From Laboratory Experiments to Design of a Conveyor-Belt Dryer via Mathematical Modeling

A conveyor-belt dryer for picrite has been modeled mathematically in this work. The necessary parameters for the system of equations were obtained from regression analysis of thin-layer drying data. The convective drying experiments were carried out at temperatures of 40, 60, 80, and 100°C and air velocities of 0.5 and 1.5 m/sec. To analyze the drying behavior, the drying curves were fitted to different semi-theoretical drying kinetics models such as those of Lewis, Page, Henderson and Pabis, Wang and Singh, and the decay models. The decay function (for second order reactions) gives better results and describes the thin layer drying curves quite well. The effective diffusivity was also determined from the integrated Fick's second law equation and correlated with temperature using an Arrhenius-type model. External heat and mass transfer coefficients were refitted to the empirical correlation using dimensionless numbers (J_h, J_D = m · Reⁿ) and their new coefficients were optimized as a function of temperature. The internal mass transfer coefficient was also correlated as a function of moisture content, air temperature, and velocity.     

Coupling CFD and Diffusion Models for Analyzing the Convective Drying Behavior of a Single Rice Kernel

The drying behavior of a single rice kernel subjected to convective drying was analyzed numerically by solving heat and moisture transfer equations using a coupled computational fluid dynamics (CFD) and diffusion model. The transfer coefficients were computed simultaneously with the external flow field and the internal diffusive field of the grain. The model was validated using results of a thin-layer drying experiments from the literature. The effects of velocity and temperature of the drying air on the rice kernel were analyzed. It was found that the air temperature was the major variable that affected the drying rate of the rice kernel. The initial drying rates (in first 20 min) were 7, 12, and 19% per hour at inlet air temperatures of 30, 45, and 60 ^° C, respectively. Important temperature gradients within the grain existed only in the first few minutes of the drying process. The moisture content gradients reached a maximum value of 11.7% (db) mm ^?1 at approximately 45 min along the short axis in the thickness direction. The variation in the inlet air velocity showed a minor effect on the drying rate of the rice kernel. The heat and mass transfer coefficients varied from 16.57 to 203.46 W·m ^?2·K ^?1 and from 0.0160 to 0.1959 m·s ^?1, respectively. The importance of the computation of the transfer coefficients with the heat and mass transfer model is demonstrated.     

DRYING CHARACTERISTICS OF THE HAZELNUT

Abstract

Equilibrium moisture content isotherms for Spanish hazelnut (Corylus avellana L.) at different temperatures (30°C-80°C) were determined using static gravimetric method. Thin layer drying experiments were done with forced air circulation and were conducted with different operating conditions to determine the drying characteristics of hazelnuts. The effect of air temperature (30°C-70°C), air velocity (0.5 m/s - 2 m/s) and drying bed loading density (50 kg/m² - 150 kg/m²) on drying of unshelled and shelled hazelnuts was studied. Six mathematical models were used to fit the experimental equilibrium moisture content data, from which the G.A.B. model was found to give the best fit. Diffusion coefficients were determined by fitting experimental thin-layer drying curves to the Fick's diffusion model. Variation of the effective diffusion coefficient with temperature was of the Arrhenius type. The Page equation was found to describe adequately the thin layer drying of hazelnut. Page equation drying parameters k and n were correlated with air temperature and relative humidity.     

SUPERHEATED STEAM IMPINGEMENT DRYING OF TORTILLA CHIPS

ABSTRACT

Low-fat snack products are the driving forces for the drying of tortilla chips before frying. Super-heated steam impingement drying of foods has the advantage of improved energy efficiency and product quality. The temperature profile, drying curves, and the physical properties (shrinkage, crispiness, starch gelatinization and microstructure) of tortilla chips dried at different superheated steam temperatures and heat transfer coefficients were measured. Results indicated that the steam temperature had a greater effect on the drying curve than the heat transfer coefficient within the range of study. The microstructure of the samples after steam drying showed that higher steam temperature resulted in more pores and coarser appearance. The modulus of deformation and the shrinkage of tortilla chips correlated with moisture content. A higher steam temperature caused less shrinkage and a higher modulus of deformation. The pasting properties showed that samples dried under a higher steam temperature and a higher heat transfer coefficient gelatinized less during drying and had a higher ability to absorb water. Comparison of the superheated steam drying and air drying revealed that at elevated temperatures the superheated steam provided higher drying rates. Furthermore, there was a less starch gelatinization associated with air drying compared to superheated steam drying.     

