Air Flow Model for Mixed-Mode and Indirect-Mode Natural Convection Solar Drying of Maize

An air flow model for mixed-mode and indirect-mode natural convection solar drying of maize to help understand the factors that influence air flow in the dryer is presented. Temperatures at various sections of the dryer obtained from drying experiments were input to the air flow model to predict the respective thermal buoyancies. The air flow rate was determined by balancing the sum of the buoyancy pressures with the sum of the flow resistances in the various sections of the dryer. To validate the model, the predicted air flow was compared with measured air flow from experiments. For both the mixed-mode and indirect-mode, the biggest driver of the air flow is the thermal buoyancy created in the collector, while the grain bed is the dominant pressure drop. Thermal buoyancy on top of the grain bed is largely responsible for the variation in air flow, translating into low mass air flow during the early stages of drying when grain moisture is high, and higher air flow in the later stages when grain moisture is low. The heating of the grain bed by direct radiation in the mixed-mode translates into a slightly higher air flow rate than the indirect-mode. The implications are that a thinner grain bed results in shorter drying time as it has a higher air flow rate than a thicker one. To mitigate the low air flow at the early stages of drying, the collector length should be appropriately designed for a desired air flow.


Introduction
Mixed-mode and Indirect-mode solar dryers have a separate compartment, the collector, in which the air from ambient is heated before passing through the grain bed. In addition, for the mixed-mode, the top surface of the grain bed is heated directly by solar energy through a transparent cover. The heated air performs two functions: a) it supplies heat for the evaporation of moisture from the grain and, b) it takes away the evaporated moisture (Bala & Woods, 1994). Consequently, for a natural convection solar dryer, the air flow is one of the main factors that affect its performance. A deeper understanding of the behaviour of the air flow at the various sections of the dryer will enable the design of better performance solar dryers. Maundu, Kiptoo, Eliud, Kindole, and Nakajo (2017) studied air flow distribution and velocity across the drying chamber in a natural convection solar dryer by the use of Particle Image Velocimetry technique which is an effective tool in visual analysis of air flow distribution and provides real experimental air flow analysis. Al-Neama and Farkas (2016) modelled air flow in a natural convection solar dryer and showed that the velocity of air in the chimney was a function of temperature change across the chimney. Vintilă, Ghiauş, and Fătu (2014) used computational fluid dynamics to simulate the velocity field, pressure distribution and temperature distribution in the solar collector and in the drying chamber of a solar dryer. Berinyuy, Tangka, and Weka Fotso (2012) used the relationship developed by Brenndorfer et al. (1987), where the air flow is related to the pressure drop across the dryer, and the depth of the material being dried in their design of a natural convection solar tunnel dryer with integrated collector and chimney. Rigit and Low (2010) carried out modelling of velocity distributions inside a natural convection solar dryer using computational fluid dynamics. The maximum air velocity that could be achieved was found at the area near the chimney outlet. fluid flow. According to Benson (1974), the apparatus can be classified into two groups with the first group exploiting the effect of the stream on the temperature of a heated body such as in the hot wire anemometer. In the second group, a certain amount of heat is added to a confined stream and the resultant temperature rise is then used to calculate the mass flow rate. One device in this group, the Thomas flow meter, was devised to measure mass flow rates of gas in pipes. Dunn (2006) reported that anemometers are now widely used and among the many advantages they have is minimal obstruction to flow because of their very small size. Since the air flow rates in natural-convection solar dryers can be very small, in fact, too small to be measured with most flow meters which operate on the principles of obstruction and pressure drop, anemometers with their small probes do not present large obstructions to the flow and are therefore suitable for this work.
The objective of this study is to develop an air flow model for mixed-mode and indirect-mode natural convection solar drying of maize and validate it with experiment.

