Modeling the Drying Kinetics of Pigeon Pea [Cajanus cajan (L.) Millspaugh]

We set out to model the oven-drying kinetics of a legume known as pigeon pea, harvested in the Bouenza department in the south-west of the Republic of Congo. The drying kinetics of pigeon peas was carried out in an oven under experimental conditions using temperatures of: 50°C, 60°C and 70°C. Seven mathematical models were used to describe pigeon pea drying. During drying, water loss was faster and shorter at 70°C [10.446 g/25 g wet weight (wwb) for 320 min (5.3 h)] compared to 50°C [10.996 g/25 g wet weight (wwb) for 520 min (8.6 h)] and 60°C [10.616 g/25 g wet weight (wwb) for 420 min (7.0 h)] where it was slower and longer. With regard to modeling, and based on the principle of choosing the right model focusing on the high value of R2 and low values of χ2 and RMSE, two models were selected, the Midili model for temperatures of 50°C and 60°C and the Henderson and Pabis model modified for temperature of 70°C showed better results. The R2, χ2 and RMSE values calculated for pigeon pea are 0.99985, 3.93404E-5 and 0.00627;0.9997, 9.245E-5 and 0.00962;0.99996, 1.56332E-5 and 0.00395 respectively at 50°C, 60°C and 70°C.

Hydric Properties Evolution of <i>Spirulina platensis</i>during Drying: Experimental Analysis and Modeling

Hydric properties evolution during drying differs from one product to another and has been the subject of various studies due to its crucial importance in modeling the drying process. The variation of these parameters in the solid matrix and in time during the drying of Spirulina platensis has not known an advanced understanding. The objective of this study was to evaluate the evolution of the water content profile, the mass flow, the concentration gradient and the diffusion coefficient during the drying of Spirulina platensis taking into account the shrinkage. Modeling and experimental analysis (at 50°C and HR = 6%) by the cutting method a cylinder 20 mm in diameter and 40 mm thick were carried. The water content profiles of two different products grown in semi-industrial farms from Burkina Faso and France with initial water contents respectively of the range from 2.73 kgw/kgdb and 3.12 kgw/kgdb were determined. These profiles have been adjusted by a polynomial function. Identical water behavior is observed regardless of the origin of the samples. Water distribution is heterogeneous. Mass flow and concentration gradient are greater at the edge than inside the product. The water transport coefficient, ranging from 1.70 × 10?10 to 94 × 10?10 m2/s, is determined from a linear approach.

Modeling of temperature-humidity for wood drying based on time-delay neural network

The temperature-humidity models of wood drying were developed based on Time-delay neural network and the identification structures of Time-delay neural network were given. The controlling model and the schedule model, which revealed the relation between controlling signal and temperature-humidity and the relation between wood moisture content and temperature-humidity of wood drying, were separately presented. The models were simulated by using the measured data of the experimental drying kiln. The numerical simulation results showed that the modeling method was feasible, and the models were effective.

Mathematical Modeling and Effect of Various Hot-Air Drying on Mushroom(Lentinus edodes)

An experimental study was performed to determine the characteristics and drying process of mushroom （Lentinus edodes） by 6 different hot-air drying methods namely isothermal drying, uniform raise drying, non-uniform raise drying, uniform intermittent drying, non-uniform intermittent drying and combined drying. The chemical composition （dry matter, ash, crude protein, crude fat, total sugars, dietary fiber, and energy）, color parameters （L, a＊, b＊, c＊, and h~） and rehydration capacities were determined. Among all the experiments, non-uniform intermittent drying reached a better comprehensive results due to the higher chemical composition, better color quality associated with high bright （26.381＋5.842）, high color tone （73.670＋2.975）, low chroma （13.349a：3.456） as well as the highest rehydration （453.76% weigh of dried body）. Nine kinds of classical mathematical model were used to obtained moisture data and the Midili-kucuk model can be described by the drying process with the coefficient （R2 ranged from 0.99790 to 0.99967）, chi-square （X2 ranged from 0.00003 to 0.00019） and root mean square error （RMSE ranged from 0.000486 to 0.0012367）.

