THE GEOMETRY OF SOLAR RADIATION ENERGY EQUILIBRIUM DISTRIBUTION ON DOUBLE-PASS SOLAR AIR HEATER WITH THE ADDITION OF FIN ELEMENTS: CASE STUDY IN LIBYA

The drying process is the most important process in the Libyan agricultural sector for agricultural products export value. Libya uses a direct drying system from solar radiation, but it provides a large energy loss and decreases the agricultural products quality. Solar air heater technology was developed to solve these problems. One indicator of the solar air heater performance is infl uenced by the solar radiation energy absorption distribution to heat the airfl ow, which can be seen from the changes in air temperature and infl uences the thermal effi ciency. The addition of fi n elements can optimize these mechanisms. This research was conducted to analyze the effect of fi n elements (geometry and fi n number) on air temperature rise through three methods i.e. measurement of air fl ow characteristics, heat transfer rate and thermal effi ciency of solar air heater. The results showed that fi n elements with a length of 1 m and a high range between 0.197 m to 0.221 m and the fi n number of 10 pieces were able to increase the air temperature from 350C to 71.80C so that the thermal effi ciency of solar air heater reached 51.5%. The performance of this technology can be applied to the agricultural products drying process in Libya.


INTRODUCTION
Drying agricultural products is an important process in Libya's agricultural sector, because Libya's dry agricultural products have a high export value on the international market, and are able to increase Libya's gross domestic product (GDP) value by 12.1% [1]. The working principle of drying is to reduce the product moisture content to reach a safe level through the evaporation process by controlling heat energy from solar radiation as an energy source so that the saving life of products is longer and easier [2][3][4]. The solar radiation energy each region is different because it depends on the conditions of the solar irradiance tilt angle, and latitude of a country [5][6][7]. Libya has a latitude of 32.9 0 N and a sunshine slope of 34.10 0 , where this condition can receive solar radiation energy of 2300 kWh/m 2 /year up to 2956.5 kWh/m 2 /year with a sunshine duration of 3500 hours/year [6,8,9]. The energy potential of solar radiation can improve the drying process of agricultural products [5]. The drying process in Libya still uses conventional methods through direct drying under the sun, however, this drying process has some disadvantages, among others, its dependence on weather conditions which causes an increase in solar radiation energy losses, and agricultural products are attacked by insects and thus reduce the agricultural products quality [10]. One of the technologies that can be utilized for the drying process in Libya is the technology of solar air heater, where this technology uses indirect drying process that utilizes the solar radiation energy absorption to heat the airfl ow so that the air fl ow temperature increases [11,12] then the air fl ow can be used for the drying process of agricultural products. The solar air heater technology can be shown in Figure 1. The solar air heater has main parts among others are air fl ow ducts, glass cover, absorbent plate, and insulation plate [15,16]. Based on these parts the solar air heater is divided into two types i.e. single-pass and double-pass [17][18][19]. The single-pass uses an air fl ow mechanism through the top or bottom of the absorbent plate from the inlet to the outlet of the solar air heater [20]. The double-pass type uses an air fl ow mechanism through two types of fl ow i.e. counter-fl ow or parallel-fl ow where the air fl ow through the top as the solar air heater inlet and the absorbent plate bottom as the solar air heater outlet so that the air fl ows twice, therefore the airfl ow utilizes solar radiation energy optimally [20]. Both types of solar air heater have different effi ciency levels, where double-pass types have a higher effi ciency level of 10% to 15% compared to the single-pass effi ciency [15,20,21]. Some research have also developed the solar air heater design by adding fi n elements to the absorbent plate part. The design development with the addition of fi n elements to expand the heat energy absorption fi eld area a) b)  from solar radiation has the aim of increasing the solar air heater outlet air fl ow temperature so that it infl uences the thermal effi ciency rises of the solar air heater and can be used for drying agricultural products. The modifi cation of fi n elements that have waveforms by changing the length and amplitude of fi n elements, where it can increase the amplitude and length reduction of the fi n element which produce a solar air heater thermal effi ciency of 78.6% to 78.8% [22]. The addition of fi n elements using the type of offset where each increase in distance and height of the offset fi n