Theory
The laboratory natural convection mixed-mode solar dryer under consideration is illustrated in Figure 1. Under mixed-mode configuration, the dryer has glass covers on both the collector and the drying chamber. To use it as an indirect-mode dryer, the drying chamber glass is covered with plywood to block radiation to the top of the grain bed. The air flow through the solar dryer is initiated by the buoyancy-induced pressure head that is created above the atmospheric pressure. The temperature of air in the collector and drying chamber is higher than that in the ambient. This makes the air inside the collector and drying chamber less dense than that in the ambient and therefore creates the buoyancy pressure. Note. collector length, L = 1.2 m; collector and drying chamber width, W = 1.0 m; drying chamber length, E = 0.35 m; space above grain bed, J = 0.15 m; collector angle,  = 18.5; spacing between absorber and glass cover; and also drying chamber exit vent, s = 0.05 m; grain bed depth, B = 0.04 m for10 kg and 0.02 m for 5 kg capacity) (Simate, 1999).
As the air flows through the dryer, pressure drops occur in the various sections of the dryer such as the collector and the grain bed. The pressure drop across the grain bed is dominant. These pressure drops are equal to the buoyancy induced pressure (Oosthuizen, 1987).

Air flow Model
By balancing the buoyancy pressure with the flow resistance in the dryer, the air flow rate can be determined from the following equation (Bala & Woods, 1994): where TB total , the total thermal buoyancy pressure, is the sum of the individual thermal buoyancy pressures in the various sections of the dryer, and PD grain , PD coll and PD exit are pressure drops through grain bed, through collector, and at exits of collector and drying chamber, respectively. Each section of the dryer with a vertical height and a mean temperature difference above ambient contributes to the total thermal buoyancy as follows:

Thermal Buoyancy in Collector
The temperature difference between the mean temperature of air in the collector (T collector mean ) and that of ambient (T am ) creates the thermal buoyancy pressure in the collector (TB collector ) and is given by; Assuming that there are no heat losses in the plenum, the temperature of the air coming out of the collector (T out ) is the same as that at the bottom of the grain bed. Therefore, this gives a temperature difference which acts on the vertical height from the bottom of the grain bed to the collector exit and the resulting buoyancy pressure (TB collector out ) is given by;

Thermal Buoyancy on Top of Grain Bed
The air on top of the bed, which comes from within the bed, introduces an additional buoyancy force, a product of the air temperature above that of the ambient (air temperature on top of the grain bed, T top , less the ambient temperature) and the height of the space it occupies. In addition for a mixed-mode solar dryer, the top surface of the grain bed is heated by the solar radiation coming through the transparent drying chamber cover. Consequently, the air entering the dryer, whose temperature may already be higher than that of the ambient, is heated by the grain bed surface. The height of the space above the grain bed varies since the glass cover is at an angle  with the grain surface and so the height from the grain surface to the drying chamber exit is used to calculate the thermal buoyancy on top of the grain bed (TB top grain ) as follows:

Thermal Buoyancy in Grain Bed
The final contribution to the buoyancy pressure is created in a grain bed of depth B due to the difference in the density between the hot air contained therein and the ambient. It is given by; where  a = the density of air inside the grain bed The thermal buoyancy pressure inside the grain bed (TB grain ) is finally given as; where T av = average air temperature in the grain bed.
The pressure drops at different sections of the dryer are given as follows:

Pressure Drop across Grain Bed
The pressure drop across the grain bed is related to the air velocity through the bed and is given by Brooker (1969) as; Where V is air velocity through the grain bed in m/min, PD grain is pressure drop across the grain bed in kPa/m, the coefficients are A = 41.0 and R = 0.867, for a range of pressure drop of 0.009 -0.021 kPa/m.

Pressure Drop across Collector
The pressure drop across the collector (PD coll ) is due to the resistance of the inner surface of the collector to air flow and can be expressed from equation (8) (Daly, 1979) The friction factor relationships are given by Bayazitoglu and Ozisik (1988)  As the air exits from the collector and from the drying chamber into the atmosphere, a loss in pressure head (PD exit ) occurs. This pressure loss is presented here by using the dynamic head loss coefficient K ex , at the exits of the collector and dryer. a ex exit The dynamic head loss coefficient is obtained from a table of various expansion and contraction geometries as presented by Daly (1979). Values of 0.65 and 1.0 were used for the collector and dryer exits respectively.