OPTIMIZATION OF CONVECTIVE DRYING PROCESS BASED ON ECONOMIC INDICATORS

ABSTRACT

Drying of lightly salted sardine (Sardinella aurita) was accomplished using three air temperatures (35°C, 40°C, 50°C) and three air velocities (0.5 m/s, 1.5 m/s, 2 m/s); the effects of drying conditions on drying kinetics were studied. As for all biological products, air temperature is the main factor influencing the drying kinetics. However, over a given temperature which seems to correspond to protein modification (50°C), and at a high air flow rate (2 m/s and 2.5 m/s) a crust formation on the surface of the fish, due to the combined effect of heat and salt was observed. This phenomenon inhibited the drying rate. From the drying curves, two falling rate periods were observed. The dimensionless drying rate versus a dimensionless moisture content data were regressed by the Marquardt Levenberg non-linear optimization method to obtain an empirical equation describing the salted sardine characteristic drying curve.     

Modeling Superheated Steam Vacuum Drying of Wood

Abstract

A two-dimensional mathematical model developed for vacuum-contact drying of wood was adapted to simulate superheated steam vacuum drying. The moisture and heat equations are based on the water potential concept whereas the pressure equation is formulated considering unsteady-state mass conservation of dry air. A drying test conducted on sugar maple sapwood in a laboratory vacuum kiln was used to infer the convective mass and heat transfer coefficients through a curve fitting technique. The average air velocity was 2.5 m s^?1 and the dry-bulb temperature varied between 60 and 66°C. The ambient pressure varied from 15 to 11 kPa. Simulation results indicate that heat and mass transfer coefficients are moisture content dependent. The simulated drying curve based on transfer coefficients calculated from boundary layer theory poorly fits experimental results. The functional relation for the relative permeability of wood to air is a key parameter in predicting the pressure evolution in wood in the course of drying. In the case of small vacuum kilns, radiant heat can contribute substantially to the total heat transfer to the evaporative surface at the early stages of drying. As for conventional drying, the air velocity could be reduced at the latter stage of drying with little or no change to the drying rate.     

Surface Stickiness of Drops of Carbohydrate and Organic Acid Solutions During Convective Drying: Experiments and Modeling

Abstract

Drying kinetics of low molecular weight sugars such as fructose, glucose, sucrose and organic acid such as citric acid and high molecular weight carbohydrate such as maltodextrin (DE 6) were determined experimentally using single drop drying experiments as well as predicted numerically by solving the mass and heat transfer equations. The predicted moisture and temperature histories agreed with the experimental ones within 6% average relative (absolute) error and average difference of ± 1°C, respectively. The stickiness histories of these drops were determined experimentally and predicted numerically based on the glass transition temperature (T _g ) of surface layer. The model predicted the experimental observations with good accuracy. A nonsticky regime for these materials during spray drying is proposed by simulating a drop, initially 120 µm in diameter, in a spray drying environment.     

Temperature Changes during Microwave-Vacuum Drying of Sliced Carrots

Abstract

The temperature changes during microwave-vacuum drying of sliced carrots were investigated. Sliced samples were dried to 7–10% moisture content (wet basis) at a wide range of microwave power and vacuum pressure levels. The experiments showed that for sample thickness less than 8 mm, the core temperature of the sample was the same as its surface temperature, with uniform temperature distribution within the sample. However, for sample thickness more than 8 mm, temperature gradient developed along the thickness of the sample. The experiments also showed that, with the decrease of moisture content X _w (dry basis), for samples with thickness ≤ 8 mm, the drying process of sliced carrots experienced three distinct periods: a warming-up period (X _w  = 7.68) without removal of moisture when the product temperature increased linearly with drying time until it reached the corresponding saturation temperature of water in the food at the vacuum pressure; a constant temperature period (2 ≤ X _w  < 7.68) in which most of moisture evaporated and flowed out of the sample efficiently with little resistance; and a heating-up period (X _w  < 2) in which the drying rate decreased and sample temperature increased rapidly. The mathematical models for predicting sliced sample temperature were also developed based on the energy conservation and regression of the experimental date.     

