Henderson-Pabis Model Research Articles

Evaluation of convective drying with cold and hot air of mint (Mentha spicata) leaves

Mentha spicata, commonly known as peppermint, is a medicinal herb that is used for its pharmacological properties, obtained from its extracts and essential oils that have different health benefits, such as antioxidants, anticancer, antiparasitic, antimicrobial, and antidiabetic effects. In Mexico, it is estimated that around 130 tons of this perishable product are wasted per year, mainly due to various marketing problems. To minimize this loss, it is proposed to dehydrate it and thus prolong its shelf life. Two methods were used: first, hot air at 50 °C and 1 m/s velocity; the second one, with air at room temperature and the same velocity for 90 min and then, raise of temperature to 50 °C and the same velocity of air. In the first case 220 min and a total energy of 1800 W were needed, and with the combination of ambient temperature and later with hot air, 1700 W were required, but 290 min were used in total. In this later case the energy saving was marginal, so it is necessary to make a valorization between both methods. With respect to the numerical model that best simulates the behavior, the Henderson-Pabis model was suitable in both cases. Also, the color variation was very small, so both drying methods render similar results in the quality of the dried product.

Evaluation of Banana Sale Drying Performance Using a Tray Dryer with Mathematics Modeling

The drying process of Banana Sale involves two mathematical modeling approaches: the Newton model and the Henderson-Pabis model. The bananas are sliced and dried for 220 minutes at a temperature of 60°C with a drying rate of 4.5 m/s, and observations are made every 20 minutes. The research includes the analysis of moisture content, texture, and mass changes in banana chips. The modeling using the Newton and Henderson-Pabis models shows significant results. The drying rate coefficient (k) in both models is 0.00335, and the R2 values for both models are 0.98961 and 0.98967. These results indicate that both models are theoretically suitable for explaining the banana chips drying process, providing essential insights for understanding and optimizing this process.

Some Aspects of the Modelling of Dried Red Beets Rehydration Process

Some dehydrated products must be rehydrated before consumption or further industry processing. Optimization of the rehydration process needs mathematical models of the process. Despite the widespread use of computers and their associated software, empirical equations are still widely used in view of their simplicity and ease of computation. The mathematical description of the kinetics of mass gain, volume increase, dry matter loss, and moisture content increase and changes of rehydration indices during the rehydration of dried red beets was investigated. The effects of drying air temperature (Td), drying air velocity (vd), characteristic dimension (L), and rehydration temperature (Tr) on model constants were also examined. Red beets cubes (10 mm) and slices (5 and 10 mm) were dried in natural convection (vd = 0.01 m/s), forced convection (vd = 2 m/s), and fluidization (vd = 6 m/s) at Td = 50, 60, and 70 °C. The rehydration was conducted in distilled water at Tr = 20, 45, and 70 °C. The kinetics of rehydrating dried red beets was modelled applying five empirical models: Peleg, Lewis (Newton), Henderson–Pabis, Page, and modified Page. Equations were developed to make the model constants dependent on Td, vd, L, and Tr. Artificial neural networks (ANNs) (feedforward multilayer perceptron) were adopted to condition the rehydration indices on Td, vd, L, and Tr. The following models can be recommended as the most acceptable: (1) the modified Page model for mass gain (RMSE = 0.0236–0.0897) and for volume increase (RMSE = 0.0213–0.0972), (2) the Peleg model for dry mass loss (RMSE = 0.0161–0.610), and (3) the Henderson–Pabis model for moisture content increase (RMSE = 0.0350–0.1062). The ANNs performed the rehydration indices in an acceptable way (RMSE = 0.0528–0.2285). Both the rehydration indices and model constants depended (but to a different degree) on the investigated drying and rehydration conditions.