Second-order difference scheme for a nonlinear model of wood drying process

A numerical simulation for a model of wood drying process is considered. The model is given by a couple of nonlinear differential equations. One is a nonlinear parabolic equation and the other one is a nonlinear ordinary equation. A difference scheme is derived by the method of reduction of order. First, a new variable is introduced and the original problem is rewritten into a system of the first-order differential equations. Secondly, a difference scheme is constructed for the later problem. The solvability, stability and convergence of the difference scheme are proved by the energy method. The convergence order of the difference scheme is secondorder both in time and in space. A prior error estimate is put forward. The new variable is put aside to reduce the computational cost. A numerical example testifies the theoretical result.

Modeling and simulation of solvent behavior and temperature distribution within long stick propellants with large web thickness undergoing drying

Drying is a complicated physical process which involves simultaneous heat and mass transfer in the removal of solvents inside propellants.Inappropriate drying techniques may result in the formation of a hard skin layer near the surface to block the free access of most solvent through for long stick propellants with large web thickness,which lead to lower drying efficiency and worse drying quality.This study aims to gain a comprehensive understanding of drying process and clarify the mechanism of the blocked layer near the propellant surface.A new three-dimensional coupled heat and mass transfer(3D-CHMT)model was successfully developed under transient conditions.The drying experiment results show that the 3DCHMT model could be applied to describe the drying process well since the relative error of the content of solvent between simulation and experiment values is only 5.5%.The solvent behavior simulation demonstrates that the mass transfer process can be divided into super-fast(SF)and subsequent minorfast(MF)stages,and the SF stage is vital to the prevention of the blocked layer against the free access for solvent molecules inside propellant grains.The effective solvent diffusion coefficient(Deff)of the propellant surface initially increases from 3.4×10^(-6)to 5.3×10^(-6)m^(2)/s as the temperature increases,and then decreases to 4.1×10^(-8)m^(2)/s at 60-100 min.The value of Deffof surface between 0-1.4 mm has a unique trend of change compared with other regions,and it is much lower than that of the internal at100 min under simulation conditions.Meanwhile,the temperature of the propellant surface increases rapidly at the SF stage(0-100 min)and then very slowly thereafter.Both the evolution of Deffand temperature distribution demonstrate that the blocked layer near the propellant surface has been formed in the time period of approximately 0-100 min and its thickness is about 1.4 mm.To mitigate the formation of blocked layer and improve its drying quality of finial propellant products effectively,it should be initially dried at lower drying temperature(30-40℃)in 0-100 min and then dried at higher drying temperature(50-60℃)to reduce drying time for later drying process in double base gun propellants.The present results can provide theoretical guidance for drying process and optimization of drying parameters for long stick propellants with large web thickness.

Analysis and Modeling of Wangqing Oil Shale Drying Characteristics in a Novel Fluidized Bed Dryer with Asynchronous Rotating Air Distributor

In order to replace the conventional distributor, a novel asynchronous rotating air distributor, which can optimize the drying ability of fluidized bed and strengthen the drying performance of oil shale particles, is creatively designed in this study. The rotating speed of the asynchronous rotating air distributor with an embedded center disk and an encircling disk is regulated to achieve the different air supply conditions. The impacts of different drying conditions on the drying characteristic of Wangqing oil shale particles are studied with the help of electronic scales. The dynamics of experimental data is analyzed with 9 common drying models. The results indicate that the particles distribution in fluidized bed can be improved and the drying time can be reduced by decreasing the rotating speed of the embedded center disk and increasing the rotating speed of the encircling disk. The drying process of oil shale particles involves a rising drying rate period, a constant drying rate period and a falling drying rate period. Regulating the air distributor rotating speed reasonably will accelerate the shift of particles from the rising drying rate period to the falling drying rate period directly. The two-term model fits properly the oil shale particles drying simulation among 9 drying models at different air supply conditions. Yet the air absorbed in the particles' pores is diffused along with the moisture evaporation, and a small amount of moisture remains on the wall of fluidized bed in each experiment, thus, the values of drying simulation are less than the experimental values.

