Mathematical Models for drying behaviour of green beans

The main objectives of this paper are firstly to investigate the behavior of the thin layer drying of beans, peas and tomato experimentally in a microwave oven for different power density (1; 2 and 3W/g) and secondly to perform mathematical modeling by using thin layer drying models from literature. The variation of the moisture content of the products studied and four statistical models are tested to validate the experimental result. A non-linear regression analysis is used to evaluate the models constants. The Page and the modified Page models were found to be the most suitable to describe the microwave drying curves of beans, peas and tomato respectively. The effective diffusivity for beans, peas and tomatoes was ranged from 0.326×10 -9 to 1.609×10 -9 m²/s, from 0.169×10 -9 to 1.024×10 -9 m²/s and from 0.484×10 -9 to 2.127×10 -9 m²/s, respectively. The experimental data of the products have been analyzed to obtain the values of the effective diffusivity as a function of power den...

Case Studies in Thermal Engineering, 2019

This study investigated the modelling of moisture diffusivity of processed locust beans under forced and natural convection mode using solar drying with thermal storage materials (gravel). The experimental data obtained were fitted into eleven existing thin layer models and the best model choice was based on a comparison of statistical parameters including determination coefficient (R 2), reduced chi-square (ᵪ 2), root mean square error (RMSE), square error sum (SSE) and normalised root mean square error (NRMSE) between the experimental and predicted data. The results showed that the Lewis model gave the best description of solar drying of locust beans under forced and natural convection mode. Thus, this model may be adjudged to represent the drying characteristics of locust beans in a thin layer within the experimental range of study. The obtained moisture diffusivity values were 2.73496 and 1.82331 � 10-11 m 2 /s for the solar drying of locust beans under forced and natural convection mode respectively. The predicted Arrhenius constant and activation energy values were respectively 2.54 � 10-11 m 2 /s and 21.65 kJ/mol.

Journal of Food Process Engineering, 2014

The kinetics of the hot-air drying of soybeans was modeled in order to evaluate the influence of temperature and velocity on the kinetic parameters. A convective dryer with air temperature from 30 to 195C and air flows of 0.75, 1.35, 2.0 and 2.5 m/s was used. Three different mathematical models were applied to simulate the drying process (two empirical equations, exponential and Page's, and Fick's diffusion model) and the diffusivity coefficient increased from 2.5 × 10 −11 to 6.69 × 10 −10 m 2 /s for a range of air temperature between 30 and 195C. Both temperature and velocity influenced drying rate. The differential evolution optimization method was used toward parameter estimation. The goodness of fit of the proposed models, evaluated using linear regression coefficient (R 2 ), chi-squared parameter (χ 2 ) and root mean square error, indicated a satisfactory validation, mainly regarding to the exponential and Page's models.

Journal of Food Engineering, 1990

A simplified mathematical model based on basic physical and transport properties, such as mass and heat difisivities, is proposed for the prediction of the behaviour offoods during drying. The model takes into account the effect of moisture-solid interaction at the drying surface by means of any sorption equation available and the change in solid density due to shrinking. Fourier's and Fick's laws describe the transfer of heat and mass in the solid. At the surface, mass and heat balances together with the chosen sorption equation are used to represent the vaporization of water. Temperature and moisture-content profiles are obtained by integration of the resulting set of partial differential equations, an implicit-finitedifferences algorithm being used. The model, which predicted experimental results for the drying of apple slices and carrot cubes to within I.1 % of the moisture content and 12% of the drying rate, can therefore be used for the determination of drying profiles. NOTATION 2 Water activity External surface area of the solid (m') ci Empirical parameters for eqn (13), i = 1 to 4 cP Heat capacity of the solid, at constant pressure (kcal/kg "C) D Moisture-effective diffusivity within the solid (m2/s) E" Latent heat of vaporization of water (kcal/kg) h Air-solid heat-transfer coefficient (kcal/m2 s 'T) *To whom correspondence should be addressed.

