1.1. Solar drying

In general, the solar dryers are classified in three categories, as shown in Figure 2.

Figure 2. Classification of solar dryers ^[4]. 

In this context, this work will focus on the direct solar dryer, because the moisture of the product to be dried is eliminated by its direct exposure to sunlight, with or without natural air circulation ^[4]. A schematic view of the direct solar dryer is indicated in Figure 3. The direct solar dryer has a drying chamber, an insulated box wrapped with a glass or plastic transparent cover, which has holes for letting the air move in and out of the chamber ^[5]. When the solar radiation affects the glass or plastic cover, the air warms and circulates naturally, or by wind pressure using an external source or a combination of both..

Figure 3. Direct solar dryer ^[5]. 

The construction of the direct solar dryer is simple and cheaper, and protects the product being dried from dust, rain, debris, dews, etc.; however, it also presents some drawbacks in its operation, such as product overheating, undesirable quality and limited drying capacity ^[6]. Tomar and Norton ^[7] developed a crop dryer consisting of a solar air heater and a tunnel dryer, for drying a variety of agricultural products, as can be seen in Figure 4. In comparison with the traditional solar drying methods, the drying time and the massive losses were significantly reduced with the amortization period of 1-3 years. For example, it was reported that the energy necessary for drying 1000 kg of grapes varies from 11.2 to 23.0 kWh depending on the weather conditions, with a cost between 1.2 and 2.0 USD which was absolutely insignificant as compared to the additional profit. However, the dissemination of the solar drying system to a particular area depends on the availability of electricity and of its needs.

Figure 4. Solar tunnel dryer ^[7].  

Neama and Farkas ^[8] presented an experimental study to increase the crop drying efficiency using a photovoltaic cell. The dryer reached a temperature of 76 °C and reduced the moisture content between 50 % and 60 %. The schematic view of the solar dryer with photovoltaic cell is shown in Figure 5. Ogheneruona and Yusuf ^[9] designed and manufactured a direct natural convection solar dryer for drying tapioca, and reported a reduction of the moisture content from 79 % to 10 % wet basis at environmental conditions (32 °C and 74 % of relative humidity).

Figure 5. Photovoltaic solar dryer ^[9]. 

Tefera et al. ^[10] evaluated the performance of wooden box and pyramidal shape direct solar potato dryers, which reduced the general drying time between 2 and 3 hours compared to the open sun drying. The pyramidal dryer performed better in the generation of a more favorable drying environment, with a better economic viability. Similarly, Eke and Arinze ^[11] developed a prototype of a direct natural convection solar dryer made with clay, for drying corn. It was observed that the moisture content was reduced from 29 to 12 % wet basis, achieving a 55 % savings in drying time against open sun drying. It was found that the drying efficiency of the dryer and of the open sun drying method were 45.6 % and 22.7 %, respectively. Therefore, the direct solar dryers are the devices mostly used for drying agricultural and food products. It is observed that the mean drying efficiency of direct solar dryers varies from 20 to 40 % depending on the types of products, the flow of air, and the drying location. The quality of the product obtained using direct solar dryers is acceptable, and can be improved by means of the use of certain types of pretreatment chemical processes.

2.1. Extent of the research

This research spanned a period of four months (interval between June 2019 and September 2019). The collection of data and valuable information was consulted in the following documents: i) NTE INEN 2507 ^[12], ii) Ecuadorian Standard of Construction NEC-11, chapter 14 Renewable Energy ^[13].

2.2. Planimetric survey

Dimensions of all the components that constitute the marquee are presented, as indicated in Figure 6.

Figure 6. Marquee prior to taking the measurements. 

The dimensions of the marquee are 3 m high, 3 m wide and 6 m long; it consists of six beds for coffee drying, with dimensions 1 m wide x 6 m long. Figures 7 and 8 show the coffee drying beds located on the left and right hand sides, respectively, of the marquee.

Figure 7. Coffee drying beds located on the left hand side inside the marquee. 

Figure 8. Coffee drying beds located on the right hand side of the marquee. 

2.3. Acquisition of real measurements

The acquisition of real measurements concerning the marquee, where it is evident the front view (Figure 9), right side view (Figure 10), left side view (Figure 11) and internal part (Figure 12).

Figure 9. Dimensioned front view. 

Figure 10. Dimensioned right side view. 