Comparative Study On Shade Drying, Sun Drying And Direct Solar Drying Of Mint Leaves

Aromatic herbs are in high demand in food processing industries, Cosmetics, biotechnology and pharmaceuticals. Mint leaves can be used as a flavoring agent in food; they are also valued for their antibacterial and antioxidant properties. Mints (Mentha spp.) are a well-known medicinal and aromatic plant. The mint leaves are used as fresh due to high moisture content. Drying helps to inhibit bacterial growth and decrease water activity. The purpose of this study was to enhance their shelf life and save packaging and shipping costs. A comparative study on the drying process of mint leaves was conducted under shade drying, sun drying and direct solar dryer. Fresh mint leaves were collected from the medicinal block of Krishi Vigyan Kendra Vaishali, Bihar, India. They were washed and the excess amount of water was removed from the surface of the leaves. The various parameters recorded hourly in the experiments were temperature and relative humidity inside and outside the direct solar dryer; the weight of the mint leaves was recorded hourly. Temperature plays a great impact in the drying process. The maximum temperature reached in solar drying up to 560 C as compared to 420 C in sun drying. The minimum relative humidity reached in the direct solar dryer was 17 percent as compared to 28 percent in sun drying.The drying curve data suggest that the drying displays a falling rate period. Henderson pabis model was fitted for drying processes in shade drying, sun drying and direct solar drying. The highest sensory score is reached with color (8.7), flavor (8.5), appearance (9) and overall acceptability (8.7) when dried in a Solar dryer. To fabricate a low -cost environment friendly solar dryer is quite a challenging task. The solar dryer was built by locally available ply-wood and low- cost materials. The dryer consists of transparent glass, exhaust fan, wire mesh screen, solar cell. Another challenge is to use the maximum solar radiation inside the solar dryer. Inclination angle of the Transparent glass was made 15o to get maximum radiation. Future scope: World is suffering from harmful gases originated from burning of fossil fuels. Solar energy is a safer and cleaner energy source. Solar dryer can also reduce up to 34 % CO2 emission. This study aims to maintain best sensory quality of dehydrated herbs and spices.it is also aiming for low -cost clean drying technology and sustainable development.

Influence of two-stage drying methods on the physical properties and drying characteristics of sweet potato slices

The effects of single-stage freeze-drying, two-stage mid-infrared assisted freeze-drying and vacuum pre-drying and freeze finish-drying on the operational time, energy uptake, color and hardness properties of sweet potatoes were investigated. Prior to the drying procedure, the samples were unpretreated and pretreated in citric acid solution. Drying curves of sweet potato were determined for mid-infrared and vacuum pre-drying at different drying temperatures (40, 50 and 60°C). The combination of mid-infrared and freeze-drying showed the largest reduction in both drying time (52%) and specific energy consumption (52%) compared to single-stage freeze-drying. Four different empirical thinlayer drying models were compared based on their coefficient of determination and root mean square error to estimate the drying curves. The results showed that the Polynomial and Henderson-Pabis models were the most appropriate to describe the drying of sweet potato slices. The total color difference and hardness values of sweet potato degraded while increasing the pre-drying temperature. The citric acid pretreatment enhanced the texture and color of dried sweet potato.

Mathematical description of the drying process of mulberry leaves

Three mathematical models were used in this study: the Newton model, the Henderson-Pabis model, and the Page model. Three models were chosen for comparison with experimental data because they are commonly used to describe the drying characteristics of thin films and are simplifications of the theoretical model derived from the diffusion equation (Fick’s second law). The Newton model is a mathematical model for drying a thin layer, also called the Lewis model. Lewis described that the transfer of water from food and foodstuffs can be shown by analogy with the outflow of heat from the body when the body is immersed in a cold liquid. The Henderson-Pabis model has been used in thin-layer drying of various agricultural products, including drying of corn, wheat, coarse rice, beans and tubers. The Page model is a modified model of the Lewis model. Page proposed this model to correct the shortcomings of the Lewis model. Page’s model has created models that are suitable for describing the drying of various agricultural products and are easier to use than other equations.