Mathematical Model for the Drying Process of Granular Materials in a Fluidized Bed

The experiment of granular materials, barley, drying in a fluidized bed was carried out to investigate the influence of the factors, inlet air temperature, air moisture, bed height and original moisture content of the dried materials on drying process. Based on the experimental data, a corresponding mathematical model is presented. As a conclusion, a higher inlet air temperature and a reasonable bed height should be used so as to increase the dring rate and to improve the product quality.

Adjustment of Mathematical Models and the Quality of Drying the Pulped Coffee at Different Air Conditions

The aim of the study was to describe the drying kinetics of washed coffee (Coffea arabica L.) and evaluate the best mathematical model to fit the experimental drying data conducted with different air humidity (40%, 50% and 60%), temperatures (23, 40 and 60 °C) and the quality of the coffee. The cherries coffee were separated and standardized in the processes of washing, mechanical and manual separation. Then, approx. 85 kg of coffee cherries were pulped and taken directly to the yard. The washed coffee was completed dried in a mechanical dryer and yard. The results showed that the different conditions of the ambient air significantly influenced the processes of drying. The water content of the hygroscopic equilibrium of pulped coffee is directly proportional to the water activity and relative humidity (RH), decreasing with increasing temperature, for the same value of equilibrium. The Oswin model was best represented by the hygroscopicity of the pulped coffee, while the Midilli model shows the best fit to describe the drying curves of the washed coffee. The effective diffusion coefficient increases with increasing temperature of the drying air and reducing of RH, being described by the Arrhenius equation. Electrical conductivity, potassium leaching, total titratable acidity and grease acidity increase with increasing drying temperature regardless of the type of processing. Reducing sugars, total sugars and the sensorial quality was negatively affected with increasing drying temperature regardless of the type of processing. The drying at 60 °C/40% RH negatively affected the coffee quality.

Sauna Technique, Drying Kinetic Modeling and Effectiveness on Solar Drying Compared with Direct Drying in Drying Process of <i>Kappaphycus striatum</i>in Selakan Island Malaysia

A sauna drying technique—the solar drier was designed and imposed, constructed and tested for drying of seaweed. The seaweed moisture content was decreased around 50% in 2-day sauna. Kinetic curves of drying of seaweed were known to be used in this system. The non-linear regression procedure was used to fit three different drying models. The models were compared with experimental data of red seaweed being dried on the daily average of air temperature about 40℃. The fit quality of the models was evaluated using the coefficient of determination (R2), Mean Bias Error (MBE) and Root Mean Square Error (RMSE). The highest values of R2 (0.99027), the lowest MBE (0.00044) and RMSE (0.03039) indicated that the Page model was the best mathematical model to describe the drying behavior of sauna dried seaweed. The percentage of the saved time using this technique was calculated at 57.9% on the average solar radiation of about 500 W/m2 and air flow rate of 0.056 kg/s.

Mathematical Models for Vacuum Drying Characteristics of Pomegranate Aril

The aim of this study was to investigate and determine the best mathematical models in describing vacuum drying characteristic of pomegranate arils in the range of 55-75 ℃. The vacuum batch dryer used in the evaluation was successful in drying a thin layer of pomegranate arils from the initial moisture content of 464.02% （d.b.） to 6.18% （d.b.） within 6.5 to 13.5 hr of continuous drying at the above mentioned temperature range. The drying rates increased with an increase in temperature and drying time. Five of the well known semi-theoretical and empirical models were fitted to the vacuum drying of pomegranate arils. The semi-empirical Midilli model has shown an excellent fit to predict drying behavior of the pomegranate arils because this model gave the highest coefficient of determination （RE）, the least chi-square （X2）, and the lowest root mean square error （RMSE）. The total drying occurs during falling period, signifying the influence of moisture diffusion during the drying. The effective diffusivity varied from 1.25× 10^10 to 2.91 × 10^10 m^2/s over the temperature range. Temperature dependence of the diffusivity was well documented by Arrhenius models. The activation energy of moisture diffusion during drying was found to be 40.46 kJ/mol.