Figure 11. Dimensioned left side view. 

Figure 12. Internal view of the marquee. 

2.4. 3D survey

For taking measurements of the different components of the marquee, it is proceeded to make the survey in three dimensions; for this it is required an interactive software and different applications, both for learning technical drawing and for engineering analysis; SolidWorks is chosen ^[14]. In the following, it is detailed the front (Figure 13), right side (Figure 14), upper (Figure 15) and isometric (Figure 16) views.

Figure 13. Front view of the marquee. 

Figure 14. Right side view of the marquee. 

Figure 15. Upper view of the marquee. 

Figure 16. Isometric view made with the SolidWorks software. 

2.5. Architectural presentation

For a better finish and future projection of a scale prototype, the model made by SolidWorks is converted to a real environment using the Rendering software ^[15] applied in the architectural field. Figures 17 and 18 present the isometric design made by Rendering.

Figure 17. Marquee designed by Rendering. 

Figure 18. Isometric view of the marquee. 

2.6. Materials and costs

In parallel with taking the measurements, a revision of the materials that constitute the marquee was carried out. Table 1 presents the main elements.

Table 1. Materials implemented in the marquee 

The estimated costs of the materials that are available in the domestic market are indicated in Table 2.

Table 2. Costs of materials employed 

2.7. Experimental design

The results of the analyses and the graphs regarding drying time and efficiency, were obtained from the statistical software STATGRAPHICS Centurion XV (Trial version 16.1.18) ^[16]. A factorial design of one or various factors was used as the experimental design. The theory of the efficiency of the collector of Duffie and Beckmen ^[17] was established in the thermal study. The following equation (1) is utilized for calculating the thermal efficiency of a greenhouse.

(1)

Where nempty is the percentage of thermal efficiency of the empty greenhouse, C_p is the air specific heat (kJ/kg °C); ma, mass flow of air; T₀, initial temperature of the greenhouse; T_i, final temperature of the greenhouse; A_s area of the greenhouse and Is is the solar intensity on the wall and roof of the greenhouse.

3.1. Analysis of the structural coupling

The software engineering techniques are utilized for modeling systems, specially the design and simulation of tunnel greenhouses. Traditional concepts of object oriented technology, are focused on developing software based on software engineering components, similar to the model-based design, the specification of the components and standards, applying the use of libraries and the reutilization of design structures ^[18, ^19]. All these techniques are common in the design of greenhouses, as indicated in Figure 19. Figures 20 and 21 present the structure of the marquee made by SolidWorks, detailing the design of the coupling of assembly in the corners and in the rear part, indicating the type of tube and its specifications, with the purpose of providing an easy access of assembling and disassembling for its quick mobilization. When there is the need to model multitunnel greenhouses, methods that include concepts of reutilization, class hierarchy and succession are applied, which enable the user to have available different technological applications, with the purpose of constructing a series of basic blocks for manufacturing greenhouses, once the design has been revised. From this point of view, a greenhouse is no more than a series of blocks adapted to a space; the efficiency in the use of such space constitutes a critical issue ^[20].

Figure 19. ASome software engineering techniques for greenhouse modeling ^[18]. 

Figure 20. Coupling of assembly of the marquee. 

Figure 21. Detail of the structure. 

3.2. Analysis of the shelving

At present, the unified modeling language (UML) is utilized in different engineering disciplines for modeling systems, which enables to understand and describe the structure and operation of a system under study; for example, the UML is utilized in industrial systems: automotive sector ^[21, ^22], teleoperation ^[20], robotics ^[22, ^23], and production systems for monitoring ^[24]. Therefore, UML has been employed in the agricultural sector as a complementary technique for modeling greenhouses. The technique of Computer Aided Design (CAD) is used for the analysis of the shelving, as indicated in Figure 22, which shows the length and height, Figure 23, which shows the separation of the coffee drying beds and the type of tube employed with its specifications. At last, Figure 24 details an isometric view of the shelving constituted by six drying beds, and specifies the composite material and its dimensions.

Figure 22. Dimensions of the coffee drying beds. 

Figure 23. Distance between columns of drying beds. 

Figure 24. Isometric view of the shelving and its specifications. 

