Abstract
The paper presents a detailed mathematical model for performance prediction of a smooth duct solar air heater validated against the experimental results. Experimental study on a solar air heater having absorber plate with half-perforated baffles on the air flow side shows thermal efficiency enhancement of 28%–45% over that of the smooth duct solar air heater, which is attributed to the heat transfer enhancement (of the order of 180%–235%) due to the perforated baffles attached to the absorber plate and reduction in the mean temperature of the absorber plate by 20°C–25°C as compared to the temperature of absorber plate of smooth duct air heater. Using the mathematical model, the performance plot for the baffled duct air heater has been presented, and the effect of the variation of ambient parameters on the predicted thermal efficiency has been studied.
1. Introduction
Flat plate collectors have been used to deliver heated air for space heating, crop drying, and similar applications requiring air at low-to-medium temperature (slightly above the ambient to about 100°C). The thermal efficiency of a smooth duct flat plate solar air hater is lower than that of a solar water heater because of a low value of heat transfer coefficient between the absorber plate and the air flowing through the collector duct. This leads to a high operating temperature of the collector, especially the absorber plate, resulting in greater heat loss from the collector. Hence, the researchers have directed their efforts towards enhancement of heat transfer coefficient by creating turbulence near the heat transferring surface using artificial roughness in various forms, such as solid roughness elements of various shapes and in different arrangements and perforated or detached roughness elements [1–18].
The solid roughness elements have been shown to significantly enhance the heat transfer coefficient, but the associated increase in the friction factor is of serious concern. Further, hot zones develop in the wake of these roughness elements because of a recirculating flow in the wake region. The detached elements or elements with perforations allow a part of the flow to pass through the perforations or gap, and thus, the adverse effects of the hot zone and form drag are reduced [12–18]. Hwang and Liou in [14] studied the effect of the half-perforated turbulence promoters symmetrically mounted on two opposite walls on the heat transfer and friction in a rectangular channel. They found that the half-perforated turbulence promoters with perforations on the lower half of the ribs performed better than those with the solid type or fully perforated promoters.
In the transitional flow regime (), which is of interest in the solar air heaters, the resistance to the heat transfer extends up to the buffer layer between the laminar sublayer and turbulent core. Hence, elements projecting beyond the sublayer, such as baffles, may be useful. To enhance the heat transfer in an asymmetrically heated rectangular section duct, Karwa et al. [17] employed solid and fully perforated baffles attached to the uniformly heated broad wall of the duct. Karwa and Maheshwari [18] carried out an experimental study of heat transfer and friction in such ducts with fully perforated (open area ratio of 46.8%) or half-perforated baffles (open area ratio of 26%) at pitch to baffle height ratio of 7.2–28.8 and flow Reynolds number of 2700 to 11150. The study showed an enhancement of 79%–169% and 133%–274% in the Nusselt number over the smooth duct for the fully perforated and half-perforated baffles, respectively, while the friction factor values are reported to be 2.98–8.02 and 4.42–17.5 times of that for the smooth duct, respectively. They found that the half-perforated baffles at a pitch to baffle height ratio of 7.2 provided the greatest performance advantage of 51%–75% over a smooth duct at equal pumping power.
Since the boundary conditions in the studies of Karwa and coauthors [17, 18] correspond closely to those found in solar air heaters, the objective of the present experimental study has been to study the effectiveness of the half-perforated baffles in the solar air heater duct in the thermal performance enhancement. Half-perforated baffles of Karwa and Maheshwari [18], as shown in Figure 1, have been used with the absorber plate of the baffled duct air heater. A mathematical model for the performance prediction of the smooth duct solar air heater is also to be presented and validated against the experimental results for such air heater so that the same can be used for the performance prediction of smooth or baffled duct air heaters under a range of operating conditions.
(a) A half-perforated baffle
(b) Longitudinal section of the solar air heater
2. Mathematical Model for Performance Prediction
Karwa and Chauhan [19] have presented a detailed nonlinear mathematical model for a smooth duct solar air heater. The model calculates the useful heat gain from the iterative solution of basic heat transfer equations of top loss and equates the same with the convective heat transfer from the absorber plate to the air using proper heat transfer correlations for the smooth duct air heater. The back loss from the collector is calculated from the iterative solution of the heat balance equation for the back surface, while the edge loss is estimated from the equation suggested by Klein [20].
Figure 2 shows the schematic diagram of a solar air heater. The heat balance on the air heater gives the distribution of incident solar radiation into useful heat gain and the heat loss . The useful heat gain or heat collection rate can be expressed as whereis the area of the absorber plate, () is the transmittance-absorptance product of the glass cover-absorber plate combination. The heat loss from the collector is a sum of the losses from top , back and edge of the collector as depicted in Figure 2.
