The PTSAH utilizes solar energy to heat the ambient air. When the sun’s rays hit the interior of the aluminium foil-covered parabolic trough collector, they are reflected to the focal line where the receiver tube is located. The receiver tube is painted matt black to enhance solar radiation absorption and is designed to absorb concentrated solar energy. An axial fan pushes ambient air through the heated receiver tube, transferring heat from the hot receiver tube to the ambient air passing through it. Therefore, the system generates hot air at the absorber tube outlet, which can easily be directed to a greenhouse solar dryer to speed up the drying of various agricultural and industrial products.

An existing GD was studied to establish the ideal PTSAH size to be constructed. A literature review on tomatoes that were to be dried was done. It was established from Ringeisen et al., [16] , Benedict et al., [19] and Patil and Gawande [20] that the initial moisture content of tomatoes ranged from 90% to 96%, and the final safe moisture content ranged from 10% to 18%. Design calculations were formulated using two drying tables inside the GD, each with a holding capacity of approximately 15kg and initial and final moisture content on a wet basis as 94% and 10%, respectively.

a) PTSAH Area Determination

This section systematically describes how to use equations to determine the size of the PTSAH aperture used to preheat air for drying in the GD.

Step 1: Mass of the water (M_w) to be removed.

The calculation of the mass of water (M_w) to be removed or evaporated from the fresh tomatoes was derived using Equation (1) [21] :

$M_w=\frac{m_p\left(m_i-m_f\right)}{100-m_f}$(1)

M_w is the mass of water to be removed from the fresh tomatoes, m_p is the initial mass of the tomatoes to be dried, m_i is the initial moisture content of fresh tomatoes, % wet basis, m_f is the final moisture content of dried tomatoes, % wet basis.

Step 2: Enthalpy required, h

Equation (2) was used to evaluate the enthalpy (h) of air [19] :

$h=1006.9T+w\left(2512131+1552.4T\right)$(2)

where T is the temperature of drying air in ˚C, and w is the humidity ratio of water vapour per kilogram of dry air. Using the psychrometric chart, the initial enthalpy was evaluated at ambient conditions. The final enthalpy was also evaluated using the psychrometric chart at the optimum drying temperature.

Step 3: Drying Rate, d_r

To determine the average drying rate (d_r) of tomatoes, Equation (3) was used:

$d_r=\frac{m_w}{t_d}$(3)

where m_w = the mass of moisture evaporated from the tomatoes and t_d = the reasonable estimated time of drying in hours.

Step 4: Mass flow rate, m_a

Equation (4) was used to calculate the required mass flow rate, m_a. of air for drying:

$m_a=\frac{d_r}{w_f-w_i}$(4)

The initial and final humidity ratios are w_i (kg H₂O/kg dry air) and w_f (kg H₂O/kg dry air), respectively, and d_r is the average drying rate.

Step 5: Volumetric airflow rate, V_a

The evaluation of volumetric airflow rate V_a in m³/hr is calculated by Equation (5):

$V_a=\frac{m_a}{{\rho }_a}$(5)

where m_a is the mass flow rate of drying air and ${\rho }_a$ is the density of air.

Step 6: Total useful thermal energy, E

The equation used to calculate the thermal energy of the drying air that is useful, E in Joules, required to evaporate water from fresh tomatoes is Equation (6), [22] :

$E=m_a\left(h_f-h_i\right)t_d$(6)

where m_a is the air mass flow rate in kg/hr, h_f and h_i are the enthalpy of drying air and ambient air, respectively, in J/kg of dry air, and t_d is the estimated drying time in hours.

Step 7: Collector area, A_a

The total area required for the PTSAH under solar radiation was calculated from Equation (7) [23] :

$E=A_a\cdot I\cdot n_{PTSAH}$(7)

where E is the total useful thermal energy, in Joules, A_a is the PTSAH aperture area in m², I is the total incident radiation on the PTSAH surface, and η_PTSAH is the PTSAH aluminium foil reflectance efficiency.

b) PTSAH Geometrical Parameters

The parabola’s Equation (8) below, described the geometry of the solar parabolic trough, which was used in the fabrication process [24] [25] .