Pressure Drop through Perforated Metal Tray
In case of grain on a perforated metal tray, the pressure drop through the perforations is small compared with that through the grain mass if the hole area is 10% or more of the total surface area (Brooker, Bakker-Arkema, & Hall, 1992). The perforated metal base for the tray used in the experiments and in the design had 33% hole area and pressure drop was therefore taken as negligible.

Model Prediction and Validation
The data that was used in the model to predict air flow was obtained from drying experiments where maize was dried from a moisture content of 24.7 % to 12.6 % wet basis. For validation, data was obtained from air flow experiments done on dry maize with a moisture content of 13.4 % wet basis. Both experiments were performed using the same dryer and maize variety under similar laboratory conditions of the solar simulator radiation intensity of 634.78 W/m 2 at the University of Newcastle upon Tyne, United Kingdom. Details of both experiments are given in Simate (1999) and Simate (2001).

Model Prediction
Temperatures at various sections of the dryer obtained from the drying experiments were input to the air flow model to predict the thermal buoyancies at various sections of the dryer with respect to elapsed drying time. The total thermal buoyancy (sum of thermal buoyancies at various sections of the dryer) was then balanced with the total pressure drop (sum of pressure drops at various sections of the dryer) in order to determine the mass air flow through the dryer. The above procedure was done in Microsoft Excel.

Model Validation
A thermal apparatus, Thomas flow meter (Benson, 1974), was constructed and coupled to the inlet of the collector of the solar dryer used to measure the air flow. The construction of the Thomas meter involved making a rectangular heater box of 0.5 m length, 1 m width and 0.05 m depth and open at two ends one end of which was aligned and joined to the inlet of the collector. Two sets of type-T thermocouples (measurement range: -200 to 350 °C; sensitivity: 43 µV/°C; accuracy: ± 0.75 %) were each positioned near each of the two open ends of the heater box. Each set had five thermocouples placed equidistant on an aluminium strip across the 50 mm depth of the heater box. The five thermocouples near the collector inlet formed the hot junctions and were joined, in a differential set up, to their corresponding cold junctions at the other end of the heater box ( Figure 2). This set up therefore, constituted five pairs of differential thermocouples. A data logger Campbell Scientific CR10X was used to record the temperatures. The heater was made from nichrome wire with a resistance of 47.5 Ω and was placed across the whole width of the heater box between the two sets of thermocouples. The wire was connected to a variable voltage power supply, and a setting of 40 volts was found adequate in order to avoid high radiation losses from the heating wire but at the same time provide enough heat to raise the air temperature by at least 1°C. The heater was placed nearer to the inlet of the heater box in order to allow more mixing of the heated and incoming air before the air entered the collector.
The air flow measurements were performed with two grain capacities of 10 kg and 5 kg operating in mixed-mode. After loading grain into the dryer, the solar simulator lights were switched on. The whole solar dryer and in particular the solar collector had to be at the stable operating temperature. Initial calculations showed that the collector had a time constant of about one hour and therefore the whole dryer was allowed to stabilise for this period of time before making any recordings. At the end of the stabilising period, the data logger was switched on to start recording the five differential temperatures every five minutes throughout the experiment. The heater was switched on for 60 minutes but the temperatures were recorded for a total period of 135 minutes with the first 15 minutes and the last 60 minutes when the heater off. This procedure was done for both the 10kg and 5 kg capacity.
The mass air flow rate is given by, where ṁ = the mass air flow rate, kg/s P = energy input to the heater, W C pa = specific heat capacity of air, J/kg K ∆T = temperature difference, °C With a 40 volts power supply and a resistance of 47.5 Ω, the energy input to the heater was calculated as 33.67 W. The ∆T was calculated from the graphs of temperature difference with time by taking the difference between the average ∆T with heater on and the average ∆T with heater off for all the 5 differential thermocouples. The specific heat capacity of air was taken as 1005 J/kg/K.

