AUTHORS’ CONTRIBUTION
J.H.F. Silva contributed in the conception of the work, investigation, methodology, data collection, data analysis and interpretation, critical revision, writing and final approval of the version to be published. J.S. Silva Neto assisted in writing, critical reviews, discussion of concepts and data analysis. E.S. Silva contributed in data collection, writing and critical reviews. D.E.S. Cavalcanti contributed in the conception of the work, discussion of concepts, methodology and critical reviews. P.M. Azoubel participated in the conception of the work, data analysis and interpretation, critical revision, writing, supervision, final approval of the version to be published and funding acquisition. M. Benachour took part in the conception of the work, data analysis and interpretation, critical revision, writing, supervision and funding acquisition.
Drying is one of the most traditional processes of food preservation. It is widely used for reducing the water content and, thus the water activity, inhibiting or reducing microbial growth and enzymatic reactions, increasing the shelf life without the aid of additives (
Sound waves propagate mechanically,
Drying presents some difficulties in understanding the mechanisms related to convective heat and turbulent fluid in the exchange zones. For its optimization, it is not enough only to apply synergistic techniques but also to investigate such mechanisms. Therefore, a better understanding of the physical phenomena of convective drying of foods using predictive tools has become important (
Considering drying as an important food preservation method, the present work aims to study, experimentally, different melon drying conditions with and without ultrasound pretreatment. Also, numerical simulation of heat transfer using computational fluid dynamics (CFD) served to show the temperature profile of the melon slice.
Mature melons of the yellow variety (
Melon samples were weighed, placed in 100mL beakers containing distilled water, and placed in an ultrasonic bath (model USC2580A; Unique, Indaiatuba, Brazil), without mechanical agitation, at approx. 25 °C. Ultrasound application time was 10, 20 and 30 min. The sample/distilled water mass ratio used was 1:4, and the ultrasound frequency was 25 kHz (154 W), according to the literature (
where
where
The moisture content of the samples without ultrasound treatment (W/O US) was 88.16%. Sample moisture content increased to 90.19% after a 10minute pretreatment with ultrasound (US10), 90.74% after 20minute ultrasound (US20), and 90.94% after 30minute ultrasound (US30).
Convective drying of melon slices with and without (control treatment) ultrasound pretreatment was performed at 50, 60 and 70 °C, using a stainlesssteel fixed bed dryer (tray dryer) with a fixed air velocity of 2.0 m/s. The choice of the temperature range in this study was to avoid very long drying time (temperatures below 50 °C) and high temperatures, which would cause the loss of nutritional components (temperatures above 70 °C).
Samples were weighed using a semianalytical balance. The time intervals used for weighing were 15 min during the first hour of drying and 30 min until the equilibrium condition was reached (
where
The following equation presents the solution to Eq. 3 proposed by Crank (
where
The linear dependence of the Arrhenius equation, which is a linear function of the logarithm of the diffusivity and the inverse of the temperature, was tested during the drying process using the following equation:
where
Three empirical models were used for drying data fit (
where
The fit of all the models to the experimental data and their parameters was verified with TIBCO Statistica v. 10.0 (
where
To simulate the temperature profile during the melon drying, the thermal conductivity (
The computational domain was solved using the finite volume method, responsible for solving the NavierStokes equations based on conservative principles (
The greatest concentration of mesh elements occurred in the wall and contact regions (interface) due to the choice of ‘curvature and proximity’ as criteria to be considered when generating the mesh for the domains. The nodes in the mesh elements were generated by the drop method, which does not generate nodes between the vertices of the geometric element. Due to the importance of the fluid (air) domain, the unstructured mesh was chosen for this domain, which is generated through the Delaunay triangulation and which provides more details for the results. However, the solid domain (melon slice) was represented by a structured mesh, because of its geometric simplicity (
Schematic representation of: a) melon slice (I) and simplified dryer body (II), b) structured and unstructured mesh zones used in the XY plane, and c) denser unstructured zone around the melon (I), structured mesh zone used to represent the melon (II) and less dense mesh area, representing the external fluid medium (drying air) (III)
Since the trays used here consisted of a network of fine stainlesssteel wires, instead of using perforated plates which would affect the airflow into the dryer, they were not considered in the geometric domain used for simulations. Such presumption was necessary since the computational cost associated with the mesh refining would be higher. Also, the wires are very thin, so their interference with the airflow can be neglected.
Regarding the presumptions made, the effect of shrinkage, generation of heat inside the product, and radiation effects may be neglected. Thermal properties were considered constant. For the turbulence, medium intensity (5%) and eddy (turbulent) viscosity ratio 10, as its use is recommended when there is no information on the turbulence at the entrance, were considered (
Conservation of mass (law of continuity):
Conservation of momentum (Newton's second law of motion):
Conservation of energy (first principle of thermodynamics):
where
The generalized energy equation (Eq. 16) had its velocity terms zeroed, a necessary condition when used for solids.