Physical Model of Drying Shrinkage of Recycled Aggregate Concrete

We prepared concretes（RC0, RC30, and RC100） with three different mixes. The poresize distribution parameters of RAC were examined by high-precision mercury intrusion method（MIM） and nuclear magnetic resonance（NMR） imaging. A capillary-bundle physical model with random-distribution pores（improved model, IM） was established according to the parameters, and dry-shrinkage strain values were calculated and verified. Results show that in all pore types, capillary pores, and gel pores have the greatest impacts on concrete shrinkage, especially for pores 2.5-50 and 50-100 nm in size. The median radii are 34.2, 31, and 34 nm for RC0, RC30, and RC100, respectively. Moreover, the internal micropore size distribution of RC0 differs from that of RC30 and RC100, and the pore descriptions of MIM and NMR are consistent both in theory and in practice. Compared with the traditional capillary-bundle model, the calculated results of IM have higher accuracy as demonstrated by experimental verifi cation.

Modeling the Drying Kinetics of Earth Bricks Stabilized with Cassava Flour Gel and Amylopectin

Earth bricks could contribute to alleviate the housing shortage in the world, thanks to their low cost, easy production, and low environmental impact. However, to manufacture bricks with required properties, many raw soils must be ameliorated. In Central and Eastern Africa, the waste water of the cassava processing is used to improve earth brick mechanical properties. This technique is interesting, because it is sustainable, low-cost and easy to implement. But, studies on this stabilization method are scarce, in particular on the drying kinetics of these bricks. Now, it is important to know the drying duration, because the earth brick’s strength is strongly correlated to its moisture content. Thus, this study aims to quantify and to model the effect of adding cassava flour gel and amylopectin on the drying kinetics of earth bricks. Depending on the soil nature, the drying duration decreases from 7% to 25% for a stabilizer content of 20%. For the five models used, the coefficient of determination is superior to 0.997 and the chi square is inferior to 3 × 10&#8722;4. In average, the best model is Khazaei, followed in order by Avrami-Page, diffusion, Yong and Peleg. The effective coefficient of diffusion of water is about 4 × 10&#8722;5 m&#8901;s&#8722;2. The parameter T of the Khazaei’s model is strongly correlated to the drying duration and the stabilizer content, and their relationships have been deduced.

Kinetic Models for Drying Techniques—Food Materials

Drying operations can help in reducing the moisture content of food materials for avoidance of microbial growth and deterioration, for shelf life elongation, to minimize packaging and improving storage for easy transportation. Thin-layer drying of materials is necessary to understand the fundamental transport mechanism and a prerequisite to successfully simulate or scale up the whole process for optimization or control of the operating conditions. Researchers have shown that to rely solely on experimental drying practices without mathematical considerations for the drying kinetics, can significantly affect the efficiency of dryers, increase the cost of production, and reduce the quality of the dried product. An effective model is necessary for the process design, optimization, energy integration and control;hence, the use of mathematical models in finding the drying kinetics of agricultural products is very important. The statistical criteria in use for the evaluation of the best model(s) has it that coefficient of determination (R2) has to be close to unity while the rest statistical measures will have values tending to zero. In this work, the essence of drying using thin-layer, general approaches to modeling for food drying mechanisms thin layer drying models and optimization of the drying processes have been discussed.

A Convective Thin Layer Drying Model with Shrinkage for Kent Mango Slices

In this work, a model of convective drying of mango slices was developed and validated by experiments. This model was established by considering slices shrinkage in the energy and the mass balances during the thin layer drying. The drying kinetics and the temperature curves of the product were simulated using the model at various drying temperatures. The simulated curves were then compared to the experimental curves obtained using a convective dryer controlled in temperature and moisture. The results showed that the drying curves were suitably fitted by the thin layer drying model with a correlation coefficient r2 = 0.997. Thus, taking shrinkage into account, it is possible to predict more effectively the thin layer drying kinetics of mango slices. This study therefore contributed to the mango drying modelling and to the mango dryer setting.