elements resulted in an increase in thermal effi ciency of the solar air heater starting from 30.56% to 74.57% [23]. The utilization of fi n elements with three types among others are rectangular, triangular, and elliptical, where the rectangular fi n type produces the higher thermal effi ciency of 5.5% to 12.5% compared to the other two types of fi ns [13]. The fi n elements made changes the geometry using the herringbone corrugated type, where this type uses zig-zag-shaped fi n elements to obtain a thermal effi ciency of 71.4% [24]. The effect analysis of fi n elements by the number and height factor of fi n elements, where the increasing number of fi n elements was able to increase the thermal effi ciency of solar air heater by 60%, while an increase in fi n elements height could reduce thermal effi ciency by 35% [25]. The solar air heater used a transverse type fi n element on a single-pass and double-pass types, where the double-pass has a higher thermal effi ciency of 15% compared to a single-pass [15]. Based on some previous fi n elements research can be explained that fi n elements most infl uence the thermal effi ciency condition of solar air heater. This research was conducted to analyze the fi n elements effect applied to the absorbent plate to increase the air temperature at the outlet of the solar air heater by using fi n geometry factors (length and height) and the fi n elements number adjusted to the solar radiation energy conditions in Libya. The aims of research are to produce the optimum air temperature for the drying process of agricultural products, and increasing the thermal effi ciency of solar air heat-ers applied in Libya. The research method is carried out through the calculation of energy equilibrium in the heat transfer process in the solar air heater, and calculation of thermal effi ciency.

METHOD
This research analyzes the performance of double-pass type solar air heater with counter fl ow conditions that have a material composition with the ability to absorb solar radiation energy optimally, which is adjusted to Libyan conditions. The solar air heater with double-pass type can be seen in Figure 2.
The Solar Air Heater has four parts, among others are airfl ow ducts, glass cover, absorbent plate, and insulation plate [15,16]. The addition of fi n elements to the absorbent plate section was the main factor of research in determining the solar air heater performance. The material composition of the double-pass type solar air heater ( Figure 2) can be seen in Table 1.
Based on Table 1 can be explained that the glass cover uses glass material which has a high heat transmission coeffi cient of 0.935 [26,27], where the coeffi cient makes the glass cover absorb and collect enough solar radiation energy for heating the primary air fl ow on the inlet section of the solar air heater. The absorbent plate material uses copper material with a heat conductivity rate of 400 W/mK [28]. The high rate of thermal conductivity makes the absorbent plate absorb solar energy directly from the environment or solar radiation energy which Airfl ow: Fins elements: Where: s not utilized on the primary air fl ow heating process. The addition of fi n elements applied on the absorbent plate also increases the area of solar thermal radiation energy absorption towards secondary airfl ow on the outlet section of the solar air heater [29]. The fi n elements utilization is also infl uenced by the fi n geometry (lengthheight) and the fi n number. The cork utilization as insulation plates can reduce the energy losses because of the viscoelastic cork characteristics, and impermeable to liquids or gases, moreover this material has a low thermal conductivity rate of 0.063 W/mK up to 0.065 W/mK [30,31]. The mechanism of primary and secondary air fl ow on the solar air heater that undergoes a heating process can be seen in Figure 3. The solar air heater performance experiment is carried out by energy equilibrium analysis between airfl ow and the solar air heater parts. Energy equilibrium measures are carried out by air fl ow characteristics analysis and heat transfer that occur in the solar air heater system. The addition of fi n elements on the absorbent plate with parameters are geometric and fi n elements number are the main factor. The two measurements were carried out following the four conditions of the solar air heater, among others, the stable performance of the solar air heater system, the overall constant convection coeffi cient of heat transfer between the pipe ducts and air fl ow, the constant thermal conductivity between absorbent plate and fi n elements, and the high temperature air fl ow utilization which is uniform along the solar air heater pipe ducts [16]. The level of solar air heater performance is measured by the thermal effi ciency and the effectiveness of solar radiation energy distribution on air fl ow which is known from the airfl ow temperature difference in the solar air heater system.