Thin Layer Drying Kinetics of Salt Water Crab (Cardisoma Guanhumi)

Crab meat undergoes rapid microbial deterioration after death, placing it in the category of highly perishable sea foods (the Crayfish and lobsters alike) Thus, this affects its economic value. Drying is one of the techniques that will provide consumers with ready-to-use dried crabmeat to incorporate into daily meals such as soups, sauces, and so on. This study thus, investigated the drying behavior of the crab on thin-layers. A laboratory convective oven dryer was used as the heating source, on the temperature (range of 60 - 100°C) applied in a varying manner on multiples of 10℃. The layer thickness was about 45-mm. as with high moisture sea foods, the drying profile showed a typical falling rate period with no distinct constant rate period for all the temperature levels used in this work. Moisture loss (diffusion) data obtained from the experiments were fitted to three popular semi-empirical thin-layer models of Lewis, Henderson-Pabis, and Page, and their suitability was validated using statistical parameters such as Root Mean Square,( R2), X2 and RSME. This was done to select thin-layer model that would suitably describe the drying kinetics of the samples over the range of temperature levels chosen in this work. Consequently, the Henderson-Pabis model and that of Page model were taken to have reliably predicted the drying behavior of the samples at the chosen temperature levels.

Radio frequency combined hot air (RF-HA) drying of tilapia (Oreochromis niloticus L.) fillets: Drying kinetics and quality analysis

Hot-air assisted radio frequency (RF-HA) heating was utilized for tilapia fillets drying to achieve rapid, uniform drying and improved sample physical properties. Effects of sample thickness (5, 8 and 10 mm) and with or without wrapping material (skin or gauze) were investigated under both HA and RF-HA drying treatments. The drying characteristics and quality parameters of tilapia fillets in hot air (HA) and RF-HA drying were then determined. Results show the drying rate of RF-HA drying is 1.1–1.4 times of that of HA drying for tilapia samples with different thicknesses. RF-HA dried samples are with higher rehydration rate and lower volume shrinkage rate, especially for fillets with larger thickness. The wrapped gauze did not show significant influence on the color of tilapia sample in RF-HA drying but improved the rehydration rate, while the samples with preserved fish skin resulted in a lower overall quality under both HA and RF-HA drying treatments. Page model and Henderson-Pabis models were suitable to be used describing the drying kinetics of RF-HA drying and HA drying tilapia, respectively.

Experimental and modelling studies of convective and microwave drying kinetics for microalgae

Conventional microalgal drying consumes huge time and contributes to 60–80% of downstream process costs. With the aim to develop an effective and rapid drying process, the present study evaluated the performance of microwave based drying (MWD) with a power range of 360–900 W and compared with the conventional oven drying (OD) at 40–100 °C. MWD was found to be efficient due to uniform and volumetric heating because of dipolar interaction, with an effective diffusivity of 0.47 × 10−9−1.63 × 10−9 m2 s−1, comparatively higher than OD. Activation and specific energy of 32.43 W g−1 and 42.9–56.07 kWh kg−1 was projected respectively, and a falling rate period with best fit for Newton and Henderson-Pabis model was observed for MWD. Uniform heating from internal sub-surface avoided cell distress, resulting in 14.4% higher lipid yield and significant preservation of biochemical components that can be processed into bioenergy and valuable products in microalgal biorefinery.

Influence of UV-B Pretreatments on Kinetics of Convective Hot Air Drying and Physical Parameters of Mushrooms (Agaricus bisporus)

The present study aimed to investigate the effects of ultraviolet-B (UV-B) pretreatments on selected physical properties (shrinkage, rehydration, color, texture) and drying kinetics and to model the drying kinetics of hot air dried mushrooms using several mathematical models, such as the Henderson–Pabis, logarithmic, two-term, Verma, Wang and Singh, Midilli, and modified Henderson–Pabis models. Results showed that the use of UV-B pretreatment before mushroom drying reduced shrinkage, color changes, firmness, and drying time and increased rehydration and the effective moisture diffusion coefficient. The amount of activation energy increased from 16.55 ± 1.3 kJ/mol (control sample) to 18.27 ± 2.2 kJ/mol (UV-B treated samples for 30 min), 19.72 ± 1.4 kJ/mol (UV-B treated samples for 60 min), and 21.9 ± 1.9 kJ/mol (UV-B treated samples for 90 min). However, increasing the drying temperature increased the shrinkage and firmness of samples. The modified Henderson–Pabis model with the highest correlation coefficient (R2) and lowest root mean square error (RMSE) and chi-square (χ2) showed the best fit for every drying curve, proving to be an excellent tool for the prediction of drying time.