$y=\frac{x^2}{4f}$(8)

The length (L) multiplied by the width (W_a) resulted in the total collector aperture area (A_a) as follows:

$A_a=W_a\cdot L$(9)

After rearranging Equation (9) to determine the aperture area and assuming an aperture width of 1.2 m, the length of the PTSAH was calculated as follows:

$L=\frac{A_a}{W_a}$

The calculation of the rim angle (φ_r) utilized the aperture width (W_a) and focal length (f), as shown in Equation (10) below [26] :

${\phi }_r={\tan }^{-1}\left[\frac{8\frac{f}{w}}{16{\left(\frac{f}{w}\right)}^2-1}\right]$(10)

The focal length, the radius, and the height/depth of the parabola were calculated using Equations (11), (12), and (13) [27] respectively:

$f=\frac{W_a}{4\tan \left(\frac{\phi }{2}\right)}$(11)

$r=\frac{2f}{1+\cos \left(\phi \right)}$(12)

The depth or height h parabolic of the parabolic trough collector was given by;

$h=\frac{W_a^2}{16f}$(13)

In addition, the focal length of the PTSAH was defined and verified mathematically as follows [26] .

$f=\frac{Y_s^2}{4h}$(14)

where: f = the focal length of the parabolic trough solar collector, Y_s = the half-length of the collector aperture, h = the height/depth of the PTSAH, φ = the rim angle.

Parabola arc length was calculated using Equation (15) [28] :

$S=2f\left\{\sec \left(\frac{\phi }{2}\right)\tan \left(\frac{\phi }{2}\right)+\ln \left[\sec \left(\frac{\phi }{2}\right)+\tan \left(\frac{\phi }{2}\right)\right]\right\}$(15)

The equation for the absorber area (A_ro), which is the outer area of the tube, is given as follows [29] :

$A_{ro}=\pi \cdot D_{ro}\cdot L$(16)

The ratio of the collector aperture area (A_a) to the absorber area (A_ro) gives the geometrical concentration ratio (CR) [29] :

$CR=\frac{A_a}{A_{ro}}$(17)

After designing the parabolic trough solar air heater, the obtained parameters were used in 3D modeling using SolidWorks. The PTSAH was essentially made up of the following major components: solar parabolic trough concentrator, receiver/absorber tube, axial fan, support structure, and adjustable stands, as shown in Figure 1 .

a) Solar Parabolic Trough Concentrator

The solar parabolic trough concentrator was made up of galvanized iron sheets, aluminium foil, shutter plywood, and self-tapping screws.

The solar parabolic trough concentrator had an aperture width of 1.2 m and a height of 0.345 m. A through hole of diameter 0.027 m was drilled at the focal point of each plywood where the receiver tube was to pass. Taking into account the locking mechanism of the PTSAH when manually tracking the sun, 17 through holes of diameter 4.5 mm each were drilled at a radius of 0.211m from the focal point, separated by 10˚ from each other.

Galvanized iron sheets measuring 2 m × 0.9 m each were cut to fit the parabolic curve. Rivets of diameter 0.004 m were used to join the galvanized iron sheets, with the distance between them arbitrarily chosen as 0.1m to maintain uniformity. An aluminium kitchen foil with a reflectance efficiency of 80% was fitted with a Tuff Stuff contact adhesive. Self-tapping screws of diameter 0.004 m by 0.02 m length were used to join the aluminium foil-covered galvanized iron sheets onto the curved surface of the shutter plywood material to take the shape of the parabola. Finally, the solar parabolic trough concentrator was reinforced with four parallel mild steel square tubes of dimensions 2 m × 0.02 m × 0.02 m to prevent possible twisting of the concentrator. Figure 2 shows the fabricated solar parabolic trough.

b) Receiver

The primary goal of the PTSAH was to heat ambient air to a higher temperature. This was achieved by placing a receiver tube concentrically along the focal line of the collector, where the reflected and diffused solar beams were concentrated and converted into heat energy. While different shapes, such as squares, were possible, a circular section was chosen due to its availability and minimal coverage area to avoid shading on the reflector. A galvanized iron (GI) circular pipe with inner and outer diameters of 0.0216 m and 0.0253 m, respectively, was used. The receiver tube was painted matt black to ensure maximum heat absorption. An axial fan with a reducer was connected to the absorber tube using a two-inch to three-quarter-inch reducer.

c) PTSAH Support Structure and Adjustable Stands

A rigid supporting structure ( Figure 3 ) was designed and fabricated with rigid flat bars and mild steel square tubes to maintain the collector’s stability and accuracy. The joining mechanism of the individual parts employed diameter 4 mm rivets and M6 × 50 mm bolts and nuts. Adjustable stands slanted the PTSAH to the desired slope and inclination angle.

