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Effects of roof angle, inlet gap size and drying time on dryer mass flow rate and moisture content in a chimney-dependent solar crop dryer using design of experiments (DOE)

A chimney dependent solar crop dryer (CDSCD) was designed and developed. Design of Experiments (DOE) was used to carry out experiments using a statistical three level non randomized factorial experimental design in Minitab statistical software version 19.0. The effect of three drying parameters, roof angle (º), Inlet gap size (mm), and time (h) on dryer inlet mass flow rate (kg/s) and moisture content (%) were studied. The regression results showed that there was a satisfactory fit of the model variability for both dryer inlet mass flow rate and crop moisture content. The p-value for each parameter was less than 0.005, which is statistically significant. The R-squared (R 2 ) value was 94.67% for inlet air mass flow rate study and 99.72% for moisture content. It was observed that the optimal values for achieving a low moisture content response (≤ 24%) were roof angle of 81º, inlet to outlet cross-sectional area ratio of 1.08768:1 and a minimum drying time of 24 hours while the optimal values for achieving high inlet air mass flow rate (≥ 0.357 kg/s) were roof angle of 51º, inlet to outlet cross-sectional area ratio of 1.08768:1 and a minimum drying time of 5 hours. The findings could be implemented and utilized for achieving optimum ventilation and drying performances to refine dryer (CDSCD) design.