Statistical Examination of Uncaria gambir Roxb Drying Modeling

This study investigates the drying modeling of Uncaria gambir Roxb using convective desiccant examined by statistical parameters. Three types of drying modeling are investigated, i.e. the Newton, Page and Henderson-Pabis models. The drying conditions of Uncaria gambir Roxb were set at 35oC, 45oC and 55oC and air velocity of 1.2 m/s. The results show that the Page modeling is the best fit model for this investigation based on values of R2 (coefficient of determinant), RMSE (root mean square error) and χ2 (chi-square) goodness of fit test derived from (MR) moisture ratio equation. The Page modeling shows R2 value nearest to unity and lowest values of RMSE and χ2 are obtained for all given temperatures (35oC, 45oC and 55oC) at air velocity of 1.2 m/s. The drying modeling is useful for optimization in design process encountered with product quality and cost of production.

Study of the drying kinetics of the malt bagasse in a pneumatic transporter

Malt bagasse is a by-product of the brewing industry that has high moisture, making it very unstable and susceptible to fast microbial deterioration. This work evaluated drying kinetic models of malt bagasse during pneumatic transport with air flow at 30, 45 and 60?C and layouts of 4.5 and 7.0 m. The results showed that the decrease of moisture from malt bagasse was favored at higher air temperature due to the higher diffusion coefficient. In the ranges measured, the values of the effective moisture diffusivity and heat transfer coefficient were obtained between 2.05?10?10 to 12.74?10?10 m2/s and 175 to 363 W/(m2 K), respectively. Average energy for liquid diffusion in the malt bagasse drying process was 44.30 kJ/mol. Pneumatic transport with air flow at 60?C and layout of 7.0 m reached rapidly the final moisture of 12% (w.b.), which may reduce transport costs and allow for long periods of stable storage for malt bagasse. The statistical tests results showed that the experimental data presented excellent fit using the modified Henderson-Pabis model, in the temperature range for both layouts.

Kinetic study, optimization and comparison of sun drying and superheated steam drying of asam gelugor (Garcinia cambogia)

The purposes of present study are to compare the kinetic drying of the G. cambogia through sun drying and superheated steam drying (SSD) method and optimizing the quality of SSD of it through response surface methodology. G. cambogia fruit rinds were dried at temperature of 150°C, 200°C and 250°C. The drying curves were fitted into the mathematical model of Page, Lewis and Henderson-Pabis models. Page model was found to be the best in describing the drying behavior of G. cambogia. Drying rate constant (k) increased as temperature increased and SSD method had overall higher drying rates ranged from 5.929 x 10-5 to 5.861 x 10-4 min-1 than sun drying method which was 4.980 x 10-6 min-1 . Total acid number showed a trend of increased followed by decreased over drying time. superheated steam drying process of G. cambogia fruit rinds was optimized by using response surface methodology employing a central composite design. Drying time and temperature were the factors in optimization while moisture content (wet basis), acid number and lightness (*L) were the response parameters. Experimental results were fitted to a second-order polynomial model and the model fitness and optimal drying condition were determined by regression analysis and analysis of variance. The optimal conditions for superheated steam drying of G. cambogia fruit rinds were identified as 46.60 mins and 150°C with the composite desirability of 0.913. Application of superheated steam drying under controlled conditions resulted in faster drying process and better quality of dried G. cambogia than conventional sun drying technique.