The experimental setup of the PTSAH consisted of a solar parabolic trough collector, a galvanized iron pipe receiver painted matt black of length 2.15 m, a 220 V powered axial fan connected to one end of the receiver absorber tube, and a support structure with adjustable stands. During the experiment, parameters of interest were continuously measured, recorded and stored by a multichannel datalogger. These parameters included the temperature of the air at the inlet and the outlet of the absorber tube, the ambient air, the temperature at the receiver’s central surface, the amount of solar radiation, and the wind speed. The outdoor testing was conducted in September and October of 2022. The testing system was oriented in the North-South direction at an angle of 15 degrees, equal to the test location’s latitude, to capture maximum solar insolation, as shown in Figure 4 .

The temperature was the main parameter of interest in the experimental setup. Pre-calibrated thermocouple temperature sensor probes (Campbell Scientific Inc., model: 108-L accuracy ±0.01˚C) were used to measure the temperature of the ambient air that entered through the axial fan, as well as the receiver tube surface temperature and the temperature of the hot air that exited. For safety reasons, to prevent accidentally touching or holding the hot absorber tube during experiments, a hand-held infrared thermometer (model: UT301A, accuracy of 0.1˚C, range of −18˚C to 350˚C) was used to digitally measure and read the temperatures of the hot absorber tube. The solar radiation and the wind at the test location were also measured using a pyranometer (Kipp & Zonen Delft BV, model: CM11, irradiance range: 0 - 1,400 W/m², sensitivity: between 4 and 6 𝜇V/Wm⁻²) and airflow speedometer (model: KUSAM MECO 909, accuracy of 0.1 m/s, range of 0 - 30 m/s), respectively. Thermocouple temperature sensor probes and the pyranometer were connected to a multichannel data logger (Campbell Scientific Inc., model: CR 1000) that recorded and stored readings at one-minute intervals. The data was retrieved from the datalogger using a laptop via a universal serial bus (USB 2.0) cable for analysis. Figure 5 shows some of the instruments that were used in data collection.

a) Receiver Tube Heat Losses

According to Motwani et al. [30] , the receiver tube experiences heat loss through convection, conduction and radiation. The energy balance equation explains the heat the transfer fluid dissipates to the tube’s outer surface and subsequently to the surrounding environment and is given by Equation (18):

$Q_T=Q_{conduction}+Q_{convection}+Q_{radiation}$(18)

where:

If we ignore heat loss through conduction, we can express the equation above as follows:

$Q_T=Q_{convection}+Q_{radiation}$(19)

The equation for calculating convective heat transfer loss (Q_convection) from the surface of the absorber tube to the surroundings was determined as follows:

$Q_{convection}=h_c\left(T_s-T_a\right)A_s$(20)

where:

$h_c=4d^{-0.42}{v}_w^{0.5}$(21)

V_w is the average wind velocity in m/s and d is the outer diameter of the absorber tube in meters.

Radiation heat loss from the surface of the absorber tube to the surroundings was calculated using Equation (22):

$Q_{rad}=\sigma {\epsilon }_{ab}A\left(T_s^4-T_a^4\right)$(22)

where:

$A_s=\pi d_{o}L\left({\text{m}}^2\right)$(23)

b) Thermal Efficiency

The thermal efficiency of a PTSAH (η_th) under steady-state conditions is given by Equation (24) [32] :

${\eta }_{th}=\frac{Q_u}{A_{ap}{I}_D}$(24)

where:

Q_u is the useful energy transferred to the heat transfer fluid defined as follows;

$Q_u=\stackrel{\dot{}}{m}{C}_{p.f}\left(T_{out}-T_{in}\right)$(25)

a) Systems Characteristics

The system characteristics of the designed and fabricated PTSAH are shown in Table 1 .

b) Parabolic Trough Solar Air Heater Assembly

A new PTSAH module was designed and constructed. The individual components, such as the solar parabolic trough collector, receiver absorber tube, axial fan, support structure, and adjustable stands, were fabricated and assembled to make a complete unit. Figure 6 shows the assembled PTSAH.

