THERMAL PERFORMANCE INVESTIGATION OF A HYBRID SOLAR AIR HEATER APPLIED IN A SOLAR DRYER USING THERMODYNAMIC MODELING

Hybrid air heater is a device taking advantage of two or more energy sources directly or indirectly for heating air. This study aims to analyze energy and exergy for a hybrid air heater. It is assumed that no thermal gradient exists along glass thickness and one-directional variation of temperature is in flow direction and thermal capacity of glass, absorber plate, and thermal insulations are negligible. To avoid food oxidation in dryers, effects of heating fluid such as air, carbon dioxide, and nitrogen on temperature, heat transfer, and thermodynamic first and second law efficiencies are also investigated along with the effects of hybrid heating on the aforementioned parameters. The problem is solved using MATLAB software and invoking iterative method with convergence criterion of 0.0001 for temperature. Results indicate the positive effects of using carbon dioxide. Applying hybrid system is also shown to increase the efficiency of air heater.


INTRODUCTION
Solar energy is among the most important renewable energy sources on Earth which is not only compatible with environment, but also it is always available in the large part of Earth's surface and human beings have always Saxena et al. [3] evaluated the thermal performance of air heater by studying active solar air heater. In this work, temperature inside air heater and thermal performance were enhanced by applying two halogen lights of 300 W. The results included enhancement of thermal efficiencies by 18.04% to 20.78% in compared with natural convection and by 52.21% 80.05% in compared with forced convection.
The focus in the study conducted by Singh et al. [4] was placed on obtaining heat in different times.
Temperatures were calculated from 9 AM to 6 PM and study was carried out on a solar air heater packed with stone. In this research, it was proved that using this type of air heater is highly suitable due to its heat storage. Temperature in the bed packed with stone is directly related to output temperature of air flow.
In addition to experimental and laboratorial researches, many studies for numerical modeling as well as analytical researches have been conducted. Work of Choudhury et al. [5] is considered as the first studied on air heaters. They investigated two types of air heaters with absorber glass in 1996. In this research, behavior and efficiency of air heater were observed by changing flow rate, glass thickness, length and depth of duct. As hybrid investigations, Amori and Abd-AlRaheem [9] studied the thermal performance of photovoltaic/thermal hybrid collectors for Iraq climate and discussed their thermal efficiency and output temperature.
In addition to the conducted studies, other researches have also been carried out for reviewing the thermal performance  [20] performed a techno-economic analysis of a roofintegrated solar air heating system for drying fruit and vegetables. He showed that the cost of drying 1 kg pineapple with this system was roughly half of that of an electric dryer. Yıldırım and Özdil [21] theoretically investigated a solar air heater which roughened by ribs and grooves. They examined ratio of the relative roughness height, relative roughness pitch, and groove positions to pitch (GP/PR) for Reynolds number range from 3000 to 21,000. In an experimental investigation Singh et al. [22] studied the effect of triangular protrusions as roughness geometry on As a summary of experimental, numerical and analytical works performed in the field of air heaters, the effect of various variables has been investigated on the performance of air heaters such as number of collectors, mass flow inlet, angle of positioning, gap, length to thickness ratio, roughness, flow path, etc. In some other works, researchers tried to increase their thermal performance with changes in absorber plate (porous media, phase change material, etc.) or glass layer (single or two layers, absorber glass, glass thickness, etc.). Addition of auxiliary heat source is another way to increase thermal performance but with high primitive cost.
In the present study, assuming that an auxiliary heating system is added to air heater, thermodynamic analysis is performed and effects of different powers of auxiliary system on thermal performance of air heater are discussed.
Moreover, provided that the hybrid air heater is used as energy supplier of a food dehydrator, heated inert gases such as nitrogen or carbon dioxide can also be substituted for air to prevent food oxidization. Therefore, effect of heated gas on thermal performance of air heater is also considered in the present study. The novelty of this research can be explained in two ways: 1) Exergy analysis for a thermal air heater with auxiliary heat source. 2) Evaluation of thermal performance of the heater using inactive gases instead of air in the drying process.

Thermodynamic analysis
The heater operates in the way that the radiation emitted by the sun passes through a glass plate and is absorbed by an absorber plate. The fluid flow streaming above the absorber plate is heated along its length.
Energy of flow is calculated by thermal balance equation. The following assumptions are also made for simplifying and solving governing equations: 1. Thermal capacity of glass, absorber plate, and thermal insulations are assumed to be negligible. 2. There is no air leakage.
3. Flow temperature varies only in streamwise direction.
4. There is no thermal gradient along glass thickness. 5. The heat produced by auxiliary system is entirely transferred to the absorber plate.
A schematic of the system which is analyzed in this paper is illustrated in Fig. 1.