Introduction
MOFA [1] observed that although agriculture is the largest sector of the economy in Ghana, contributing about 39% of GDP, it is still confronted with high post-harvest losses as a result of poor post-harvest management. For instance, Zakari [2] estimates that the average postharvest loss of mango is between 20 % and 50 %. The main causes for the losses being attributed to fruit flies, diseases, poor management and storage during transit to the market. Drying, if used effectively could minimize crop losses. Crop drying refers to the process of removing moisture from a crop. Solar dryer is a solar energy application in drying and conserving agricultural food products and other products [3]. Traditionally, farmers spread their crops on mats in the open sun to dry them, therefore exposing them to environmental conditions such as rain, pest, rodents and different types of unhygienic conditions. Harnessing solar energy is becoming more and more popular in drying. In solar drying, solar energy is the main source of energy used. Recent studies have shown that using solar energy in preserving agricultural products like grains, fruits, and vegetables is economical and ideal for farmers in the developing countries [4]. However, the use of solar energy alone as the source of heat for drying and preservation during the rainy season, is not feasible and therefore proves difficult [5]. As a result, it calls for different ways in which the solar energy is utilized to overcome the challenge. Different designs for drying have been proposed and tested to solve these problems. The use of a chimney allows improved ventilation. A dryer's chimney combined with an inclined roof, inclined at right angle in a drying chamber design, when coupled with a suitable inlet exit area ratio, was observed to increase the ventilation in direct mode dryer [6][7][8][9][10]. A solar dyer with a tent dryer architecture, generally works on the principle that in operation, radiant energy of short wavelength from the sun is transmitted through transparent drying chamber and chimney glazing to fall on absorbers in the dryer. The absorbers, after absorbing this radiant energy, in turn emit heat energy of long wavelength that gets trapped but does not pass through the glazing back into the atmosphere. The trapped energy heats up the air in the chamber and chimney and effectively dries the product in the drying chamber. That is, cold air flows through the dryer by entering the bottom inlet, gets heated up and dries the crops inside the drying chamber. During this process, the air absorbs moisture from the crops and flows through the solar chimney where its density drops after absorbing more heat and is then driven upwards to exit through the top vent into the surroundings, effecting a continuous flow where the cold, dense air is drawn in to displace the warm air flowing through the dryer [6][7][8][9][10]. It has been confirmed by other researchers that properly designed solar chimneys have been observed to improve the flow of air in an enclosed chamber [11][12][13][14][15]. Generally, high amount of moisture in dried seeds increases incidence of insect infestation and growth of microorganisms. Fast drying of agroproducts reduces their moisture content and therefore prevents conditions favourable for the growth of fungi and microorganisms that affect food quality during storage [16]. Molds that produce aflatoxins (Aspergillus flavus) also grow on products stored under conditions with high relative humidity and temperature [18][19]. Aflatoxins can cause many different health issues and diseases like liver cancer, renal diseases, and gastroenteritis, and they could also be associated with child growth impairment [20]. The rate of insect infestation of post-harvest crops worsens with increase in relative humidity and temperature. Drying could be classified generally into three: Sun, Mechanical, and Solar drying. Sun drying is the direct exposure of a product to the sun on a surface, resulting in direct heating by solar radiation and eventual removal of moisture through circulation of air, naturally. Sun drying needs no additional source of energy other than sunlight and is therefore the cheapest method of drying [21]. However, this method is not efficient and is also labor and time intensive. It is not efficient because natural air flowing around the crop to be dried could introduce moisture and also remove essential heat which otherwise could enhance the drying process [22]. Mechanical drying is a process in which heat is introduced artificially to increase the drying medium's temperature to cause evaporation of excess moisture from a product. The heat source is usually either fossil fuel or electricity. Major types of mechanical dryers include bin, cabinet, mixed flow, and continuous cross flow dryers. The solar dryer is the third group and the most economically sustainable option for developing countries. A solar dryer, unlike sun drying, is a customized enclosure which regulates the process of drying and shields the product against contamination with dust and rain, as well as infestation with insects [23], thereby reducing the drying time significantly, and improving the quality of dried product vis a vis that of sun drying [24]. That is, the drying temperature rises as the relative humidity falls, resulting in a reduced moisture content in dried product. Solar dryers come in different forms. They may be classified as direct or indirect, based on whether the material to be dried is exposed to direct insolation or not. On the other hand, they may be classified based on the mechanism of air flow through the dryer, thus solar dryers can be either natural convection solar dryers or forced convection solar dryers [17]. Air flows through such dryers due to thermally induced density gradient. In dryers using forced convection, a pressure difference, generated by a fan, forces air to flow through the drying chamber [17].
On the other hand, based on indirect or direct solar dryer classification, in the indirect solar dryer, a solar collector is used to heat the air entering the drying chamber. Through convection heat is exchanged between the crop being dried and the hot air, and in the process heated air is forced to flow on the drying bed to remove moisture [21]. Though there are different drying methods for food products, drying food in an indirect solar dryer is a prominent technology nowadays [25]. The direct solar dryer, is one in which a frame covered with transparent material and the sides protected with boards is used to protect the product being dried. The product to be dried and the drying chamber's inner surfaces absorb solar radiation, and thus raise the product temperature and that of its enclosure to effect drying [26]. The direct dryers are appropriate for locations that have direct sunshine for long periods during day time [4]. Mixed mode solar dryers integrate characteristics of both direct and indirect solar dryers [21]. Heat needed to dry the produce is partly supplied by the solar collector which pre-heats the air and by direct solar insolation on the produce [26]. Lingayat et al. [27] reports that the indirect mode dryer could be more effective and efficient than the direct mode dryer. Another category of solar drying is the Hybrid solar dryer. Hybrid solar dryers go a step further to make the dryer operational even during cloudy periods. In addition to using solar energy, hybrid systems incorporate other means of heating the air for drying a produce. All solar dryers have a means to let out exhaust air. Most solar dryers let out exhaust air which collected moisture from the produce to be dried through a chimney. The air passes through the drying chamber and then flows out through the chimney due to the buoyancy effect or stack effect [28].
Nasution et. al. [29] and Abedini et al. [30], studied deep bed drying performance on paddy and shrimp respectively, using hybrid infrared-solar dryer and found it to be more effective than solar dryer only. Using an organic paraffin wax, with a melting point of 60 ℃ as phase change material (PCM) in a solar dryer chamber with black stones as the base, Radhakrishnan et al., [31] dried coconut from an initial moisture content of 55.5% to a final moisture content of about 9%, observing that the drying time of coconut decreased by about 28 and 52 h on using 100 g and 200 g of PCM, respectively, compared to open sun drying; the sensory characteristics like colour, taste, flavour, quality, and texture of the dried coconut sample were superior to the sun-dried coconut sample. Senthil et al., [32] also found the integration of PMC in the solar dryer to enhance drying and reduced drying time up to 60% over a solar dryer without PCM. Afriyie [6] observed from trials on a CDSCD that even though open sun drying could proceed very well at the initial phases of drying, the CDSCD always finishes the drying process faster. Therefore, improving on direct solar dryer is good and worth exploring. Afriyie [6] cautioned that, relying on one particular feature of the CDSCD for performance improvement may render the dryer uneconomical or unstable, and recommended that a reasonable moderate change in two or more features, or design characteristics, could be the best method of improvement of a CDSCD. Design of experiments (DOE) is a good method of studying the combined effects of two or more features on a system and was therefore used for this study. Design of Experiments (DoE) is a statistical method that allows the variation of different factors and combination of factors at the same time to study a system for optimum values [33].
Design of Experiment (DOE) has so many advantages over traditional experimental methods where most of the time one parameter is studied at a time and then through try-and-error modifications are made in new experiments to improve a system. Some of the advantages of DOE include the ease of its use in the evaluation, comparison and optimization of design configurations, evaluation of possible material alternatives, selection of design parameters and configurations for robust products that can work under different field and environmental conditions [34]. Ultimately, DOE allows one to make more informed decisions during the problem-solving process, and conclude with better solutions within a shorter time [33]. The main disadvantages of DOE are that it requires a lot of skills, strong knowledge of statistical methods, discipline and effective communication between members of a project team for it to work reliably [33]. It can therefore be concluded that DOE improves process yields, reduces variability, promote closer conformance to nominal or target requirements and specifications, reduces development time, and reduces overall costs [34]. Therefore DOE was selected as the method for this study.