CLASSIFICATION AND COMPARISON OF WOOD DRYING MODELS

The Various models established by many scholar in the near years areclassified and compared between them.

NaOH Activation of Raw Soils: Effect of NaOH Content on the Drying Kinetic and Its Modelling

NaOH activation of soils is an affordable and promising way to improve mechanical properties of earthen bricks. If for well-activated geopolymers, the hard polymeric network limits the influence of water on mechanical properties, for the weakly activated one, as non-calcined raw clayey soils, the influence of water on these properties would be more critical. This work aims to determine the effect of sodium hydroxide concentration on the drying kinetics of bricks made with raw clayey soils, and to model this kinetics. The results show that the drying kinetics is governed by the diffusion of water due to the absence of free water. The drying duration increases linearly with the increasing of NaOH content, while the volumetric shrinkage decreases, probably thanks to the reduction of the material porosity during the formation of the zeolitic structures. Besides, the drying duration is strongly and negatively correlated with the initial drying rate (&#8722;0.97) and bricks did not show visible cracks. Among the five parametric models tested, the Khazaei’s model is the best in terms of all statistical criteria considered. For all models used, the coefficient of determination is ranged from 0.993 to 0.999, and the evolution of the models’ parameters is in accordance with that of the drying kinetics observed.

Experimental Performance and Neural Network Modeling of a Large-scale Greenhouse Solar Dryer for Drying Natural Rubber Sheets

This paper presents experimental performance and artificial neural network modeling of a large-scale greenhouse solar dryer for drying of natural rubber sheets. The dryer consists of a parabolic roof structure covered with polycarbonate sheets on a concrete floor. The dryer is 9.0 m in width, 27.0 m in length and 3.5 m in height. Nine 15-W DC fans powered by three 50-W PV modules were used to ventilate the dryer. To investigate its performance, the dryer was used to dry six batches of natural rubber sheets. For each batch, 750 kg of rubber sheets were dried in the dryer. Results obtained from the experiments showed that drying temperatures varied from 32 ~C to 55 ~C and the use of the dryer led to a considerable reduction of drying time, as compared to the open air sun drying. In addition, the quality of the product from the dryer was high-quality dried products. A multilayer neural network model was developed to predict the performance of this dryer. The predictive power of the model was found to be high after it was adequately trained.

3D Model Simulating the Hydro-mechanical State of Unsaturated and Deformable Material during Hot air Drying

A three dimensional model to predict the hydro-mechanical state of unsaturated and deformable material during hot air drying has been proposed.The material viscoelastic behaviour was formulated using Bishop’s effective stress theory for partially saturated material using the liquid saturation as the Bishop parameter.The hydro-thermal and mechanical equations were coupled by the fluid pressure and the solid matter velocity.The model was applied to a deformable material(innovative clay-cellulose fibers composite)subjected to convective drying.A generalized Maxwell model with five elements,whose parameters were measured experimentally and correlated to water content was used to describe the material’s viscoelastic behavior.The hydro-thermal part of the proposed model was validated on the basis of a comparison of experimental and simulated drying rate curves.The Von Mises stress was simulated and compared to the experimental tensile strength in order to predict the time and the region of material failure.For a drying process at 95°C,the region of failure risk was identified.The failure may occur on the lateral surface of the slab in contact with air at a drying time of 2.5h.

The Application of a Mathematical Modelling of Drying Kinetics in the Natural Solar Drying of Banana

In this work, a new mathematical modelling of drying kinetics is described. At first, the modelling of the transfer speed （St） of water was performed. Then St was used as basis to state the drying rate model. The drying rate depends not only on drying time, but also on some modelling parameters which are themselves time-dependent. All the modelling parameters are calculated directly from the experimental drying data. Then the theoretical model of the moisture content was stated. Subsequently, the drying kinetics of natural solar drying of plantain banana was studied as illustration. The drying rate was investigated. The comparison with other models encountered in literatures proved that the current theoretical model was decidedly more accurate. Then the modelling of moisture content of banana was performed and the results were compared with the Henderson and Pabis model. The current theoretical modelling provided by far the best fit.