Development of a new drying correlation for practical applications

This paper deals with the development of a new Biot number–drying coefficient (Bi–S) correlation. The developed correlation is used to determine the moisture transfer parameters in terms of moisture diffusivity and moisture transfer coefficient involved in the solids drying process. In the development of this correlation, a large number of experimental data taken from various sources in the literature are employed. In order to verify the validity of the present correlation, three sets of experimental moisture content variations for three different products such as potato, apple and yam are compared with the moisture profiles calculated using the correlations results and a good agreement is found. Thus, it is believed that the developed correlation will be helpful to design engineers and workers in the drying industries, in calculating the parameters affecting the drying process in a simple and accurate manner and optimizing the process. Copyright © 2002 John Wiley & Sons, Ltd.     

Drying kinetics of pumpkinseeds

The drying of pumpkinseeds was investigated in the present study. Pumpkinseed has a thin liquid film on its surface and has rough‐surfaced peel. The most important parameter affecting its drying kinetics and increasing the drying rate is the temperature of the drying air. Drying was carried out with the surrounding air first at ambient temperature, and secondly an experimental rig was built to increase air temperature by using solar energy. A single layer of the pumpkinseed was dried in two different ways by free and forced convection. In these methods, pumpkinseeds were either placed in the tray exposed to the natural environment or placed in sieves on the experimental rig. The drying curves and variation of drying rate curves obtained were dependent on product moisture content. The drying air velocity can take moisture until saturation has a secondary effect on the moisture transfer. In the analysis, pumpkinseed was considered like a measurable rectangular prism. Fick's analytical solution, including effective diffusion coefficient, was applied to the present model. The results obtained from the present analytical model were compared with the experimental data and a good agreement was found. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

An exact modelling for thermal diffusivities of solid objects exposed to heating

A new simple model for determining the thermal diffusivities of solid geometrical objects (i.e., infinite slab, infinite cylinder, and sphere) being heated in a heating medium is proposed. In the unsteady-state heat transfer modelling, the lag factor and heating coefficient for heating applications were well-defined as being in a cooling process. In addition, new characteristic equations for the case of 0 < Bi < 100 in the transient heat transfer were developed instead of the existing complicated equations, and these were employed. In order to test the present model, the literature heat transfer data were used as an example and the use of the model was described in detail. The results of this study indicate that the heating coefficient has a direct influence on the thermal diffusivity and that the present model permits the determination of the thermal diffusivity values of solid geometrical objects in a simple and accurate manner.     

An approach for determining surface temperature distributions of solid objects subjected to heating applications

This study presents a simple technique of determining surface temperature values and/or distributions of solid objects of various geometrical shapes (e.g. infinite slab, infinite cylinder, and sphere) during heating in a medium under natural or forced convection conditions. In the model, the boundary condition of the third kind (i.e., 0.1 < Bi < 100) in transient heat transfer, which is commonly encountered, is used. In many practical applications ranging from metallurgy to food engineering processes, the measurement of surface temperatures of such solid objects is a remarkable problem; however, centre temperature measurements are quite easy. For this reason, simple and accurate models are required for use in practice. The proposed model depends on the centre temperature and determines the surface temperatures using the centre temperature measurements. In order to test the present analytical model, an actual example for a slab object was given and the centre and surface temperature profiles were drawn. In addition, the centre and surface temperature distributions for infinite slab, infinite cylinder, and sphere were computed for the values of 0.1, 1, 10, and 100 of the Biot number and were exhibited as reference graphics. As a result, the present model is capable of determing surface temperatures of various geometrical objects heated in any medium using their centre temperature measurements in a simple and accurate manner.     

Graphical determination of drying process and moisture transfer parameters for solids drying

In this paper a simple graphical method is proposed to determine the drying moisture transfer parameters such as moisture diffusivity and moisture transfer coefficient for solid products. Once the lag factor and the drying coefficient are obtained from the experimental moisture content data, the proposed graphical method can be used to estimate the drying moisture transfer parameters in a quick and efficient manner. Drying time can also be easily determined for a solid whose drying process parameters are known. Two illustrative examples are given to highlight the importance of the topic and validate the use of the present methodology for practical drying applications.     

Investigation of moisture transfer mechanism in porous media during a rapid drying process

In this work, the moisture transfer mechanism in wet porous media during a rapid drying process was investigated experimentally and analytically. By means of scanning electron microscopy, the rapid drying processes for potato, carrot, and radish species were observed and recorded. A new displacement model using the pressure gradient in a porous material during rapid drying was suggested. To analyze this displacement flow in a porous material, the variables of this flow in a single capillary tube, such as velocity, flow rate, as well as the displacement time of internal moisture, were calculated. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 22–27, 2001     

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.     

A simple moisture transfer model for drying of sliced foods

The mathematical formulation of mass transfer in drying processes is often based on the nonlinear unsteady diffusion equation. In general, numerical simulations are required to solve these equations. Very often, however, indirect and simplified methods neglecting fundamentals of the processes are used. In this work, a new mathematical model approach for the mass transfer occurring during drying of sliced foods is proposed. The model considers fundamentals of the drying process and takes internal resistance to moisture transfer into account. The parameters in the formulation have physical meaning and permit giving clear view of the moisture depletion process occurring during drying. The proposed model has an analytical solution and allows finding effective diffusion coefficient accurately. The verification of the model is made with basic drying experiments performed for chili red peppers sliced in slab form. The results reveal that there is nearly perfect match between the drying curves obtained by the model and the experiments.     

