Analytical studies on the multiple-pass SAH.
Abstract
Multipass air collectors are commonly used because they produce higher air temperature than that of a single-pass one due to reduced top heat loss. In this chapter, two mathematical models of convection and radiant heat transfer in a double-pass solar air heater were presented. They included an average temperature model and a model of temperature variation along the airflow direction. The method for solving these two mathematical models was reported. The average temperature model was solved by dealing with a system of linear algebraic equations, whereas the other model was derived as ordinary differential equations and solved by a numerical integration. The calculation programs were developed in EES software. The computation time of temperature variation model was about 0.9 s, but that of the average temperature model was negligible. Outcomes from two solutions were almost identical. The largest error of the outlet air temperature was 2.1%. The models are applicable to multipass collectors with or without recycling airflow.
Keywords
- temperature gradient
- numerical integration
- multiple-pass heat exchanger
- convection heat transfer
- radiation heat transfer
1. Introduction
Energy conversion is a current concern for developing countries because the industrial development is premium strategic target and the traditional fuel is increasingly scarce. Solar thermal energy conversion is deployed massively in countries near the equator due to the availability and stability of solar intensity. Converting thermal radiation into hot air is widely applied in drying agriculture, space heating, desiccant regeneration, timber seasoning, and natural ventilation. A solar air heater (SAH) has a simple structure and is easily made from local materials [1]. However, it has the disadvantage that the convection heat transfer coefficient (HTC) of the air is low, and the heat loss is considerable. Therefore, solutions to enhance heat transfer are proposed and applied. It may be the addition of inserts into the SAH duct to remove the viscous sublayer close to the absorption plate. They can be vortex generators [2, 3, 4], baffles [5, 6, 7], fins [8], or ribs [9]. Increasing the number of air passes in the SAH duct is also a measure to reduce heat loss due to the high temperature of the absorber plate. SAH having two, three, or four passes with or without airflow recycling has demonstrated a high thermohydraulic performance. The solution method for the mathematical model of a multiple-pass SAH has always been of interest to researchers since the SAH has several glasses, absorber plate, back plate, and multiple airflows. There are two commonly used analytical models: local solution and mean solution. The local solution establishes ordinary differential equations (ODEs) along with the air temperature boundary conditions. The mean solution approximates the temperature gradients to the temperature differences in each air pass to form a system of linear algebraic equations. It is obvious that the mean solution is more straightforward than the local solution and able to calculate by hand. However, the local solution can predict the temperature of fluid flow and heat exchanger surfaces along the collector length. From these temperature profiles, temperature cross or temperature meet phenomena can be detected and local corrections can be made. Table 1 presents literature review on solutions studied on multiple-pass SAH during the last 15 years. Both the solutions are almost equally used by researchers. Typically, there are four research groups on the analytical model of multiple-pass SAH. The research group of Ho et al. employed the local solution. Meanwhile, the research teams of Velmurugan et al. and Matheswaran et al. applied the mean solution. Our research group (Phu et al.) used both the solutions.
No. | Researchers (year) | Local solution | Mean solution |
---|---|---|---|
1 | Ho et al. (2005) [10] | ✓ | |
2 | Ramani et al. (2010) [11] | ✓ | |
3 | Yeh and Ho (2013) [12] | ✓ | |
4 | Hernandez et al. (2013) [13] | ✓ | |
5 | Ho et al. (2013) [14] | ✓ | |
6 | Karim et al. (2014) [15] | ✓ | |
7 | Velmurugan and Kalaivanan (2015) [16] | ✓ | |
8 | Velmurugan and Kalaivanan (2015) [17] | ✓ | |
9 | Velmurugan and Kalaivanan (2015) [18] | ✓ | |
10 | Velmurugan and Kalaivanan (2016) [19] | ✓ | |
11 | Singh et al. (2018) [20] | ✓ | |
12 | Ho et al. (2018) [21] | ✓ | |
13 | Matheswaran et al. (2018) [22] | ✓ | |
14 | Matheswaran et al. (2019) [23] | ✓ | |
15 | Luan and Phu (2021) [24] | ✓ | |
16 | Phu et al. (2021) [25] | ✓ | |
17 | Ahmadkhani et al. (2021) [26] | ✓ | |
18 | Ho et al. (2021) [27] | ✓ | |
19 | Phu and Tu (2021) [28] | ✓ | |
20 | Phu et al. (2021) [29] | ✓ |
From the above extensive literature review, there has not been a study on comparing the heat transfer model for a multiple-pass SAH using both the solutions. Hence, in this chapter, both the solutions are applied to a typical double-pass SAH to realize the mathematical model, the solution method, and the result. From the analysis in this chapter, it can be developed for a variety of air collectors and further research on hydraulics and energy performance.