Energy balance in the heat transfer process
The heat transfer process between the air fl ow towards the solar air heater parts determines the solar radiation energy distribution effectiveness and thermal effi ciency of the solar air heater. The heat transfer process occurs at a steady state thus, the energy equilibrium in the air fl ow and every part of the solar air heater can be measured by Equations 1 through Equation 7 [24]. Calculation of energy equilibrium in fi n elements is in-  Figure 4: Energy balance scheme of fi n elements fl uenced by geometry (height-length) and number of fi n elements. These factors affect the circulation condition of air fl ow around the absor-bent plate and fi n elements area. The energy balance mechanism in fi n elements can be shown in Figure 4.
Based on Figure 4 is explained that the heat energy of solar radia-tion driving from the absorbent plate to the fi n element which the solar radiation energy is able to heat the air fl ow in the end plate of fi n element [32,33]. The energy equilibrium conditions in the solar air heater system described in Equation 1 until Equation 7 are infl uenced by the temperature parameters in each part of the solar air heater and air fl ow temperature, which can be measured using Equations 8 to Equation 11 [24].
Glass cover: Insulation plate: Absorbent plate: Airfl ow: Meanwhile, the condition of the air temperature at the outlet section of the solar air heater can be determined by Equation 12 [18]. Where,

Thermal Effi ciency
The total energy used in heat transfer process is calculated, where it is explained in the form of air mass fl ow rates, specifi c air heat and differences in air temperature between the inlet and outlet, where the calculations by Equation 13 [18,22].

RESULTS AND DISCUSSION
The energy potential of solar radiation can be used as an energy source in the drying process of agricultural products in Libya. However, the conventional drying process that utilizes radiation energy directly still has a large level of solar radiation energy losses which decrease the agricultural products quality. The utilization of solar radiation energy potential by using solar air heater technology is the possible solution because the solar air heater is able to collect and distribute solar radiation energy to heat the air fl ow in the solar air heater pipe ducts as a heat source in the drying process of agricultural products. Increasing the air fl ow temperature that occurs in the inlet to the outlet section of the solar air heater can explain the solar radiation energy distribution effectiveness in the solar air heater system as a performance parameter of the solar air heater. The air fl ow type passes the solar air heater pipe duct uses the counter fl ow concept, where the concept is able to heat the airfl ow twice at the top and bottom of the solar air heater. The air fl ow rate at the top section gets solar radiation energy through the collector plate, while the air fl ow rate at the bottom section gets solar radiation energy through absorbent plates and fi n elements. The solar air heater system works in conditions adapted to the Libyan environment, where the inlet air temperature has the same value as the ambient air temperature of 35 0 C. The air temperature has increased at the end of the top pipe ducts section by 44.5 0 C. Then, the air temperature is increased again at the bottom section so that it gets an air temperature in the outlet section of 71.  Table 2: Air temperature condition on solar air heater parts er outlet, it can be explained that the addition of fi n elements on the absorbent plate is important in the solar air heater system, because fi n elements can increase the absorption area of solar radiation energy which comes from the energy residue output of solar radiation that is not utilized in the heating process of airfl ow at the top of the solar air heater or radiation energy directly from sunlight so as to increase the air temperature twice compared to the increase in air temperature on the top of the solar air heater. The effect of air velocity and air fl ow rate also infl uences the solar radiation energy distribution to air fl ow. The results of the airfl ow temperature on the solar air heater outlet towards the parameters of air velocity and air fl ow rate as results of Equation 11 can be seen in Figure 5. Based on Figure 5 can be explained that the optimum conditions of energy solar radiation distribution for the air heating process occur at an air fl ow rate of 0.05 kg/s and an air velocity of 0.5 m/s. The magnitude of air fl ow velocity and minimum air fl ow rate make solar radiation energy absorption more effective, due to an increase in the airfl ow area to absorb solar radiation energy. The energy losses factor of solar radiation to be used in the heating process of air fl ow also decreases due to the increase in the absorption area of solar radiation energy which causes friction between the air fl ow and the surface of the solar air heater pipeline to decrease. In addition to the outlet air temperature condition, the air temperature conditions in some parts of the solar air heater can be analyzed by the equations calculation among others are air temperature in the collector plate, absorbent plate, top-bottom section pipe duct, and insulation plate, where it can be shown by equation 8 until equation 11. The calculation results can be seen in Table 2.