The factor in (1) is termed as overall loss coefficient and is defined as where is the mean absorber plate temperature and is the ambient temperature.
The collected heat is transferred to the air flowing through the air heater duct. Thus, where is the air flow rate through the collector duct and is flow rate of air per unit area of the absorber plate.
From the heat transfer consideration, the heat gain is where is the mean temperature of air in the solar air heater duct and is the heat transfer coefficient.
2.1. Top Loss
The heat loss from the collector glass cover, termed as top loss , is calculated from the iterative solution of the basic heat transfer equations given below.
Heat transfer from absorber plate at a mean temperature to the inner surface of the glass at temperature takes place by radiation and convection. Hence, where and are the emissivity of the absorber plate and the glass cover, respectively, and is the convection heat transfer coefficient.
The conduction heat transfer through the glass cover of thickness is given by where is the thermal conductivity of the glass and is temperature of the outer surface of the glass.
From the outer surface of the glass cover, the heat is rejected by radiation to the sky at temperature and by convection to the ambient. Hence, where is termed as wind heat transfer coefficient. It can be considered to be about 5–10 Wm−2K−1 (corresponding to the no wind to the usually encountered maximum wind velocity in the western part of Rajasthan, India). The sky temperature is a function of many parameters. Some studies assume the sky temperature to be equal to the ambient temperature, because it is difficult to make a correct estimate of it, while others estimate it using different correlations.
In the equilibrium,
To estimate of the convective heat transfer coefficient between the absorber plate and glass cover , the following three-region correlation of Buchberg et al. [21] has been used: where is Rayleigh number for the inclined air layers between the absorber plate and glass cover (collector slope for horizontal). The Rayleigh number is given by where = gap between the absorber plate and glass cover, is the mean temperature of the air in the gap, and is the kinematic viscosity of the air at .
2.2. Back and Edge Losses
The back loss from the collector, refer to Figure 2, is calculated from the following equation where is the insulation thickness, is the thermal conductivity of the insulating material and is the temperature of the bottom surface of the collector duct, which has been estimated from the iterative solution of the heat balance equation detailed below.
Heat transfer by radiation from the heated absorber plate to the duct bottom surface is calculated from
The heat flows from the heated bottom surface to the surroundings through the back insulation and to the air flowing through the duct at mean temperature ; that is,
The absorber plate inner surface and duct bottom surface long wave emissivity values and in (11b) have been assumed to be 0.9. The heat balance for the surface gives .
For the estimate of the edge loss, the empirical equation suggested by Klein [20] has been used, which is where is the area of the edge of the air heater rejecting heat to the surroundings.
Knowing the useful heat gain, the outlet air temperature is calculated from
The thermal efficiency of the solar air heater is the ratio of the useful heat gain and the incident solar radiation on the collector plane; that is,
Niles et al. [22] used the following equations to calculate the outlet air and mean plate temperatures when the solar air heater operates in open loop mode (i.e., ):where . Parameter is termed as heat removal factor and is given by where is termed as efficiency factor. It is given by
The mean air temperature equation in terms of heat removal factor and efficiency factor is
The accuracy of the results of the performance analysis strongly depends on the use of appropriate heat transfer and friction factor correlations for the solar air heater ducts.
For the asymmetrically heated high aspect ratio rectangular ducts of smooth duct solar air heater, Karwa et al. [8] used the following correlation of Ebadian and Dong [23, Equations (5.206) and (5.207)] for the apparent friction factor in the laminar regime, which takes account of the increased friction in the entrance region of the duct
The heat transfer correlation from Hollands and Shewen [24] for the thermally developing laminar flow for the smooth duct is
The friction factor correlation of Bhatti and Shah [25] for the transition to turbulent flow regime in rectangular cross-section smooth duct is where
They report an uncertainty of ±5% in the predicted friction factors from the above correlation.
Considering the entrance region effect, the apparent friction factor in the turbulent flow regime is determined from the following relation for flat parallel plate duct [25]:
The Nusselt number correlations for the transition and turbulent flow regimes in the rectangular solar air heater duct from Hollands and Shewen [24] are
An uncertainty of an order of 5%-6% in the predicted Nusselt number can be expected [8]. As suggested by Karwa et al. [8], the laminar regime has been assumed up to .