Comparative kinetic analysis of convective and vacuum dried Opuntia ficus-indica (L.) Mill. cladodes

Opuntia ficus-indica (Linnaeus) Miller more usually known as fodder palm or nopal belongs to family Cactaceae. In the present study, the drying behavior of the O. ficus-indica cladodes was observed. The study concentrates on comparatively studying two types of commercial drying methods viz., forced convective drying (tray drying) and vacuum drying to dry nopal cladodes at three different temperatures viz. 40, 50 and 60°C. The equilibrium moisture contents for forced convective drying was achieved at 540–720 min and for that of vacuum drying at 600–840 min. Three mathematical drying models for thin layer drying viz. Page, Lewis and Henderson-Pabis model were evaluated for both convective drying and vacuum drying. Statistical parameters such as the coefficient of determination (R<sup>2</sup>), root mean square error and reduced χ<sup>2</sup> were used to fit the models. Page model was found to be satisfactory for both forced convective and vacuum drying of the nopal cladodes at 40 and 50°C respectively. Among these, two drying methods, forced convective drying method was found to be more suitable than the vacuum drying method for nopal cladodes on the basis of drying time and statistical parameters.

Drying kinetics modeling of apple and zucchini slices vacuum impregnated with anthocyanins

ABSTRACT: The aim of this research was to study the drying kinetics of apple and zucchini slices enriched with anthocyanins and to evaluate the influence of drying temperature on the anthocyanin content of apple and zucchini snacks. Apple (Granny Smith) and zucchini (Cucurbita pepo) slices were enriched with anthocyanins by vacuum impregnation with blueberry juice. Then, slices were dehydrated at 40, 50 and 60 ºC with 1.0 m/s air flow. Dehydrated samples were referred to as anthocyanin enriched snacks. Diffusion coefficient values improved by increasing the drying temperature, within the 2.81×10-10 to 5.78×10-10 m2/s range for apple slices and 2.02×10-10 to 3.99×10-10 m2/s for zucchini slices. The activation energy was 31.19 kJ/mol and 80.33 kJ/mol for apple and zucchini slices respectively. Page, Weibull, Logarithmic, Henderson-Pabis and Lewis models best fitted the experimental data. Snacks obtained at 60 °C retained a higher concentration of anthocyanins, reaching values of 592.81±52.55 and 464.62±48.44 mg of cyaniding-3-glucoside equivalent/kg dry matter in apple and zucchini snacks respectively. Combination of vacuum impregnation and hot air drying was a technological alternative for producing snacks with functional properties.

Kinetics of microwave heating and drying of drilling fluids and drill cuttings

ABSTRACTDrill cutting decontamination by microwave drying has been studied over the past few years and has proved to be a promising technology. This study aimed to investigate fundamental aspects of kinetics of heating and drying of drilling fluids and drill cuttings by microwaves. The microwave heating curve of cuttings free of fluid, drilling fluids, and pure organic compounds usually used in the formulation of these fluids was evaluated to understand the behavior of each component in microwave cutting decontamination. Furthermore, commercial software was used to describe the heating kinetics of the drilling fluids used in this study. The drying kinetics of cuttings contaminated with these drilling fluids was also studied at three temperatures of control. Some classic models of conventional drying of solids were used to describe the removal kinetics of the liquid components present in contaminated cuttings (water and organic compounds). Important aspects related to the interaction of these components in the drying operation and solid heating, water evaporation, and the drag of organic compounds were investigated. Both drilling fluids showed a very similar kinetic heating. Pure organic bases did not show a significant heating. For the same drying time, the removal of paraffin is more intense than the olefin. In respect to organic component removal from cuttings contaminated with both fluids, the kinetic drying curves are similar. The Page model was the one that best describes the drying operation of drill cuttings contaminated with both drilling fluids. The microwave drying model (MDM) model is proposed in this work as a simple modification in the Henderson–Pabis model: the addition of a third parameter. The incorporation of this parameter enabled a better fit of the experimental data. Computational simulations show an electric field with symmetrical patterns for the two BR-MUL fluids analyzed.