Liquid diffusion model for drying a stack of rough rice

Drying of a stack of rough rice was experimentally and theoretically investigated. Stacks of rough rice having different heights were dried with forced convection of warm air. A theoretical model was developed for predicting the bulk drying kinetics of a stack of rough rice using the analytical solution of liquid diffusion equation based on Fick's law. Effective diffusion coefficients were obtained minimizing the sum of squared differences between the theoretical results and experimental data obtained for various drying conditions. Drying air temperature is the most effective factor on the total rate of moisture removal from the stack. The bulk drying rate of a stack of rough rice was considerably reduced as compared to that of a single layer as the height of the stack increased. Agreement between the theoretical and experimental result is very good. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Influence of uncertainty in diffusion coefficients on moisture field during wood drying

The paper presents an experimental measurement of diffusion coefficients of wood and theoretical analysis (stochastic analysis) based on influence of uncertainty in these coefficients on moisture field during wood drying simulations. Experimental measurement was used to verify of analytic equations for calculation of diffusion coefficients, which were implemented in the numerical simulations. Histograms show on normal distribution, but stochastic analysis was used for uniform distribution as well. Mean value of diffusion coefficient in tangential direction was calculated as 1.016·10^?10 m² s^?1 and standard deviation as 0.153·10^?10 m² s^?1. Stochastic analysis is based on the Monte Carlo method. The analysis proves that final moisture field has a same probability distribution as the diffusion coefficient (normal or uniform distribution) and also depicts a character of course and distribution of uncertainty in lumber during drying.     

New correlations for heat transfer coefficients during direct cooling of products

An analytical method for determining the heat transfer coefficients of food products being cooled in water and in air flows is presented. Food products are idealized as geometrical solid objects of regular shapes. New correlations between heat transfer coefficients and cooling coefficients are developed in simple forms for practical use in the refrigeration industry. These correlations are then used to determine the heat transfer coefficient for a cylindrical carrot cooled in air flow as an illustrative example. In addition, evaluating the heat transfer coefficients for several products using the available experimental cooling coefficient values from the literature, two new correlations between the heat transfer coefficient and the cooling coefficient are also obtained for water and air cooling applications. The results show that the correlations presented in this article can determine the heat transfer coefficients of food products forced-convection cooling in a simple and accurate manner.     

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.     

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.     

An analytical method for determining the temperature dependent moisture diffusivities of pumpkin seeds during drying process

This paper presents an analytical method, which determines the moisture diffusion coefficients for the natural and forced convection hot air drying of pumpkin seeds and their temperature dependence. In order to obtain scientific data, the pumpkin seed drying process was investigated under both natural and forced hot air convection regimes. This paper presents the experimental results in which the drying air was heated by solar energy.     

Development of a new Bi-Di correlation for solids drying

In this article, a recently developed Biot number-Dincer number (Bi-Di) correlation for drying applications is presented. The developed correlation is used to determine the moisture diffusivities and moisture transfer coefficients for products subjected to drying. A large number of experimental data taken from various sources in the literature has been utilized for the development of this correlation. Dimensionless moisture distributions were obtained for three regular shaped objects such as slab, cylinder and sphere to verify them with the available experimental measurements. The results show a considerably high agreement between the predicted values from the correlation and measured experimental observations. Thus, the present correlation is considered to be of great importance to design engineers and operators in estimating the moisture transfer parameters in a reasonably simple manner.     

Thermal analysis of a fluidized bed drying process for crops. Part I: Mathematical modeling

Development of a comprehensive mathematical model to simulate the simultaneous heat and mass transfer processes in a bubbling fluidized bed is described. Although the model is applicable to a wide range of particles, wheat is chosen as an example. In the development of the model, the commonly used two‐phase theory is not used because of its insensitivity to the particle group used in the bed. Instead, a new hydrodynamic model is developed for each specific particle group. The behaviour of bubbles in a bed of group D particles (wheat) is modelled with the consideration that they grow in size as they rise in the bed, but are of the same size at any height in the bed. The voidage of bubbles, particles and interstitial gas is modelled separately. A newly developed expression to determine the minimum fluidization velocity of wet particles is used. The model considers the presence of different phases inside the bed, and their physical variation along the bed. The interstitial gas phase, the bubble phase, and the solid phase are modelled separately. The drying mechanism for the solid phase is considered in two stages: the falling rate, and the constant rate, with appropriate temperature and moisture diffusion coefficients and wall effects. The simultaneous heat and mass transfer processes during the drying process including the internal and external effects are modelled for each phase. A set of coupled nonlinear partial differential equations is employed to accurately model the drying process without using any adjustable parameters. A numerical code is developed to solve the governing partial differential equations using a control volume‐based discretization approach. Piecewise profiles expressing the variation of dependent variables between the grid points are used to evaluate the required integrals. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

Mathematical modelling of drying based on a surface evaporation source term for coupled energy and mass transfer

A mathematical model is developed by introducing a source term and using the coupled mass and energy balances based on the Luikov's system of equations. The source term is due to the surface evaporation of many particles in a solid bed. A numerical scheme based on explicit finite difference method is applied. The prediction of bulk temperature profile and moisture content from the model shows, qualitatively, the same trend as the experimental results found in literature. Additionally, parametric studies are performed to investigate the effect of different parameters such as the porosity, the heat and mass transfer coefficients and the velocity on the overall energy efficiency of the drying process. The present model provides better approximation to an actual drying process, especially in the initial and final periods of drying. Copyright © 2007 John Wiley & Sons, Ltd.