The pressure loss and pumping power are calculated from
The thermophysical properties of the air have been taken at the corresponding mean temperature or from the following relations of thermophysical properties, obtained by correlating data from NBS (U.S.) [26]:
Equations (1) to (26) constitute a nonlinear model for the solar air heater that has been used for the computation of the useful heat gain, thermal efficiency, and pumping power. The model has been solved by following an iterative process as depicted in Figure 3. For the heat collection estimate, the iteration was terminated when the successive values of the plate and mean air temperatures differed by less than 0.05 K. The iteration for the estimate of top loss has been continued till the heat loss estimates from the absorber plate to the glass cover and glass cover to the ambient; that is, and differed by less than 0.2%.
3. Experimental Setup
The experimental test facility, designed and fabricated as per ASHRAE Standard for testing of solar collectors [27], consists of 300 mm wide parallel ducts with entrance, test, exit, and mixing sections, a blower, control valves, orifice plates and provision for temperature, and pressure drop measurements as shown in Figure 4. It works in an open loop mode. The ducts are made of good quality smooth faced plywood and wooden boards. Each duct is 2880 mm long consisting of 550 mm long insulated entry and exit sections and 1.62 m long test section. The height of both the ducts has been kept fixed at 38.4 mm. The combined width of ducts (with side walls) is 850 mm.
The test section of one of the parallel ducts carries 3.25 mm thick aluminium plate in 12 equal width pieces as absorber plate with twelve aluminium sections 0.9 mm thick installed as baffles. Each baffle consists of one row of holes as shown in Figure 1(a). The other duct carries a three-piece smooth surfaced aluminium absorber plate. The sun-facing sides of both the absorber plates are smooth and blackened. Glass plates of 4 mm thickness have been used as cover over the absorber plates at a height of 60 mm. The top side of entry and exit lengths of each duct is covered with the plywood.
A 100 mm long baffled mixing section is provided to get uniform temperature of the exit air in the measuring section just after the mixing section. The exit end of each duct is connected, through a rectangular to circular transition piece, to a 68 mm ID G.I. pipe with orifice plate assembly. The throat diameter of the orifice plate is 38 mm. The other end of the each pipe is connected through control valve to the suction of a 10 HP blower using flexible pipe and a Y-section (not shown in the figure).
50 mm thick thermocole insulation has been provided on the back of the collector from test section inlet to outlet of twin duct, while the transition pieces and orifice plate assembly pipes (up to the orifice plates) are covered with foam blanket insulation. All joints are properly sealed with putty. The setup was installed horizontal (in north-south orientation) on the roof top at a height of 750 mm on an iron stand.
Butt-welded 0.36 mm calibrated copper-constantan thermocouples have been used for various temperature measurements. For the plate temperature measurement, thermocouples have been fixed with M-seal in the sun-facing side of absorber plate in small diameter holes drilled about 2.5 mm deep at nine and fourteen axial locations on the smooth and baffled absorber plates, respectively, as shown in Figure 4. Additional thermocouples have been affixed on the absorber plate of the baffled solar air heater to measure span wise variation of plate temperature. Three thermocouples are placed in temperature measuring section after the mixing section to measure the outlet air temperature, while a thermocouple placed midway in the entry section measures the inlet air temperature.
Inclined U-tube manometers have been used for the measurement of pressure drop across the orifice plates. Pressure taps, located along the axial center line of the smooth lower wall of the both test sections, have been used to measure the static pressure drop across 1.62 m long test section using a null balance type micromanometer having a least count of 0.02 mm.
Calibrated precision solarimeter and pyranometer have been used for the measurement of the intensity of the solar radiation on the collector plane. The wind velocity has been measured by an anemometer.
The details of the half-perforated baffles employed in the study and other experimental conditions are given in Table 1. The baffles have one row of holes ( diameter) drilled in the lower half (near to the duct wall).
The open area ratio β of the perforated baffles is defined as the ratio of the area of the holes to the baffle frontal area given by where is the number of the holes drilled, is the diameter of a hole, is the height and is the width of the baffle.
Before starting the experiment, the setup and various components were checked for proper functioning. The glass covers were cleaned. Then, the blower was switched on, and the flow control valves were adjusted to give desired air flow rates through the ducts. All observations were made every 30 minutes starting from about 10 am till about 2 pm, that is, equally divided about the noon.
4. Data Reduction
The mass flow rate of air is determined from the measured pressure drop across the orifice plate
Mass flow rate per unit area of the absorber plate is calculated from where is the absorber plate area.
The Reynolds number of the flowing air in the duct is calculated from where is mass velocity of air in the duct and is the hydraulic diameter of the duct.