Experimental works
A laboratory scale model for the CDSCD with three (3) substitutable roofs (each with diverse roof angles oriented to the vertical plane) was fabricated. The roof angles were oriented at 51°, 64° and 81°. Lexan sheet was used as glazing material for the drying chamber walls. The drying chamber width positioned normal to air flow was 440 mm and the length in air flow direction was 530 mm. 40 mm thick wood was used as the base of the dryer with the topmost surface of the wood painted black to function as a heat absorber of the dryer. Three plates of Lexan sheet with a length covering the dryer's width were placed at the inlet to set inlet gaps at 30, 50 and 70 mm during the experiment. A steel grate with a width of 400 mm and a length of 370 mm was placed 150 mm above the base of the dryer to serve as a drying shelf. Two extra meshes, each with about half the length of the first mesh, were also used for different shelf configurations during the drying process. The chimney had a rectangular cross-section (400 mm width, uniform gap of 80 mm and a height of 625 mm). The dryer exit was oriented at right angles to the chimney cross-section at the top and had an exit gap which was 30 mm, and a width of 335 mm but curved at the ends at a radius of 15 mm. Lexan sheet glazing material was used as the walls of the chimney. A removable back wall of wood constructions with an internal black painted surface was used as chimney absorber. Solar irradiation was simulated by setting up eight 100 W infrared lamps in front of the dryer. Thermocouple probes, handheld anemometer and handheld thermohygrometer were used to record temperature, relative humidity and air velocities within and outside the drying chamber. Details of instrumentation setup can be found in Afriyie [6] and Afriyie et al. [7]. Figures 1 and 2 present a sketch of the functional architecture and pictorial view of the laboratory setup for the CDSCD. of the dryer tray arrangements and the pictorial view of the field setup respectively.

Design of Experiments
Design of Experiments (DOE) was used. The designed drying experiments were carried out using statistical three level non randomized factorial experimental design which was implemented in Minitab statistical software version 19.0. Five drying parameters were considered in this experiment namely: Roof angle (º), Inlet gap size (mm), drying time (cm), dryer inlet mass flow rate (kg/s) and moisture content (%). The dryer inlet mass flow rate effects had a total of 216 runs, and the moisture content effects had 225 runs. Presented in Table 1 is the design summary for the inlet mass flow rate, and moisture content effects experiments. Table 2 gives the experimental design summary for the effects of roof angle, inlet gap size and time on both inlet mass flow rate, and moisture content. From Table 2, the experiments consist of three factors: roof angle and inlet gap size with three levels each, and time with 24 levels.

Results and discussions
The effects of roof angle, inlet gap size and time on dryer inlet mass flow rate is presented in section 3.1 while the effects of roof angle, inlet gap size and time on dryer moisture content is discussed in section 3.2.

Effects of roof angle, inlet gap size and time of dryer on inlet air mass flow rate
The Pareto chart of standardized effects for mass flow rate response with the confidence level set at 0.05 is shown in Figure 3. From  The p-values, which are good metrics to evaluate a statistical model, were calculated and presented together with the F-values, degrees of freedom and the mean-squares in Table 3. The p-value for each term (roof angle, inlet gap, and time) was less than 0.005 which is statistically significant. Figure 4 presents residual plots for inlet mass flow rate. From the residual plots, the pattern for normal probability plot is an S-curve which indicates a distribution with long tails. The residuals versus fits plot confirms the assumption that the residuals are randomly distributed and have a nonconstant variance with uneven spreading of residuals across fitted values as points are random on both sides of the zero-line (0) with no patterns in the point positions. Histogram plot pattern depicts long tails in both (right and left) directions which indicates a general skewness in the model. Some few bars lie far away on the left and right sides which indicates an outlier pattern. The residuals in residuals versus order plot appear randomly, close to the centre line, giving a pattern that shows independent residuals. The residual plots for air inlet mass flow rate show that the result is satisfactory. degrees of freedom (DF), sum of squares (SS), mean squares (MS)(Variance), ratio of variance of a source to variance of error (F), significance of a factor at 95% confidence level (P < 0.05).