Uncertainties and Errors in Measured Parameters
The parameter that was measured in these experiments was the air temperature at the cold and hot junctions of the heater box. Errors and uncertainties could have arisen from the design of the experiment, inaccurate reading of instruments, calibration and instrument resolution. Moffat (1988) reported that an estimate of the possible residual error in a measurement, having taken care of all corrections, is the uncertainty attributed to that measurement. Further, the root-sum-square combination of the uncertainties of all the subordinate measurements under consideration in the present measurement is the overall uncertainty of a measurement.
According to NASA (2010), the standard deviation of the sample data is used to determine the uncertainty due to repeatability or random error, while uncertainty due to systematic errors is estimated heuristically from containment limits, containment probability and the inverse error distribution. The uncertainty due to systematic error for a normally distributed error is given by equation (13); for uniformly distributed error it is given by equation (14) and, for overall uncertainty by equation (15); Where, ± L are the containment limits which may be taken from manufacturer tolerance limits, calibration records or certificates, or statistical process control limits; p is the containment probability; and ϕ -1 ( ) is the inverse normal distribution function.
Where: U overall is the overall uncertainty; U bias is the uncertainty due to reference attribute bias and persists during a measurement session; U random is the uncertainty due to repeat measurement and manifests itself as differences in eer.ccsenet.org Energy and Environment Research Vol. 10, No. 2; 2020 measured value from measurement to measurement during a measurement session; U resolution is uncertainty due to the smallest discernible value indicated in a measurement; and U operator is uncertainty due to errors introduced by the person taking the measurement and producing a systematic bias towards a measurement; U environment is due to errors introduced by changing environmental conditions such as temperature and humidity.

Uncertainty Analyses
The error contributing to measurement bias uncertainty for all the parameters measured was considered to be normally distributed with 97.5 % containment probability. The uncertainty due to reference attribute bias during the measurement session U bias was determined as ± 0.446 ⁰C from equation (13). For the temperature measurement, this was the only contributor to the overall uncertainty.
The uncertainty due to repeat measurement that manifests itself as differences in measured value from measurement to measurement during a measurement session U random was taken as zero. No repeatability, parameter values changed continuously with time according to the weather conditions.
The uncertainty due to the smallest discernible value indicated in a measurement U resolution was taken as zero since the measurements were recorded automatically in the data logger and computer.
The uncertainty due to errors introduced by the person taking the measurement and producing a systematic bias towards a measurement U operator was taken as zero; the thermocouple were handled/positioned once at start of experiment when positioning them at the measuring point.
The uncertainty due to errors introduced by changing environmental conditions such as temperature and humidity U environment was taken as zero. The biggest factor on this uncertainty is temperature and this is the parameter being measured. The changes in the resistance of the sensor are related to the temperature being measured.
The overall uncertainty U overall was therefore determined from equation (15) as ± 0.446 ⁰C.