Useful heat gain is the heat transferred to the air from the heated absorber plate and is obtained from
Thermal efficiency of the collector is ratio of useful heat gain to the incident solar radiation on the collector aperture area
The heat transfer coefficient has been calculated from where is mean plate temperature calculated as the weighted average of temperature readings noted at various points along the axial length of the absorber plate; that is,
In (33), is the mean air temperature taken as arithmetic mean of the measured inlet and outlet air temperature values
From the known values of pressure drop across the test section and the mass flow rate, the pumping power is obtained from From the analysis of uncertainties in the measurements by various instruments [28], the uncertainties (odds of 20 : 1) in the calculated values of various parameters have been estimated as follows:flow rate per unit area of absorber plate, ,heat collection rate, ,thermal efficiency, ,pumping power, %.
5. Results and Discussion
The experimentally determined thermal efficiency data for the smooth duct solar air heater are plotted in Figure 5 against the flow rate per unit area of the absorber plate along with the predicted thermal efficiency from the mathematical model at the average values of the observed solar insolation, ambient temperature, and wind velocity during the experimentation. The absorber plate emissivity has been assumed to be 0.95, long wave emissivity of glass as 0.88, and transmittance-absorptance product as 0.8. The scatter in the experimental data is due to the variation in the ambient conditions. The theoretical analysis shows that the variation in the wind velocity has greater effect as compared to the variation in the ambient temperature and solar insolation in the experimental range of these parameters. At the lowest flow rate of the study, the experimental value of the thermal efficiency is lower due to a comparatively higher average wind velocity during experimentation at this flow rate, while the reverse is true at the highest flow rate of the study. Further, it is worth to note that, in general, the ambient temperature has been seen to rise with time (10 am to 2 pm) while the solar insolation increased up to the noon and then decreased. Thus, a transient condition exists, and the efficiency values in the morning and afternoon tend to lie below and above the mean values, respectively. Hence, looking to the effect of variation in the experimental conditions, the experimental and predicted values can be regarded to be in good agreement, and the presented model can be used to predict the performance of the solar air heater under a wide range of ambient (solar insolation, wind velocity, and ambient temperature) and air mass flow rate conditions.
For prediction of the performance of a roughened or baffled duct solar air heater, the Nusselt number and friction factor correlations of smooth duct air heater in the mathematical model are to be replaced by the appropriate correlations for the employed roughness or baffles.
It can be seen in Figure 5 that the thermal efficiency increases with increase in the flow rate, which is due to the increase in the heat transfer coefficient at the increased air velocity in the air heater duct.
Figure 6 shows the enhancement in the thermal efficiency due to the use of baffles on the air flow side of the absorber plate. The efficiency ratio in Figure 6 is the ratio of the thermal efficiencies of the baffled and smooth duct air heaters. The employment of the baffles enhances the thermal efficiency by about 28%–45%; higher gain is at the lowest air flow rate of the study. The thermal performance advantage of the baffled duct solar air heater can be attributed to the heat transfer enhancement (, where refers to the smooth duct) of about 180%–235% as depicted in Figure 7. The effect of the perforated baffles on the flow structure and resulting heat transfer enhancement has been discussed earlier.
The increase in the heat transfer coefficient due to the baffles also reduces the mean absorber plate temperature of the baffled absorber plate by about 20°C–25°C as compared to the smooth duct air heater absorber plate; see Figure 8. This leads to a reduction in the heat loss from the collector, which is a function of the excess of the absorber plate temperature over the ambient temperature. The increase in the heat collection rate due to the heat transfer enhancement and decrease in the heat loss from the collector due to the lower working temperature of the absorber plate enhance the thermal efficiency of the baffled air heater.
The pumping power requirement has been found to be negligible (less than 0.5% of the heat collection rate). Thus, thermohydraulically, the baffled duct solar air heater is better than the smooth duct solar air heater.
6. Performance Prediction of Baffled Duct Air Heater
For half-perforated baffles in an asymmetric heated rectangular duct, Karwa and Maheshwari [18] have presented the following correlations of Nusselt number and friction factor: with standard deviation of 1.34% and 3.34%, respectively, from the experimental data.
Using the mathematical model presented above, performance study of baffled duct solar air heater has been carried out by replacing the Nusselt number and friction factor correlations for the smooth duct in the mathematical model by the above correlations for the baffled duct solar air heater. Table 2 gives values of different parameters used in the study.
In Figure 9, the plots of thermal efficiency and effective efficiency of the baffled duct solar air heater are presented against the temperature rise parameterfor fixed geometric and ambient parameters. Their values are also given in a tabular form. The effective thermal efficiency takes account of pumping power and is defined as [19]
In the above equation, factor is a conversion factor for calculating equivalent thermal energy for the pumping power. It is a product of efficiency of fan, motor, transmission and that of thermoelectric conversion at the power plant. For a fan-motor efficiency of 0.6 and thermoelectric conversion efficiency referred to the consumer point as 0.33, the factor works out to be 0.2. It is to note that pumping power required to overcome friction is also converted into heat.