Mathematical Modeling of Drying Characteristics of Indian Mackerel (Rastrilliger kangurta) in Solar-Biomass Hybrid Cabinet Dryer

Eight trials were conducted for drying mackerel by a solar biomass hybrid cabinet dryer (S-BHCD) and open sun drying (OSD) at air temperatures of 32.39–57.69°C, relative humidity 23.9–85.8%, and air flow rate of 0.20–0.60 m/s. The solar radiation ranged between 287 and 898 W/m² during the time of experimentation. At nighttime, drying was carried out by combusting biomass. The initial moisture content of the processed mackerel was 72.50±0.44% (w.b.) and was reduced to the final moisture content of 16.67±0.52% (w.b.) in S-BHCD and 16.92±0.54% (w.b.) in OSD. Eleven drying models were used and the coefficients of determination (R ²) and constants were evaluated by nonlinear regression to estimate the drying curves of dried mackerels. The Midilli model was found to more satisfactorily describe the drying process of mackerel in S-BHCD with R ² of 0.9999, χ² of 0.0000374, and RMSE of 0.0057. In the OSD, a two-term drying model satisfactorily described the drying process with R ² of 0.9996, χ² of 0.0000519, and RMSE of 0.0072. The variation of Free Fatty acid (FFA), Peroxide value (PV), Thiobarbituric acid (TBA), Total volatile bases nitrogen (TVB-N), Trimethylamine nitrogen (TMA-N), and histamine contents of dried mackerel by using S-BHCD showed very high corresponding coefficients of determination, where all R ² were greater than 0.90, except TBA value. Bacterial count and mold growth were decreased significantly (P < 0.05). There was no discoloration of the product during 4 months of storage. Contour plots of S-BHCD and OSD dried mackerel also showed that for all sensory attributes examined, panelists preferred fish dried with S-BHCD. The organoleptic analysis showed that the S-BHCD drying methods have a highly significant effect (P < 0.01) on texture and overall acceptability. Biochemical, microbial analysis, and sensory evaluation showed that the product was in prime acceptable form for 4 months of storage at ambient temperature.     

THIN-LAYER DRYING CHARACTERISTICS FOR GREEN CHILLI

ABSTRACT

Thin-layer drying experiments under overflow–underflow and through flow conditions of green chilli were conducted with air temperature ranging from 40 to 65°C, relative humidity ranging from 10 to 60% and air velocity ranging from 0.10 to 1.0 m/s. The single exponential equation and the Page equation were used to determine the thin-layer drying characteristics for green chilli. Both the equations fitted well to the experimental data. The Page equation was found to describe the thin-layer drying of chilli better than the single exponential equation. The parameters of the Page equation and the single exponential equation were expressed as a function of drying air temperature, relative humidity and air velocity.     

Ascorbic Acid Thermal Degradation during Hot Air Drying of Camu-Camu (Myrciaria dubia [H.B.K.] McVaugh) Slices at Different Air Temperatures

Abstract

Air drying of camu-camu slices was performed in order to estimate the effect of air temperature on the kinetics of ascorbic acid thermal degradation. Moisture variation during the air drying process was monitored gravimetrically by weighing the trays at predetermined time intervals. The experimental points were adjusted by Fick's diffusion model and by the Page empirical model. The effective diffusion coefficient (D_eff) ranged from 8.48 × 10^?10 to 1.34 × 10^?9 m²/s.The ascorbic acid content was evaluated in samples taken during the drying process using Iodine titration, and the results modeled by the Weibull equation. Concerning ascorbic acid retention the best drying condition required air at 50°C. The ascorbic acid retention was 78%, when the moisture content of the product reached 10% (wet basis).     

