to be representative of real porous medium, causes the lower drying rate and hence lower effective diffusion coefficient as compared to those predicted from the idealized network of pores with a single size. The strength of shielding is found to vary with the characteristics of pore size distribution as interpreted by the moisture concentration experienced by the pores, which is remarkably different amongst the pore size distributions. The inefficient transport of moisture through the stochastic pore network can be improved or even better with the suitable architecturally assembled structure. The minimum shielding archetype network, appearing very high porous at particle surface, is predicted to enhance greatly the drying rate. On the other hand, the maximum shielding network, which is small pores allocated onto the network exterior, exhibits the slowest drying rate.     

Mathematical Modeling of Heat and Mass Transfer during Convective Dehydration of an Anisotropic Cylindrical Foodstuff

Two‐dimensional, unsteady‐state mass transfer was studied for air drying of an anisotropic finite cylindrical body. A mathematical model was developed for predicting the temperature of the drying sample at any time and moisture in any position in the drying sample at any time. The anisotropic nature of the drying material was considered in the mathematical model by taking into account the different moisture diffusivities in the axial and radial directions. A cut fresh green bean was used as an anisotropic material and a pilot‐scaled dryer was set up to investigate the drying behavior of this foodstuff. Several length‐to‐diameter ratios of fresh green beans were considered and the mathematical model was validated by comparison of the predicted values of average moisture content with the experimental data. The model was used to predict the moisture distributions inside the drying samples. Different moisture content distributions in the axial and radial directions during drying confirms the anisotropic nature of cut green bean samples. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21119     

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.     

STOCHASTIC FINITE-ELEMENT ANALYSIS OF COUPLED HEAT AND MASS TRANSFER PROBLEMS WITH RANDOM FIELD PARAMETERS

A first-order perturbation algorithm for the computation of mean values and variances of transient temperature and moisture fields during coupled heat and mass transfer problems with random field parameters has been developed and implemented. The algorithm is based on the Galerkin finite-element discretization of Luikov's heat and mass transfer equations for capillary porous bodies and is computationally less demanding than the Monte Carlo method. The algorithm has been programmed in MATLAB and applied to a published test case of a drying process for soybean kernels. The simulations indicate that the stochastic fluctuations of the thermophysical properties and the process conditions may cause a considerable level of uncertainty in the predicted temperatures and moisture contents inside the product.     

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.     

混凝土热湿传导模型在结构早龄期裂缝分析中的应用

针对混凝土结构早龄期裂缝的产生机理,提出了混凝土三维有限元热湿传导数值计算模型,同时考虑了混凝土水化反应引起的温度变化、表面干燥失水造成的湿度非均匀分布及两者间的耦合作用,并在应力分析中采用Bazant双幂函数徐变模型考虑徐变对混凝土应力的影响.算例分析表明,该模型能很好地预测实际条件下混凝土温度、湿度变化和相应产生的应力,具有一定的工程应用价值.     

Thermal analysis of natural convective air drying of shrinking bodies

In the present paper, a method for determination of external mass transfer coefficient h_m, during drying of shrinking bodies is described under simulated natural convective air drying conditions. The effects of sample shrinkage and air temperature on h_m during drying of cylindrical potato samples of diameter 0.01 m and length 0.05 m were experimentally investigated at air temperatures 40, 50 and 60°C. The mass transfer coefficient considering shrinkage was found to be independent of sample moisture content during drying process with mean values varying from 1.06 × 10^?7 to 2.60 × 10^?7 m s^?1 for temperature range 40–60°C. However, calculated values of h_m, with no shrinkage effect taken into account, were found to be overestimated. The experimental error in terms of percent uncertainty in mass transfer coefficient measurements was computed and found to be in the range of 0.4–2.0%. It was demonstrated that higher drying air temperature caused increased values of h_m and the variation followed Kelvin's law type relation. A mathematical model to predict the drying process of cylindrical bodies with convective mass transfer boundary condition at air–solid interface is proposed. The low range of various errors between the results of moisture content ratio predicted by the model and those obtained experimentally indicates that the present methodology is capable of simulation of drying kinetics of potato cylinders. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Improved lumped-differential formulations and hybrid solution methods for drying in porous media

The present paper illustrates the construction of hybrid tools for the problem formulation and solution methodology towards the simulation of heat and mass transfer during drying in capillary porous media. First, a problem reformulation strategy is discussed, known as the coupled integral equations approach (CIEA), which offers improved lumped-differential formulations in different classes of problems, in comparison against classical lumping schemes, allowing for a reduction on the number of independent variables to be considered in specific formulations. Second, the generalized integral transform technique (GITT) is employed, as a hybrid numerical–analytical solution methodology for convection–diffusion problems. An example is provided related to drying in capillary porous cylindrical media as formulated by the two-dimensional Luikov's system of equations.