Energy conservation for glass covering
Heat transfer equation for glass surface reads [26]: The above equation provides the temperature of glass surface as [26]:

Energy conservation for absorber plate
Heat transfer equation for absorber surface is as follows: The temperature of absorber surface is also given by the following equation as:

Energy conservation for air flow
By writing heat transfer equation for air flow, we have [26]: Finally, the following equation is derived by solving and integrating the above equation [26]: In which coefficients A, B, and C are obtained by the following relations: Conductivity and emissivity are also given as [23] 10) ) ℎ = ( 2 + 2 )( + ) Parameters ℎ and ℎ are also obtained as follows invoking the definition of Nusselt number on the surface of absorber and glass [23]: Rayleigh number in Eq. (13) is also calculated by the following formula:

Efficiency calculations
First law efficiency can be generally regarded as the ratio of the desired output to the required input. First law efficiency cannot solely be considered as an actual criterion for system performance. In order to address this problem, second law efficiency has been defined which is criterion for measuring the actual performance of system against its best performance under the same conditions. For heat engines, second law efficiency is defined as the ratio of the actual thermal efficiency to the maximum possible thermal efficiency (reversible) in the same conditions.
Given the thermodynamic first law, thermal efficiency of hybrid air heater is calculated as: Analysis of second thermodynamic law requires calculating input and output exergy from system. Exergy of fluid flow passing through collector surface is outlined as output exergy in the following form [24]: In the above equation, the right hand side term denotes the absorbed exergy by air flow. The second and third terms also indicate exergy loss. Therefore, exergy efficiency is derived as follows: In which exergy of sun radiation is calculated as follows [25]: (1 − ) = 5778 is assumed for solving above equation. is the exergy of element which is also considered equal to its consuming power The Problem conditions: The considered air heater in this study is single-duct air heater. MATLAB software is used for solving this problem. To investigate the effect of fluid flow rate and element power, they are changed from 0.00117 kg/s to 0.01017 kg/s and 0 to 1000 W respectively. During these changes the radiation intensity is fixed at 400 W/m 2 and the ambient (inlet) temperature is equal to 298 K. The lower surface of absorber plate is insulated and the thermal condition of glass is combined of convection and radiation simultaneously. A heat generation from the element has been added to the absorber plate. The considered environmental conditions and dimensions in solving the problem are shown in Table 1. Air, nitrogen and carbon dioxide are also used as working fluid whose properties are listed in Table 2 [27].

VALIDATION
In this study, thermodynamic modeling and evaluation of a hybrid air heater are conducted. Since validation is highly important in every numerical analysis or thermodynamic modeling, this point is taken into account in the following. In this regard, study of Aboul-Enein et al. [26] is taken as the base of comparison. The condition that was modeled to compare with Aboul-Enein et al. [26] is demonstrated in table 3. The results of this reference are calculated in 17 July, 1996 which diurnal variations of solar intensity and ambient temperature is illustrated in figure 2.

ALGORITHM PRESENTATION
Given the importance of solution method, the presented algorithm in MATLAB software for solving problem is discussed in this section.
To solve the problem, iterative algorithm with convergence criterion of 0.0001 for temperature is considered.
Software firstly reads the preliminary data of velocity, temperature, flow rate, problem dimensions, thermal radiation  figure 4.

RESULTS AND DISCUSSION
After validating the obtained results, the effects of different variables on performance of solar air heater are investigated. In this section, the effect of changing auxiliary power caused by thermal element is discussed in the constant flow rate of 0.01017 kilogram per second. In addition, performance of air heater is evaluated in different flow rates in two cases without element and in the presence of 600-watt generated power. It should be noted that all of calculations for the three flown gasses, including air, nitrogen, and carbon dioxide in air heater are checked. Since one of the applications of solar air heaters is in food dehydrators, nitrogen and carbon dioxide are selected as working fluids and their performance is compared with that of air. Because they are neutral gas, and so in the absence of oxygen, oxidization and quality reduction do not occur in dehydrator. In addition, these gases are more economical than other neutral gases.

Effect of auxiliary input power
In figure 5, the effect of changing secondary power caused by thermal element on output temperature from air heater is shown in the constant flow rate of 0.01017 kilogram per second for three working fluids of air, nitrogen, and carbon dioxide. As it is expected, enhancement in the power of element increases output temperature of working fluid. But the most important result is that output temperatures for nitrogen and carbon dioxide are more than that of air. Output temperatures of nitrogen and carbon dioxide get close in low input power while the output temperature of carbon dioxide exceeds that of nitrogen when auxiliary power increases. The effective parameters on this behavior include physical properties of working fluids such as conduction coefficient, specific thermal capacity, density, thermal diffusivity, viscosity, and gas constant. The effect of changing secondary power due to thermal element on thermal efficiency of air heater is presented in figure 6 for three working fluids of air, nitrogen, and carbon dioxide and in the constant flow rate of 0.01017 kilogram per second. As it is seen, because increase in the power of element makes increase in the temperature gradient between input and output of air heater, efficiency is enhanced due to Eq. (16). On the other hand, power of element is placed in the denominator of this equation and it is added to sun radiation which leads to less variation in efficiency in compared with when it were alone in denominator. Therefore, the extent of increase in nominator is much more than denominator and efficiency is enhanced by increasing element power. Moreover, it is obvious that the maximum thermal efficiency is associated with air and the minimum is related to nitrogen. Also, it is seen that increasing slope of efficiency in lower powers is much steeper than that of higher powers. shown, increase of element power enhances second law efficiency with constant slope. It is also evident that more second law efficiency is obtained in hybrid air heater when carbon dioxide is applied rather than air and nitrogen. While variation of second law efficiency with auxiliary power for air and nitrogen are quite the same.