MATHEMATICAL MODELING OF ORANGE SEED DRYING KINETICS

Drying of orange seeds representing waste products from juice processing was studied in the temperatures of 40, 50, 60 and 70 °C and drying velocities of 0.6, 1.0 and 1.4 m/s. Experimental drying kinetics of orange seeds were obtained using a convective air forced dryer. Three thin-layer models: Page model, Lewis model, and the Henderson-Pabis model and the diffusive model were used to predict the drying curves. The Henderson-Pabis and the diffusive models show the best fitting performance and statistical evaluations. Moreover, the temperature dependence on the effective diffusivity followed an Arrhenius relationship, and the activation energies ranging from 16.174 to 16.842 kJ/mol

Hot Air Drying Characteristics of Sukkari Date (Phoenix dactylifera L.) and Effects of Drying Condition on Fruit Color and Texture

Abstract Convective hot air drying was used to dry date fruits at different air temperatures and velocities. The kinetics of drying was evaluated by 10 common models. The fruit color and texture were examined before and after drying. Drying time increased as both drying temperature and air velocity decreased. Best fits to the experimental data were provided by the Midilli and Kucuk model, followed by the logarithmic, two-term exponential, and Henderson–Pabis models. Drying affected the fruit color and texture. To minimize such changes, the range of drying temperature and air velocity should be 60–70°C and 2 m/s, respectively.

Drying Kinetics, Biochemical and Functional Properties of Products in Convective Drying ofAnchovy (Engraulis anchoita) Fillets

Abstract The aim of this work was to study the convective drying of anchovy (Engraulis anchoita) fillets and to evaluate the final product characteristics through its biochemical and functional properties. The drying temperatures were of 50, 60 and 70°C, and the fillet samples were dried with the skins down (with air flow one or the two sides) and skins up (with air flow one side). The drying experimental data were analyzed by Henderson–Pabis model, which showed a good fit (R 2 > 0.99 and REQM < 0.05). The moisture effective diffusivity values ranged from 4.1 × 10–10 to 8.6 × 10–10 m2 s−1 with the skin down and 2.2 × 10–10 to 5.5 × 10–10 m2 s−1 with the skin up, and the activation energy values were 32.2 and 38.4 kJ mol−1, respectively. The product characteristics were significantly affected (p < 0.05) by drying operation conditions. The lower change was in drying at 60°C with air flow for two sides of the samples and skin up. In this condition, the product showed solubility 22.3%; in vitro digestibility 87.4%; contents of available lysine and methionine 7.21 and 2.64 g 100 g−1, respectively; TBA value 1.16 mgMDA kg−1; specific antioxidant activity was 1.91 mMDPPH g−1 min−1, and variation total color was 10.72.

<b>Sorption isotherms and drying kinetics of grapefruit seeds</b> - doi: 10.4025/actascitechnol.v35i4.13658

The drying of grapefruit seeds, by-products from grapefruit processing, was studied at 40, 50, 60 and 70°C and at three air velocities, 0.6, 1.0 and 1.4 m s-1. Sorption isotherms of grapefruit seeds were obtained at each temperature by the static method using saturated salt solutions. The Henderson model adequately described the sorption isotherms, over the entire temperature range. Drying rates indicated that the drying of grapefruit seeds took place under the falling rate period. Effective moisture diffusivity in grapefruit seeds ranged from 4.36 × 10-10 to 6.82 × 10-10 m² s-1. The temperature dependence of the effective diffusivity followed an Arrhenius relationship, and the activation energies were 12.23, 11.29 and 11.79 kJ mol-1 for dried grapefruit seeds under air velocities of 0.6, 1.0 and 1.4 m s-1, respectively. Three thin-layer models were used to predict the drying curves, Page, Lewis, and Henderson-Pabis model. The Page model presented the best fit for all drying air temperatures and velocities studied.