Attrition of Victorian brown coal during drying in a fluidized bed

Analyzing the attrition of Victorian brown coal during air and steam fluidized bed drying, the change in particle size distribution over a range of initial moisture contents (60% to 0%) and residence times (0 to 60 minutes) was determined. Dried at a temperature of 130°C with a fluidization velocity 0.55 m/s and an initial particle size of 0.5–1.2 mm, both fluidization mediums show a shift in the particle size distribution between three and four minutes of fluidization, with a decrease in mean particle size from 665 µm to around 560 µm. Using differential scanning calorimetry (DSC), the change in particle size has been attributed to the transition between bulk and non-freezable water (approximately 55% moisture loss) and can be linked to the removal of adhesion water, but not to fluidization effects. This is proved through the comparison of air fluidized bed drying, steam fluidized bed drying, and fixed bed drying—the fixed bed drying is being used to determine the particle size distribution as a function of drying. The results show the three drying methods produce similar particle size distributions, indicating that both fluidization and fluidization medium have no impact upon the particle size distribution at short residence times around ten minutes. The cumulative particle size distribution for air and steam fluidized bed dried coal has been modeled using the equation P_d = A₂ + (A₁ ? A₂)/(1 + (d/x₀)^p), with the resultant equations predicting the effects of moisture content on the particle size distribution. Analyzing the effect of longer residence times of 30 and 60 minutes, the particle size distribution for steam fluidized bed dried coal remains the same, while air fluidized bed dried coal has a greater proportion of smaller particles.     

Modeling of Mass Transfer During Hot-Smoking of Fish Fillets

This work aims at evaluating the mass reduction of traditionally hot-smoked catfish ( Arius heudelotii ) during hot-air drying unit operation. Drying kinetics of fish fillets are proposed from experimental investigations, taking into account the relative contributions of water evaporation and water and fat drips. The influence of the air temperature (50 to 80 ^° C), air velocity (1 to 3 m/s) and relative humidity (15 to 40%) on drying rate functions is analyzed from a Doehlert experimental design. Based on the identification of characteristic drying rate curves, a drying model is defined and proves to be quite accurate regarding the prediction of evaporation rate during the falling rate period.     

Drying Characteristics of Purslane (Portulaca oleraceae L.)

Abstract

Thin layer drying rates of purslane were determined experimentally as a function of temperature with air velocity kept constant at 1.1 m/s and relative humidity below 5%. Thin layer drying data were obtained for purslane at four drying air temperatures (35, 70, 95, and 120°C). Five thin layer-drying models (Henderson and Pabis, exponential, Page, two-term exponential, and Thompson models) were fitted to the drying data. The color of purslane was determined after drying using a spectro-colorimeter (Hunter Lab) in terms of Hunter L, a, and b values. The Page model was found to be most suitable in describing the drying characteristics of purslane. New parameters developed for the model resulted in a good fit at different temperatures. Color measurement indicated that greenness decreased with an increase in drying air temperature. Typical drying times were 88.41, 138.53, 416.38, and 1371.85 min at 120, 95, 70, and 35°C, respectively.     

Effect of Fluidized Bed Drying Temperature on Various Quality Attributes of Paddy

Abstract

As reported by many researchers, it was found that fluidized bed paddy drying using high drying air temperatures of over 100°C affected the head rice yield and whiteness of dried rice. However, only a few studies on fluidized bed paddy drying with drying air temperatures below 100°C were so far reported. The main objective of this work was therefore to study the effect of fluidized bed drying air temperature on various quality parameters of Suphanburi 1 and Pathumthani 1 Indica rice. Paddy was dried from the initial moisture contents of 25.0, 28.8, and 32.5% dry basis to 22.5 ± 1.2% dry basis using inlet drying air temperatures between 40 and 150°C at 10°C/step. After fluidized bed drying, paddy was tempered and followed by ambient air aeration until its final moisture content was reduced to 16.3 ± 0.5% dry basis. The results showed that the head rice yield of Suphanburi 1 was significantly related to the inlet drying temperature and initial moisture content whilst there was no significant relationship between the head rice yield, drying temperature and initial moisture content for Pathumthani 1. The whiteness of the two rice varieties was slightly decreased with increase in drying air temperature and initial moisture content. It was also found that the hardness of both cooked rice varieties exhibited insignificant difference (p < 0.05) comparing to rewetted rice, which was gently dried by ambient air aeration in thin layer. The thermal analysis by DSC also showed that partial gelatinization occurred during drying at higher temperatures. Using inlet drying air temperatures in the range of 40–150°C therefore did not affected the quality of cooked rice and paddy. The milling quality of paddy was also well maintained.     