Effect of mass flow rate without auxiliary power
In this section, effect of changing flow rate of three working fluids in air heater is considered on the performance of solar air heater supplying energy only by sun radiation in the absence of thermal element. As it is seen in figure 8, increase in flow rate decreases output temperature as it reduces the heat transfer time between fluid and absorber plate. In these conditions, behavior of output temperature under variation of flow rate is similar for carbon dioxide and nitrogen gases. Decreasing slope for output temperature of air is also less than that of nitrogen and carbon dioxide. According to figure 9, by increase of flow rate, thermal efficiency is enhanced by steep slope at first and then followed by gentle slope. That is emanated from the fact that in calculating thermal efficiency, increase of flow rate dominates the reduction of the temperature gradient between input and output of air heater. Like Fig. 5, the maximum thermal efficiency of air heater is associated here with working fluid of air while its minimum is related to air heater working with nitrogen. However, the increasing slope of efficiency versus flow rate is steeper for air heater with working fluid of carbon dioxide than others.  figure 10. As it is seen in the figure, when flow rate increases, second law efficiency firstly increases and reaches its highest value in a point and then decreases. The maximum second law efficiency is obtainable for air heater with working fluid of carbon dioxide in higher flow rates. The maximum second law efficiency for air is obtained in lower flow rates in compared with other gases. It is also observed that second law efficiency has its highest value for air and its minimum for nitrogen in lower flow rates. In higher flow rates, however, the maximum and minimum second law efficiency is related to carbon dioxide and air, respectively.

Effect of mass flow rate with auxiliary power
In this section, effect of flow rate is investigated when power of element is added to air heater in hybrid mode. Figure 11 demonstrates the effect of flow rate on output temperature of air heater in the presence of thermal element. Comparing with figure 8, it is evident that variation of output temperature with changing flow rate for nitrogen is different from that of carbon dioxide and they are not in agreement anymore. This means that effects of nitrogen and carbon dioxide in hybrid air heater (unlike solar air heater) are different. The variation of output temperature with changing air flow rate has also steeper slope in hybrid mode than solar mode. Figure 11. Varation of output temperature with mass flow rate in watt=600 for different gases Effect of flow rate on thermal efficiency of air heater in hybrid mode with 600-watt element power is studied in figure 12. Comparing this figure with Fig. 8, it is seen that when air heater is in hybrid mode, air heater efficiency in lower flow rates is more for nitrogen than carbon dioxide, however, as flow rate increases, efficiency of air heater Journal of Thermal Engineering, Research Article, Vol. 7, No. 4, pp. 715-730, May, 2021 727 with carbon dioxide exceeds that of nitrogen; this is while, in solar air heater (figure 9) thermal efficiency of system working with carbon dioxide is always more than nitrogen in all flow rates.  figure 10, it is shown that in higher flow rates, behavior of second law efficiency for air heater working with air is similar to nitrogen. The maximum second law efficiency is also achieved in higher flow rates as air heater switches to hybrid mode. Considering the aforementioned results, carbon dioxide is the best working fluid in air heater used in dehydrators because it is neutral gas with which food product does not oxidize. Furthermore, it is characterized by more output temperature and second law efficiency in compared with other discussed fluids. Moreover, it is much more economical than nitrogen. 728 through air heater is evaluated by regarding nitrogen and carbon dioxide as neutral gases. The focus is placed on thermal performance of air heater, including output temperature, thermal efficiency, and second law efficiency.
The most significant results include:  The maximum output temperature and second law efficiency are associated with air heater working with carbon dioxide and the maximum thermal efficiency is related to air heater with working fluid of air.

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Increasing element power added in hybrid mode to solar air heater increases output temperature, thermal efficiency, and second law efficiency.

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Increasing flow rates of fluid in air heater always enhances the thermal efficiency, however, second law efficiency increases with steep slope at first and then it decreases with gentle slope.

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Due to higher outlet temperature and thermal efficiency, carbon dioxide is the best working fluid applying as dehydrators in air heaters in compared to nitrogen and air.