3.3. Analysis, moisture – coffee drying time

In order to estimate the relationship between moisture and coffee drying time, it is proceeded to perform a statistical analysis of linear regression, due to the little curvature exhibited by the plots in Figure 25, setting the moisture (%) as the dependent variable and the drying time (days) as the independent variable. Figure 25 indicates the plot of the model fitted, moisture – drying time, setting equations (2) and (3) as such model.

(2)

(3)

Figure 25. Plot of the fitted model moisture – drying time. 

Table 3 presents the coefficients of the relationship moisture – drying time, where it is shown the estimated and incorrect parameters of the coffee drying.

Table 3. Coefficients, moisture – drying time 

From the statistical analysis, the following values were obtained:

It can be seen in Table 4 that the P-value is smaller than 0.05, which indicates that there is a significant statistical relationship between moisture and drying time, with a confidence level of 95.0 %.

Table 4. Analysis of variance moisture-drying time of the coffee 

The statistical parameter R-squared indicates the fitted model, showing a 90.7424 % of variability in the moisture, and consequently the correlation coefficient is equal to -0.952588, which indicates a relatively strong relationship between the variables. The estimated standard error shows that the standard deviation of the residues is 6.28562 and the mean absolute error is 4.83571, since it is the average value of the residues. The Durbin-Watson (DW) statistical analysis indicates the residues with the purpose of determining if there is any significant correlation based in the order in which the collected data are presented. Since the P-value is smaller than 0.05, there is an indication of a possible serial correlation with a confidence level of 95.0 %, which means that the smaller the drying time in the greenhouse, the greater the percentage of moisture.

3.4. Analysis, Drying area – production

In places in which the solar drying has yearly productions smaller than 500 arrobas of dried parchment coffee, they usually occupy drying places such as marquees, canopies or parabolic dryers ^[25]. Table 5 presents a statistical summary showing the average and standard deviation of the samples. It should be taken into account that there is a difference of more than 3 to 1 between the smallest and largest standard deviations. This may cause problems because the analysis of variance assumes that the standard deviation of all the levels is equal, thus, the production of coffee in quintals is increasing.

Table 5. Statistical summary of the drying area and production 

Table 6 presents an ANOVA table, which decomposes the variance of the data in two components: one between groups and another inside groups. The F-ratio, which in this case is equal to 5.54178, is the quotient between the estimate between groups and the estimate inside groups, since the P-value of the F-test is smaller than 0.05; there is a statistically significant difference between the means of the three variables with a confidence level of 95 %, and thus, they are valid and accurate statistical samples in the production of coffee.

Table 6. Anova table 

Table 7 shows the mean for each column of the obtained data, and the standard error of each mean, which is a measure of the variability of the sampling. The standard error indicates a result of dividing the pooled standard deviation by the number of observations in each level. In addition, it also marks a sample of interval around each mean.

Table 7. Table of means with confidence intervals of 95% 

The intervals currently shown are based in the procedure of the least significant difference (LSD) of Fisher; it is constructed in such a way that, if two means are equal, their intervals will overlap 95 % of the times, which can be graphically observed in Figure 26. Figure 27 indicates the relationship of the drying area with the production in arrobas of dried parchment coffee; it presents that in a drying area of 18 m² of the marquee it can be produced around 1500 kg yearly.

Figure 26. Graph of means and of the 95 % of Fisher LSD. 

Figure 27. Box-and-whisker plot of the area-production relationship. 

3.5. Directional field of the heat flow inside the marquee

When Newton’s law is considered to study the effect with which a body reaches the internal temperature, as it is the case of the coffee bean inside the marquee, the temperature T of the coffee bean and the ambient temperature T_a are considered. Equation (4) is employed for studying the field of directions of the heat flow inside the marquee.

(4)

Constant K is the thermal conductivity of the medium, considering a controlled environment of 0,02 Importar imagen . The initial condition of the problem will be T(_t0) = T₀. The particular solution of the equation for time t0 = 0. (Equation 5).

(5)

From the measured temperature data inside the marquee it was established a T_a = 82Ľ, considering that there are not adiabatic losses for the analysis. The representation of the field of directions for the autonomous continuous ordinary differential equation (Equation 6, Equation 7) is shown in Figure 28, employing a set of meshed points. It can be appreciated an equilibrium point at the ambient temperature inside the marquee. It also occurs that the points below this point behave as attractor points that have an exponential growth.

(6)

(7)

Figure 28. Plot of the directional field for the direction of heat inside the marquee.