Based on Table 2 can be explained that the solar radiation energy capable of heating the glass cover reaches a temperature (T g ) of 97.59 0 C. The high temperature of the glass cover is used for the heating process of primary airfl ow (T f1 ) at the the solar air heater pipe duct top section with an inlet temperature of 35 0 C to 43.45 0 C. The temperature of the absorbent plate and fi n element (T p ) has a value of 130.13 0 C, this occurs because the absorbent plates and fi n elements have a wider area of solar radiation energy absorption compared to the collector plate capable of absorbing residue solar radiation energy from the heating process on the top section or directly from the solar light. The temperature of the insulation plate (T b ) has a value of 74.27 0 C, where it can be explained that the heat energy produced by the air fl ow has been limited to the insulation plate thereby reducing energy losses from the air fl ow. In addition, it can be said that the solar air heater system has a closed condition without any leakage that causes energy to go out into the environment. The utilization of fi n elements in expanding the absorption area of solar radiation energy in the absorbent plate part is infl uenced by several factors, among others are the geometry of fi n elements (length and height) and the utilization of fi n elements number. The factors as a parameter to measure the Equation 11. Each factor has a different effect on the temperature conditions of the airfl ow where the results of the conditions can be shown in Figure 6, 7, and 8 respectively. Figure 6 and Figure 7 can show that the length geometry and height of fi n elements needed to produce air outlet temperatures of 71.8 0 C are 1 m and between 0.197 m up to 0.221 m respectively. Based on Figure 6 can also be explained that the addition of fi n element length can reduce the air outlet temperature because the distributed solar radiation energy has a small magnitude, where this condition is related to the conduction activity between the fi n elements to the air fl ow. Based on Figure 7 it can also be explained that the addition of fi n elements can increase the temperature of the air outlet where this condition is also related to conduction activity, especially in the condition of the heat transfer area between fi n elements and airfl ow. However, increasing the air outlet temperature have a negative effect on the drying process of agricultural products, so it is necessary to control the air outlet temperature. In addition to the fi n geometry (length and height), the fi n elements number used can be taken into consideration in terms of increasing the absorption area of solar radiation energy. The effect of the fi n elements number on the airfl ow outlet temperature can be seen in Figure 8. Figure 8 shows that the fi n elements number of 1 piece produces an air outlet temperature of 77.65 0 C, while a fi n element of 10 pieces only produces an air outlet temperature of 71.75 0 C. This condition occurs because of the fi n elements numbers effect as same as the impact on the fi n element length. However, if it is connected with the thermal effi ciency condition of the solar air heater shown in Figure 9 can be explained that the increase fi n elements can increase the thermal effi ciency of the solar air heater. Based on Figure 9 can be seen that the number of fi n elements of 10 pieces can produce a thermal effi ciency of 51.5%, where it was calculated by Equation 18. This condition occurs because the displacement and distribution of solar radiation energy is evenly distributed in each fi n element related with airfl ow compared to one fi n element which makes the process of transferring solar radiation energy centered on one distribution area where the airfl ow temperature would decrease at the outlet solar air heater, and the air temperature is not optimum for the drying process of agricultural products. This whole process can be shown in Figure 10.
The thermal effi ciency produced by the solar air heater explains the hot airfl ow level for the drying process of agricultural products in Libya.