Technological advance in the dehydration processes has led to the study of techniques by which quality products can be obtained and contribute, at the same time, to reduce energy consumption by improving the efficiency of processes and equipment. Hot-air drying is one of the processes in which such interests are pursued because, in addition to its importance in the transformation of agro-food products and in the systems of post-harvest treatment, it is one of the industrial activities that involves a considerable energy consumption. For this reason, intermittent drying technology has been used in order to shorten the heating time, preserve the quality and minimize energy consumption in the drying of heat-sensitive materials and where kinetics is controlled by internal resistance to the mass and heat transfer.

The term “intermittent” groups those drying technologies that use operating conditions which vary during processing. In the case of drying where heating energy is applied periodically, the intermittence is due to consecutive heating and resting periods. The advantages of this type of intermittent drying, as compared to continuous drying, are linked to the conditions, number and duration of the resting periods. During the resting there is an increase of water close to the product surface which leads to an increase in the drying velocity, and a decrease in the heating of the material, when the product is heated again. The application of the resting periods reduces the heating time, decreasing the necessary energy and the time the product is exposed to the effect of temperature.

The objective of the present work was to contribute to the study and optimization of intermittent drying through its application to mango, in order to improve the process's energy efficiency by means of the periodical supply of thermal energy.

One of the most widely-sold cultivars of mango (Mangifera Indica L. cv. Tommy Atkins), an agricultural product of great worldwide economic importance, was used to carry out this study. Likewise, it was chosen because the products processed from this tropical fruit, in addition to offering an alternative in the use of the surplus production stock and the diversification in the offer of products of added value, have had market acceptance thanks to their nutritional properties and exotic characteristics.

For the study and optimization of the intermittent drying of mango, the prior development and validation of a model that adequately represents the physical phenomena governing the process was necessary. Furthermore, an objective function was needed to formulate an optimization problem for the energy consumption of the process and for the product quality.

To specify the process model, the mass and heat transfer phenomena were analyzed in a system with cubic geometry. The formulation of the model was performed considering the material to be homogeneous and isotropic; that the effect of the shrinkage on the transfer processes was negligible; that the thermal conductivity and effective diffusivity depended on the local values of humidity and temperature; and that the external resistances to mass and heat transfer were not negligible.

In order to complete the process model, equations to estimate the physical properties of the product and the air were considered. The equations to estimate the thermal conductivity, the specific heat and the sorption isotherm were defined from experimental information, due to the absence of bibliographic information for these properties of the cultivar “Tommy Atkins”, and to the limited information available for similar cultivars under the experimental conditions used in this study. 

The thermal conductivity of the mango pulp was determined at temperatures of between 20 and 80 ºC and moisture contents of between 1.1 and 9 kg kg-1 (b.s.), by means of the cell method. The thermal conductivity of the mango pulp was more heavily dependent on the moisture content than temperature; common behavior in high moisture foodstuffs.

The specific heat of the dry matter of the mango was determined at temperatures of between 20 and 70 ºC using differential scanning calorimetry (DSC). The specific heat of the mango dry matter was more heavily dependent on the temperature between 20 and 50 ºC.

The sorption isotherms of mango pulp were determined at temperatures of between 10 and 50 ºC using electric hygrometers. GAB's model was considered the best-suited model to represent the influence of the water activity and the temperature on the equilibrium moisture content of the mango pulp (VAR = 99.6 %, RMSE = 0.057). The sorption isotherms and isosteric heat behaved as expected in all agro-foodstuffs and a similarly to the mango pulp of other cultivars.

The process model was adjusted using experimental values of continuous and intermittent drying at heating temperatures between 45 and 65 ºC, and an air velocity of 4 m s-1, in order to identify the effective diffusivity, which was defined as a function dependent on the local moisture and local temperature. The fitting was carried out by minimizing the difference between the experimental and estimated data for the average moisture content and the temperature at the centre of the samples, and considering simultaneously experimental data of processes performed in different drying conditions. The model was subsequently validated by means of experimental data from different experiments of intermittent drying at heating temperatures between 45 and 70 ºC, air velocities of 2, 3 and 4 m s-1, and a cycle of intermittence.

The proposed identification procedure allowed the parameters of the effective diffusivity, identified by means of fitting the process model to the drying kinetics, to be independent of the experimental conditions of the experiments used in the fitting, after having considered that such parameters depended only on the material characteristics. At moisture contents between 9 and 0.03 kg kg-1 (d.b.), the value of the effective diffusivity of mango varies between 6.14×10-11 and 1.86×10-10 m2 s-1 at 10 ºC, and between 1.35×10-9 and 3.37×10-9 m2 s-1 at 70 ºC, respectively. The identified values of the effective diffusivity were within the range of expected values for the drying of agro-foodstuffs and they are similar to those obtained by other authors in the modeling of drying kinetics of mango of different cultivars. In the effective diffusivity model, the activation energy was the term that included the dependence of moisture content. The values of activation energy ranged between 39 and 41.6 kJ mol-1 at moisture contents between 9 and 0.03 kg kg-1 (d.b.), respectively, showing more variation with the moisture at values under 1 kg kg-1 (d.b.).

The experimental and estimated values for the moisture content and the temperature were satisfactorily correlated (VAR > 99.7 % and RMSE < 0.453 for the moisture content, and VAR > 91.1 % and RMSE < 5.87 for the temperature) considering the data used in both model fitting and validation.

The optimization problem of the intermittent drying process was defined as the search for the duration of the heating and resting periods, which minimize an objective function defined as the enthalpy gain of the product. The optimization problem was solved by using the previously adjusted and validated process model, in intermittent drying processes of one to three cycles, at heating temperatures of 50, 60 and 70 ºC, and air velocities of 2, 3 and 4 m s-1.

Matlab® R2007b and COMSOL Multiphysics® 3.4 were the software programs used to develop the algorithms to fit the model and to solve the optimization problem. COMSOL® was used to solve, using the finite element method, the partial differential equations of the mathematical model, and Matlab® to formulate and solve the optimization problem. 

According to the optimization results, comparing the continuous drying and the intermittent drying application, a decrease between 13.4 % and 20.1 % for the average enthalpy gain, and between 2.8 % and 8.6 % for the time of heating were attained, according to the heating temperatures and the number of cycles considered. The intermittent drying effect leads to the enthalpy gain and the heating time being equivalent to continuous drying processes developed at lower temperatures or velocities.

The application and optimization of the intermittent drying of mango, in addition to increasing the energy efficiency of the process, could improve the product quality by shortening the enthalpy content, the surface temperature and the product’s exposure to heating.  Likewise, it may minimize quality problems related to changes on the product surface, since the intermittent drying reduces the surface temperature as well as the heating time necessary to reach a given moisture content.