Figure 4. Residual plots for inlet mass flow rate.
A summary of computed regression values is presented in Table 4. Rsquared (R 2 ) which represents a goodness of fit measure for linear regressions was 94.67%. The adjusted values of R-squared (R-sq(adj)) and predicted values of R-Squared (R-sq(pred)) were 87.54% and 70.61% respectively. These regression results show a satisfactory fit of the model variability for the dryer inlet mass flow rate. The main effect plot for inlet mass flow rate is shown in Figure 5.    A response optimization was carried out to select the optimum factor values necessary to achieve high inlet mass flow rate to accelerate drying. Figure 7 presents the optimization plot after carrying out response optimization. The optimal values for achieving very high inlet mass flow rate response (≥ 0.0069 kg/s) are roof angle of 51º, inlet gap of 30 mm and a minimum drying time of five hours.  Table 4 shows analysis of variance results for effects of roof angle, inlet gap size and time on moisture content. The p-value for each term (roof angle, inlet gap and time) was less than 0.005, which is statistically significant.  The models fitted the data well. A summary of computed regression values is presented in Table 5. The R-squared (R 2 ) which represents a goodness of fit measure for linear regressions was 99.72%. The derived adjusted Rsquared values (R-sq(adj)) and predicted R-Squared values (R-sq(pred)) were 99.35% and 98.48% respectfully. These regression results show a satisfactory fit of the model variability for the crop moisture content. Presented in Figure 9 are residual plots for moisture content. The pattern for normal probability plot shows a few points lying away from the line which implies a distribution with outliers. The residuals versus fits plot verifies the assumption that residuals are randomly distributed and have a nonconstant variance with fanning or uneven spreading of residuals across fitted values as the points randomly appear on both sides of the zero line (0) with no recognizable patterns in the points. The histogram plot pattern depicts long tails on both (right and left) directions which indicate a general skewness in the model. The residuals in the residuals versus order plot are distributed randomly around the centre line and the pattern formed indicate that the residuals are independent. In summary the residual plot results show a good model fit. The main effects plot for moisture content is shown in Figure 10. The highest mean value of moisture content for roof angle effect was 119% at a roof angle of 51º. Roof angle of 64º and 81º recorded mean moisture content of 113.5% and 108% respectfully. For inlet gap effect, the lowest mean moisture content measured was 108% at inlet gap of 30 mm. The highest mean moisture content was 117% at inlet gap of 70 mm and the next was mean moisture content of 115% at 50 mm inlet gap. For effect of temperature, the highest mean moisture content drop was from 202 % to 24%, and it occurred after 24 hours. This shows the time dependency nature of a typical drying process. Figure 11 presents interaction plot for moisture content. The lowest mean moisture content response recorded for interaction of roof angle and inlet gap was 90% at 81º and 30 mm; whilst the highest was 140% at 64º roof angle and 50 mm inlet gap. The next mean moisture content recorded was 135%, at 64º and 70 mm. Results from Figure 11 show that interaction between roof angle and time and interaction between inlet gap and time were heavily influenced by the time factor; the lowest recorded was after 24 hours for both as 24% at roof angle of 81º and inlet gap of 30 mm.  The results of optimization response prediction presented in Figure 12 shows the optimal values which will improve drying efficiency. The optimal values for achieving low moisture content response (≤ 24%) are roof angle of 81º, inlet gap of 30 mm and a minimum drying time of 24 hours. The 30 mm inlet gap implies an inlet area of 0.03 m × 0.39 m or 0.0117 m 2 inlet cross-sectional area. With exit cross-sectional area of 0.03 m × 0.335 m with two (2) semi circles with 15 mm radius on either side of the exit, giving a cross-sectional area of 0.0107568 m 2 . Thus, the optimum inlet to outlet area ratio is 1.08768:1.

Conclusions
From the study on effects of roof angle, inlet gap size and time on moisture content it can be concluded that the optimal values for achieving low moisture content response (≤ 24%) are such that for a given ambient relative humidity, a roof angle of 81º, an inlet gap such that the inlet to outlet area ratio is 1.08768:1 and minimum drying time of 24 hours. On the other hand, from the study of effects of roof angle, inlet gap size and time on dryer inlet air mass flow rate, the optimal values for achieving high inlet air mass flow rate (≥ 0.0069 kg/s) are such that for a given ambient relative humidity, a roof angle of 51º, an inlet gap which gives inlet to outlet cross-sectional area ratio of 1.08768:1 and a minimum drying time of five hours. That is, for good drying conditions for a given ambient relative humidity is such that, an inlet gap which gives an inlet to outlet cross-sectional area ratio of 1.08768:1, drying time of at least 24 hours, and roof angle of either 51º or 81º are desirable. Since the ultimate focus of a dryer is to reduce moisture content of the product in the dryer, the 81º, which gives the minimum moisture content, should be preferred. The findings can be used as a guide and tool to compare various designs of dryers to improve ventilation and ultimately to target optimum design and improved drying performance of CDSCD dryers.