SINGLE-LAYER DRYING BEHAVIOR OF MEXICAN TEA LEAVES (CHENOPODIUM AMBROSIOIDES) IN A CONVECTIVE SOLAR DRYER AND MATHEMATICAL MODELING

Single-layer solar drying experiments were conducted for Mexican tea leaves (Chenopodium ambrosioides) grown in Marrakech. An indirect forced convection solar dryer was used in drying the Mexican tea leaves at different conditions such as ambient air temperature (21° to 35°C), drying air temperature (45° to 60°C) with relative humidity (29 to 53%), airflow rate (0.0277 to 0.0556 m ³/s), and solar radiation (150–920 W/m²). The experimental drying curves showed only a falling rate period. In order to select the suitable form of drying curves, 14 mathematical models were applied to the experimental data and compared according to their statistical parameters. The main factor in controlling the drying rate was found to be the temperature. The drying rate equation was determined empirically from the characteristic drying curve. The diffusion coefficient of the Chenopodium ambrosioides leaves was estimated and varied between 1.0209 × 10^?9 and 1.0440 × 10^?8 m ²·s^?1.The activation energy was found to be 89.1486 kJ·mol^?1.     

A COMPARTMENTAL MODEL OF THIN-LAYER DRYING KINETICS OF ROUGH RICE

ABSTRACT

Rough rice at about 21% (wet basis) was dried at various conditions of temperatures and evaporating capacities of air. The influence of both parameters on drying rate has been studied. At high temperatures, high drying rates can be achieved with low evaporating capacities. In addition, desorption isotherms of rough rice were measured at 35, 60 and 85°C and the experimental isotherms data were fitted using a modified Pfost equation.

A compartmental model was developed to simulate the grain moisture content. Heat and mass transfer coefficients were optimized using a Nelder & Mead method. Internal mass transfer coefficient was written as an exponential function of the average moisture content and temperature of the grain and the external mass transfer coefficient as a function of air temperature. The compartmental approach predicts very well the average moisture content with a mean error of about 5% in static and dynamic conditions.     

EVALUATION AND MODELING OF TWO-STAGE OSMO-CONVECTIVE DRYING OF APPLE SLICES

ABSTRACT

Two-stage drying kinetics of cylindrical pieces of apples were evaluated by subjecting test samples first to various osmotic treatments and then to convective air drying to complete the drying process. Osmotic drying was carried out with cut apple cylinders of three different sizes (12, 17 and 20 mm diameter), all with a length to diameter ratio of 1 : 1, in a well agitated large tank containing the osmotic solution at the desired temperature. Solution to fruit volume ratio was kept greater than 60. After the osmotic treatment, apple slices were further dried in a cabinet drier at an average temperature 58°C. A central composite rotatable design (CCRD) with five levels of sucrose concentrations (34–63°Brix) and five temperatures (34–66°C) was used for osmotic treatment. Half-drying time and solids gain time were used as measures of rate of drying and associated diffusion coefficients for moisture loss and solids gain were evaluated. Half-drying time decreased with an increase in temperature or concentration, or a decrease in sample size. Diffusion coefficients were lower for smaller samples, and were higher for migration of moisture as compared to solids. For a given level of moisture removal, air drying times were shorter than osmotic drying times. Composite models were developed to describe the effect of process variables and particle size on the drying behavior of apple slices.     

Convective Drying of Wastewater Sludges: Influence of Air Temperature,Superficial Velocity,and Humidity on the Kinetics

Abstract

The influence of air temperature, velocity, and humidity during convective drying of two different sludges (A and B) is investigated through a 3³ factorial design. For sludge A, a constant drying flux period is observed, while sludge B is characterized by a long decreasing drying flux phase. A sensitivity analysis shows that temperature is the main operating parameter affecting the drying kinetics. Mass and heat transfer coefficients as well as water evaporation capacities are calculated from drying curves. Transfer coefficients are related to operating conditions through dimensionless relations. For both sludges, a linear relation is found between water evaporation capacity and the maximal measured drying flux.     

Modeling of drying kinetics of green peas by reaction engineering approach

Modeling of particulate or 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. Simple models with a reasonable physical meaning are effective for engineering purposes. Thin-layer drying of green peas was carried out in a fluidized bed with a newly developed slotted gas distributor. Based on the reaction engineering approach, a drying model of green peas was well established, in which relative activation energy (ΔE_v/ΔE_v,b) was correlated with reduced moisture content (X ? X_b) at a drying air temperature of 80°C. The drying kinetics of green peas was discussed in terms of activation energy. In addition, activation energy based on a simplified material surface temperature profile was recalculated to evaluate the temperature sensitivity to the model establishment.