c) Tracking System

The PTSAH was designed to have an orientation axis of the North-South direction and a rotation direction of the East-West direction to track the sun. The PTSAH was designed to have a manual tracking system. Seventeen (17) through holes with a diameter of 4.5 mm each, 10˚ apart, were drilled onto the shutter plywood at a radius of 0.211 m from the focal point. The locking mechanism utilized a nail as a locking pin, onto the vertical line of the support structure. The parabolic trough was rotated after every 30 minutes. Notably, the trough was freely suspended using the receiver absorber tube. Figure 7 shows the tracking system and locking mechanism of the fabricated PTSAH.

d) Mass of the PTSAH

Due to its modular concept, the complete PTSAH weighed 38.6 kg and could easily be transported to different locations. The design ensured that the system could be scaled in a series or parallel arrangement according to user needs, such as the space available and the quantity of solar energy required to preheat the drying air. Table 2 shows the mass in kilograms of the various components of the PTSAH.

The PTSAH was tested on clear days with the experimental setup described in Figure 4 . Figure 8 indicates the variations of temperature analyzed from the data collected on September 13, 2022.

The experiment’s minimum, maximum, and average solar radiation were 346 W/m², 906 W/m², and 736 W/m², respectively. Figure 8 shows that temperatures had a direct relationship with solar radiation; respective temperatures increased as the solar radiation increased and vice versa.

The ambient air recorded had a minimum, maximum and average temperature of 25.5˚C, 34.4˚C and 31.1˚C, respectively. The receiver tube temperatures depended on the timely manual rotation of the PTSAH to track the sun every 30 minutes. A delay in rotating the PTSAH could cause temperatures to decrease, as the data could be read in real time from the laptop connected to the data logger. The minimum temperature of the absorber tube was recorded as 31˚C at 09:00 hrs when the experiment started. At 13:34 hrs, the absorber tube reached a maximum temperature of 85.6˚C. It was observed that the heat transfer fluid (air) forced through the tube absorbed significant heat from the hot absorber tube. The hot air temperature at the exit of the absorber tube ranged between 35.1˚C and 80.1˚C, with the highest temperature being 10˚C lower than that of the receiver absorber tube surface. This temperature difference was due to the heat loss from the bare absorber tube surface to the surroundings. A wind effect of 3.5 m/s during the experiment contributed to significant heat loss from the bare absorber tube surface.

Figure 9 shows various temperature variations of the PTSAH tested on 14^th September 2022. The temperatures are consistent with the results of day one, shown in Figure 8 .

The PTSAH raised air temperature by an average of 45.6˚C above the ambient temperature. It was evident that the PTSAH could reliably preheat the ambient air to considerably high temperatures (45˚C to 60˚C) suitable for drying agricultural products like tomatoes inside a GD.

Significant heat was lost from the uninsulated receiver tube to the surroundings, majorly through convection and less through radiation. The total value of heat loss calculated using Equations (20) and (22) was 379.09 W. Eighty-one percent of the heat loss was due to convection heat losses, while the rest was due to radiation heat losses. The high value of convective heat loss was attributed to the wind effect during the performance test. Ambient air that passed over the bare receiver tube carried much heat away. Such a result was expected since the design and fabrication of the SPTAH did not consider the use of transparent glass to cover the parabolic groove where the absorber tube was located. In addition, the absorber tube was not insulated in any way, hence the significant heat losses. Arunkumar and Ramesh [26] reported that heat losses are low in insulated and evacuated absorber tubes; hence, they are more efficient and thus enhance the collector’s overall performance.

The fabricated PTSAH had a thermal efficiency of 5.3%, as evaluated using Equation (24). It was satisfactory considering the design parameters, particularly the low airflow rate of 0.11346 kg/min. Key factors that determined the thermal efficiency of the fabricated PTSAH were the air flow rate inside the absorber tube and the respective temperatures viz inlet and outlet. In addition, the properties of air as the heat transfer fluid (HTF) used also significantly determined the thermal efficiency of the PTSAH. HTFs with low specific heat capacities, like air, lead to low thermal efficiencies of PTSAH and vice versa. The low value of the specific heat capacity of air contributed to the low thermal efficiency of the PTSAH. Other HTFs like water, oil, salts, and nanofluids have higher specific heat capacities than air, although they are utilized in different applications other than drying.

In a similar study [15] , a parabolic trough solar collector air heater was constructed for a GD to dry Paddy rice. The fabricated parabolic trough’s thermal efficiency was 8.73%, slightly higher than the current study’s. A possible explanation for the slightly higher thermal efficiency value is that water was used as the HTF, which has a higher specific heat capacity than air.