2. Model description
Figure 1 depicts the physical model of a double-pass solar air heater. It consists of a glass cover, an absorber plate, and a back plate. Solar radiation penetrates the glass to the absorber plate and heats the absorber plate. Airflow travels over the plate surface and receives heat. In addition, the air can receive more heat from the glass and back plate because these surfaces absorb thermal radiation from the absorber plate. The air moves from the top to the bottom channel forming two passes. The following subsection presents the five-temperature calculation models of the double-pass SAH, including glass (
2.1 Local solution
In this solution, the temperature of the collector components is a function of
The interpretation of the symbols can be found in Table 2 and Figure 1. The heat transfer coefficients (
Parameter | Symbol | Value |
---|---|---|
Collector length | 2 m | |
Collector width | 0.46 m | |
Air channel depth | 25 mm | |
Solar radiation | 1000 W/m2 | |
Inlet air temperature | 27°C | |
Absorptivity of glass cover | 0.06 | |
Absorptivity of absorber plate | 0.95 | |
Emissivity of glass cover | 0.94 | |
Emissivity of absorber plate | 0.94 | |
Emissivity of back plate | 0.94 | |
Transmissivity of glass cover | 0.84 | |
Air specific heat | 1005 J/kg K | |
Air thermal conductivity | 0.02566 W/m K | |
Thermal conductivity of insulation layer | 0.025 W/m K | |
Air viscosity | μ | 0.00001858 kg/m s |
Air density | ρ | 1.176 kg/m3 |
Thickness of insulation layer | 50 mm | |
Wind velocity | 1.5 m/s | |
Stefan constant | Σ | 5.67 × 10−8 W/m2-K4 |
Air mass flow rate | 0.01 kg/s |
Like the glass cover, the heat balance for the absorber plate is expressed as follows:
The variation of air temperature in the second pass is
The energy balance of the back plate is
In this model, the air temperature equations are ordinary differential equations (ODEs); boundary conditions for ODEs (2) and (4) are [25]
2.2 Mean solution
In this solution, the collector temperature components (
Glass cover:
The airflow in the first pass, spatial derivative of temperature is discretized as (17):
Absorber plate:
The air in the second pass:
Back plate:
Two new variables (
2.3 Common equations
The common equations of the two models above are presented in this section. The sky temperature (
The convective heat transfer coefficient of the wind on the glass cover is written as follows [17]:
The radiant heat transfer coefficient of the glass cover and the sky is
The radiant heat transfer coefficient of the absorber plate and the back plate is
The radiant heat transfer coefficient of the absorber plate and the glass cover is
It should be noted that in the local solution, the temperature of the collector components varies in the
where
The air velocity in a pass (
The heat transfer coefficient from the back plate to the surroundings is evaluated as follows:
The heat gain of air received when passing through the collector is
The thermal efficiency of the collector is
2.4 Solution strategy and validation
Table 2 presents the fixed parameters to be entered into the mathematical models to calculate the five temperatures in the double-pass solar air heater. For the local solution, the mathematical model consists of ODEs, so a certain understanding of numerical methods and computer skills is required. In our study, we use the integral function in EES software (F-chart software). The program will calculate iteratively until the difference between the temperatures
3. Results and discussion
Figure 3 presents the fluid temperature through the two approaches. For the local solution (curves), it is possible to clearly observe that the temperature profiles rise along the flow direction. The air temperature leaving the first pass coincides with the air temperature entering the second pass, i.e., the temperatures at
Figure 4 is to compare the temperatures of the heat transfer surfaces obtained by the two solutions. The glass and back plate temperatures of the two methods are quite similar. However, the absorber plate temperature of the mean solution is insignificantly higher than that of the local solution. Observing the absorber plate temperature profile in the local solution, the maximum temperature is at
The comparison of radiant heat transfer coefficient (HTC) is shown in Figure 5. In terms of magnitude, the radiant heat transfer coefficient between the absorber plate and the back plate (
Expanding the investigation, the influence of air mass flow rate in the range 0.01–0.1 kg/s on the outlet temperature and the thermal efficiency can be seen in Figure 6. As the flow increases, the temperature is reduced because the heater is well cooled. The increased flow rate increases the convection heat transfer rate, thus increasing the thermal efficiency. It can be concluded that the error in predicting the outcome parameters of the two methods is negligible. The air temperature of the mean solution is higher than that of the local solution, resulting in a higher thermal efficiency of the mean solution. The highest deviation of 2.1% is observed at the lowest airflow rate. The deviation reduced sharply with the flow rate. However, this difference is not of concern for a practical application.
4. Conclusion
Two analytical models for calculating heat transfer in a double-pass solar air heater were presented in this chapter. These included local solution and mean solution, which were commonly used to predict the performance of multiple-pass solar heaters. Some comparative results of the two models were drawn as follows:
The deviation in the two solutions was not significant. Designers can choose one of them depending on calculation requirements and computer skills.
The mean solution was simple in calculation.
The local solution predicted the temperature distribution of plates, fluids, and glass covers.
The mean solution predicted a slightly higher temperature than that of the local solution.
Both the models can be easily customized to predict heat transfer in a solar air heater with various modifications, such as multiple-pass collector, finned or ribbed or baffled absorber plate, and airflow recirculation as well.
Acknowledgements
The first author acknowledges the support of time and facilities from Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for this study.
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