The software used to build the geometry, production of the mesh, resolution of the equations, and obtaining the results was the Ansys CFX® 17.0 (
The drying kinetics data, obtained at different temperatures, are shown in
Melon drying kinetics data at: a) 50 °C, b) 60 °C, and c) 70 °C for different treatments, and d) reduction of drying time with the increase of temperature in different treatments. W/O US=drying without ultrasound, US10, US20 and US30=drying with ultrasound pretreatment for 10, 20 and 30 min, respectively. X_{ϴ}=is the dimensionless moisture
Treatment  Parameter  Temperature/°C  

50  60  70  
TT  HP  Pg  TT  HP  Pg  TT  HP  Pg  
W/O US  0.7353  0.9921    0.6638  0.9955    0.6086  0.9960    
0.1115  0.0695  0.1813  0.1500  0.0838  0.2178  0.2925  0.0952  0.3211  
    0.6886      0.6781      0.5826  
0.0272      0.0395      0.0444      
R^{2}  0.9999  0.9963  0.9999  0.9999  0.9976  0.9999  0.9999  0.9964  0.9999  
E/%  1.16  35.46  5.21  1.75  41.74  1.81  0.57  38.60  0.63  
US10  0.7377  0.9910    0.7223  0.9947    0.6253  0.9976    
0.1505  0.0779  0.3212  0.1708  0.0885  0.3257  0.2808  0.1044  0.3297  
    0.5319      0.5585      0.5989  
0.0242      0.0317      0.0498      
R^{2}  0.9999  0.9919  0.9999  0.9999  0.9951  0.9999  0.9999  0.9977  0.9999  
E/%  0.56  43.29  1.16  0.40  46.83  1.79  1.46  40.76  3.96  
US20  0.7367  0.9941    0.7092  0.9974    0.6335  0.9986    
0.1457  0.0829  0.2746  0.2245  0.1054  0.3840  0.3486  0.1167  0.3586  
    0.5982      0.5490      0.6023  
0.0297      0.0409      0.0572      
R^{2}  0.9999  0.9955  0.9999  0.9999  0.9970  0.9999  0.9999  0.9986  0.9999  
E/%  0.97  43.87  2.43  1.29  51.75  1.20  0.22  43.79  4.02  
US30  0.7529  0.9936    0.7676  0.9971    0.6800  0.9991    
0.1550  0.0847  0.3309  0.1735  0.1010  0.3555  0.2339  0.1206  0.3333  
    0.5422      0.5636      0.6382  
0.0266      0.0345      0.0589      
R^{2}  0.9999  0.9940  0.9999  0.9999  0.9970  0.9999  0.9999  0.9991  0.9999  
E/%  0.72  45.75  1.43  2.31  58.16  29.34  0.60  43.49  3.14 
W/O US=drying without ultrasound, US10, US20 and US30=drying with ultrasound pretreatment for 10, 20 and 30 min, respectively.
Despite the high R^{2} obtained in the Henderson and Pabis model, it presented errors varying 35.4658.16%, which is explained by the distribution of the data along the regression line since the error variance is constant throughout the studied range, that is, the observed responses show homoscedasticity (
Empirical modelling of experimental data for melon drying: a) without ultrasound (W/O US), and with ultrasound (US) treatment for: b) 10, c) 20 and d) 30 min. The continuous lines represent the best adjusted model, twoterm exponential model (TT), for the different temperatures. X_{ϴ} = is the dimensionless moisture
The values referring to the variation of the effective diffusivity (
Treatment  




323.15 K 
R^{2}  333.15 K 
R^{2}  343.15 K 
R^{2}  
W/O US  2.47  0.9965  3.00  0.9969  3.43  0.9974     
US10  2.75  0.9899  3.17  0.9930  3.82  0.9964  1.19 ±0.17  1.61 ±0.02 
US20  2.97  0.9944  3.85  0.9951  4.33  0.9974  1.32 ±0.28  2.20 ±0.03 
US30  3.02  0.9914  3.68  0.9953  4.50  0.9983  2.65 ±0.09  2.30 ±0.01 
W/O US = drying without ultrasound, US10, US20 and US30=drying with ultrasound pretreatment for 10, 20 and 30 min, respectively R^{2}=the coefficient of determination
Dependence of the diffusivity on the reciprocal value of temperature W/O US=drying without ultrasound, US10, US20 and US30=drying with ultrasound pretreatment for 10, 20 and 30 min, respectively
Two parameters used to determine the conditions for CFD simulation were analyzed: water loss and solid gain, and their obtained values are given in
The treatments US20 and US30 resulted in higher reductions in drying time than W/O US. As these reductions were similar between the two treatments, the use of water loss and solid gain parameters was important for determining adequate conditions. The conditions used for simulation were treatment US20 at 60 °C since water gain (negative water loss) was lower in the US20 treatment than in the US30, and this was the determining factor for the choice, as solid gain values for the two treatments were closer and relied on the dry basis of the product, representing a small fraction of the total mass. The kinetic and diffusion data (
The values of the properties used in the temperature profile simulation of the melon slice were:
Temperature profile of the melon slice pretreated with ultrasound for 20 min after: a) 30, b) 60 and c) 90 min of drying at 60 °C
The results in
Relative pressure of the: a) YX (I) and YZ (II) planes, and b) current lines in YX (I) and YZ (II) planes
The drying kinetics results showed that applying ultrasound as a pretreatment offered a positive synergy with the used temperature. The longer the exposure time to ultrasound, together with the increase in drying temperature, the higher the drying time reduction, reaching up to 40% decrease at 70 °C with the application of ultrasound for 20 min. The empirical model that presented the best fit to the experimental drying data was the Twoterm exponential, obtaining R^{2}>0.999 and errors of less than 12%. Diffusivity depended on temperature, following the Arrhenius equation. The effective diffusivity coefficient showed a tendency to increase as the melon ultrasound exposure time increased. However, at 60 °C, an anomaly was observed regarding this tendency, since, by increasing the ultrasound time from 20 to 30 min, the effective diffusivity decreased rather than increased. The values of water loss and solid gain were used, together with the kinetic and diffusive data, to choose the best pretreatment condition for computational fluid dynamic (CFD) simulation. The results of the CFD simulation for the temperature distribution along the melon slices were consistent with the data found in the literature. Therefore, the obtained profile satisfactorily describes the drying process.
FUNDING
The authors gratefully acknowledge UFPE (Universidade Federal de Pernambuco), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) for the fellowships.