Journal of Food Engineering, 2003

The effect of air conditions (air temperature, air humidity and air velocity) and characteristic sample size on drying kinetics of various plant materials (potato, carrot, pepper, garlic, mushroom, onion, leek, pea, corn, celery, pumpkin, tomato) was examined during air drying. A first-order reaction kinetics model was used, in which the drying constant is function of the process variables, while the equilibrium moisture content of dried products within the range of 0.10-0.90 water activity at two temperatures (30 and 70°C

International Journal of Food Engineering, 2009

This article aims at determining thin-layer drying curves for grains of lima bean, variety olho-de-peixe and to predict them using diffusion models. Samples of lima bean (110.0 g) with initial moisture content of 66.0% (wet basis, wb) were dried at temperatures of 40.0, 50.0 and 60.0°C. The effective diffusivity of moisture was determined by analytical solutions of the mass diffusion equation (Fick’s second law) with prescribed boundary condition for spherical, cylindrical, and infinite slab at each temperature. Comparison with the experimental data showed that the infinite slab with constant diffusivity predicted more accurately, but statistical indicators of the goodness of fit were not completely satisfactory. Thus, a model for the infinite slab with constant volume, moisture-dependent diffusivity and convective boundary condition was numerically integrated. This model was solved by the numerical method of finite volumes with fully implicit formulation. The values obtained for th...

2016

The effect of moisture content drying rate for different diameters of green peas at different temperatures is critically analyzed in this paper. The above parameters under different temperatures and diameters are analyzed without using blanching technique. It is observed that the process plays a vital role in the reduction of the moisture content under different temperatures. The drying of green peas was done in a fluidized bed dryer operating at different temperatures. The data obtained from the experiments were subjected to statistical analysis.

Thin-layer drying kinetics of bell pepper was experimentally investigated in a laboratory scale convective dryer. Experiments were performed at air temperatures of 40, 50, 60, 70, and 80ºC and constant air velocity of 2 m/s. In order to select a suitable form of the drying curve, 12 different thin layer drying models were fitted to experimental data. The high values of coefficient of determination and the low values of reduced chi-square and root mean square error indicated that the Logarithmic model could satisfactorily illustrate the drying curve of bell pepper. The Logarithmic model had the highest value of R 2 (0.9929), the lowest 2 χ (0.00003497) and RMSE (0.00481743). The Logarithmic model was found to satisfactorily describe the drying behavior of bell pepper. Fick's second law was used to calculate the Effective moisture diffusivity. The moisture diffusion coefficient varied between 1.7 × 10 -9 and 11.9 × 10 -9 m 2 /s for the given temperature range and corresponding activation energy was 44.49 kJ/mol.

Journal of Food Engineering, 2007

The drying kinetics of the red bell pepper (var. Lamuyo) was studied and modeled at different temperatures (50, 60, 70 and 80°C), using an air velocity of 2.5 m s À1 . Only the falling rate period could be observed during the experiment. Effective moisture diffusivity was estimated to be between 3.2 · 10 À9 and 11.2 · 10 À9 m 2 s À1 within the temperature range studied. The effect of temperature on the diffusivity was described by the Arrhenius equation with an activation energy (E a ) of 39.70 kJ mol À1 . The Newton, Henderson-Pabis, Page and Page modified models were applied to the experimentally obtained moisture data. The fit quality of the models was evaluated using the correlation coefficient, sum square error, root mean square error, and Chi-square. Comparisons of the experimental values with the calculated values demonstrated that the Page modified model produced the best fit for every drying curve, representing an excellent tool for estimation of the drying time.

Food Science and Technology, 2024

Convective drying of mung bean seeds was conducted to investigate drying kinetics and mass transfer parameters at temperatures of 40, 50, 60, 70, and 80°C and a fixed air velocity of 1.2 m s -1 . Drying characteristics were determined by drying rate, moisture ratio, diffusion coefficient, activation energy, Biot number, and mass transfer coefficient. Drying models such as Newton, Page, Henderson and Pabis, Logarithmic, Midilli, Two-term, and Diffusion approximation were applied and fitted to the moisture ratio of the experimental data. The drying rate was significantly affected by the drying temperature. The Midilli model was considered the most suitable for experimental drying curves. The effective moisture diffusivity ranged from 3.19×10 -9 to 10.76×10 -9 m 2 s -1 , with an activation energy of 59.78 kJ mol -1 . Similar to the mass transfer coefficient, the Biot number increased with increasing drying temperature. The simultaneous transfer of heat and mass was controlled by diffusion and surface.