Predicted (Theoretical) Air flow
The temperatures at various sections of the dryer are presented first, as thermal buoyancy which creates the air flow in the dryer depends on these temperatures. Figures 3, 4 and 5 show the variation of temperature with elapsed drying time from the drying experiments for the mixed-mode 10 kg, indirect-mode 10 kg and mixed-mode 5 kg drying, respectively. The air temperature in the grain bed increases from a value almost equal to ambient temperature and rises to one close to the temperature of air exiting the collector and entering the grain bed. This is due to the grain gaining sensible heat from hot air exiting the collector and entering the grain bed. Figure 4 shows the air temperature on top of the grain bed in the indirect-mode 10 kg dropping to values below ambient temperature in the first hour of drying which is not seen in Figure 3 and 5. Condensation of moisture laden air from the grain bed as it came into contact with the cooler space above the grain bed might have lowered the temperature. This situation did not happen in the mixed-mode 10 kg and 5 kg (Figure 3 and 5) due to the heating of the top of the grain bed by direct radiation, which in turn heated the air coming out of the grain bed to temperatures above ambient.   10 and 11 show the pressure drops at various sections of the dryer for the mixed-mode 10 kg, indirect-mode 10 kg and mixed-mode 5 kg, respectively. The pressure drop through the grain bed is dominant, whereas that within the collector, at collector exit and dryer exit are very small and can be neglected. This is in agreement with most other works on natural convection solar drying (Exell, 1980;Jindal & Gunasekaran, 1982;Oosthuizen, 1987) who reported that the pressure drop across the grain bed is the dominant one in the dryer, that the resistance to air flow due to other dryer components is negligible due to the small air flow involved.   Figure 12 shows the theoretical (model) mass air flow rates for the mixed-mode 10kg, indirect-mode 10 kg and mixed-mode 5 kg. The air flow rates increase rapidly in the first hour of drying then become constant during the last hour of drying. As the grain dries, there is less heat used in evaporating moisture from the grain, resulting in more heat contributing to the thermal buoyancy through the temperature of air on top of the grain bed, resulting in an increase in air flow from beginning to the end of drying. The mixed-mode 5 kg bed has the highest air flow as it offers the least resistance to air flow due to the thinner bed depth. For the 10 kg grain beds, the mixed-mode has a higher air flow than the indirect-mode due to the additional heating of the top of the grain bed in the mixed-mode. Although the difference in air flow between the mixed-mode and indirect-mode is very small, with a mean difference of 0.0003kg/s as given in Table 1., when the dryer is operated over a six-hour period of drying, the difference in moisture content at the end of drying may be substantial, with the air flow having contributed to the difference.

Measured Air Flow
The graphs of temperature difference during the heater on and off times are shown in Figures 13 and 14 for the mixed-mode 10 kg and mixed-mode 5 kg, respectively. From the graphs, the rise in temperature difference when the heater is on can be clearly seen. One would have expected that the temperature difference during the time the heater is off would be zero because the air inside the box is not heated. This however, is not the case. The above zero temperature difference experienced when the heater is off may be caused by the top end of the heater box conducting some heat from the collector since the two are physically joined together. There could also be some heat gain from the lights of the solar simulator to the heater box.
The temperature difference does not reach the maximum operating point immediately the heater is switched on. It also does not drop back to the off value immediately after switching off the heater. The reason for the first observation could be that the heated air has to travel a short distance from the heater wire to the hot junctions before its effect can be registered. In the second case, the heater wire takes a bit of time to drop its temperature from the operating one to that of the air surrounding it.
In general the temperature difference at 50 mm is higher than at other positions. This is reasonable as hot air is less dense than cold air and therefore rises above the cooler air. This however, does not imply that the air inside the collector has the same temperature distribution across the air gap. The absorber is the hottest part of the collector and one would expect the air nearer to it to be hotter than at other positions. The experimental values of mass air flow rate calculated from the measured temperature differences from the graphs are given in Table 2 for the mixed-mode 10 kg and 5 kg capacities. The air flow for 5 kg bed is higher than that for the 10 kg. This is reasonable because the 5 kg offers less resistance to air flow than the 10 kg.

Conclusions
An air flow model for natural convection mixed-mode and indirect-mode solar drying of maize grain has been developed by balancing the sum of the individual thermal buoyancy pressures with the pressure drops at the various sections of the dryer. The air flow predicted by the model has been found to be in good agreement with measured air flow from drying experiments.
Analysis of the results show that the thermal buoyancy on top of the grain bed is largely responsible for the variation in air flow, translating into low mass air flow during the early stages of drying when grain moisture content is high, and higher air flow in the later stages when grain moisture content is low. It would be useful in future to look at how the air flow in the early stages of drying can be increased. One way is to increase the thermal buoyancy in the collector as it is the biggest contributor to the mass air flow and is fairly constant throughout the drying period. The model also shows that the heating of the top of the grain bed in the mixed-mode translates into a higher air flow rate than the indirect-mode although the difference is small.
A comparison of the pressure drops at the various sections of the dryer show that the pressure drop across the grain bed is dominant and offers the highest resistance to the air flow rate, implying that the other pressure drops can be neglected in the model.
The model can be used to predict air flow in natural convection solar drying of other grains after replacing the grain specific equation for pressure drop in the grain bed, with that of the grain under consideration.