It can be seen in Figure 9 that the pumping power is not of a concern at low flow rates. At the highest flow rate of the study (), the effective efficiency is about 5% lower than the thermal efficiency as also given in the table.
The plot in Figure 9 can be utilized for performance prediction of such air heater. The use of the plot is simple. For example, let for a given application the required air temperature rise is 12°C when solar insolation is 800 W/m2. Then, the temperature rise parameter works out to be 0.015. A vertical line on the plot in Figure 9 at gives thermal efficiency of about 67.5%. Using the basic equation of thermal efficiency, the air mass flow rate per unit area of the absorber plate is estimated as
7. Effect of Variation of Ambient Parameters on Thermal Efficiency
The performance plot in Figure 9 has been presented for fixed values of solar insolation, wind velocity, and ambient temperature. These parameters, especially the solar insolation and ambient temperature, vary from morning to evening (9 AM to 4 PM) and also with the season of the year. The effect of their variation on the thermal efficiency of the baffled duct solar air heater is presented in Figures 10, 11, and 12
From Figures 10–12, it can be seen that effect of variation of the solar insolation from sto is not significant, while the increase in wind heat transfer coefficient from 5 W/m2K to 10 W/m2K reduces the thermal efficiency at the lowest flow rate by about 4%, which can be termed as significant. At the highest flow rate of the study (the lowest temperature rise parameter and extreme left end of these curves), the thermal efficiency is less affected by variation of these parameters. The thermal performance of the air heater improves by about 1.8% in the winter () and reduces by about 2% in summer () at the lowest flow rate. At low ambient temperature and solar insolation, the operating temperature of the collector reduces and thermal efficiency improves, while a high wind velocity increases the heat loss from the collector.
The results of the present study can be utilized for the development of enhanced performance solar air heater with half-perforated baffles.
8. Conclusions
An experimental study on thermal performance of a solar air heater having half-perforated baffles on the air flow side of the absorber plate has been carried out for air mass flow rate of about 0.02–0.073 kg/s per m2 of the absorber plate area. A direct comparison of performance with the smooth duct solar air heater has been made, and a detailed mathematical model has been presented. The main findings of the present study are as follows.(1)The predicted values of thermal efficiency from the mathematical model for the smooth duct solar air heater are in good agreement with the experimental data. Hence, the model can be used for performance prediction under wide range of operating and ambient conditions. (2)The thermal efficiency of the baffled duct solar air heater is about 28%–45% higher than the smooth duct solar air heater; highest thermal performance advantage is at the lowest flow rate of the study.(3)The heat transfer enhancement due to the baffles (of the order of 180%–235%) increases the heat collection rate and reduces the mean temperature of the baffled absorber plate by 20°C–25°C as compared to the smooth one.(4)The pumping power requirement is only a small fraction of the heat collection rate in the range of the present study.(5)Effect of variation of solar insolation on the thermal performance is negligible (0.4%–1.42%), while the variation in wind heat transfer coefficient affects the efficiency by 1.6%–4.3% and the ambient temperature by (±0.8%) to (±2.0%); the higher values in all cases refer to the lowest flow rate of the study.
Nomenclature
| : | Absorber plate area = , m2 |
| : | Collector aperture area, m2 |
| : | Orifice throat area, m2 |
| : | Hydraulic diameter of duct = , m |
| : | Height of baffle, mm |
| : | Coefficient of discharge |
| : | Specific heat, Jkg−1K−1 |
| : | Fanning friction factor |
| : | Acceleration due to gravity, ms−2 |
| : | Mass flow rate per unit area of plate = , kg s−1 m−2 |
| : | Mass velocity = , kg s−1 m−2 |
| : | Air flow duct height (depth), m |
| : | Wind heat transfer coefficient, Wm−2 K−1 |
| : | Solar radiation on the collector plane, Wm−2 |
| : | Thermal conductivity of air, Wm−1K−1 |
| : | Length of collector, length of test section, m |
| : | Mass flow rate, kgs−1 |
| : | Nusselt number |
| : | Baffle pitch, m |
| : | Pumping power, W |
| : | Prandtl number = |
| : | Ambient pressure, Nm−2 |
| : | Pressure drop across duct, Nm−2 |
| : | Pressure drop across orifice plate, Nm−2 |
| : | Relative baffle pitch |
| : | Useful heat gain, W |
| : | Gas constant, Jkg−1 K−1 |
| Re: | Reynolds number = |
| : | Ambient temperature, K |
| : | Mean air temperature , K |
| : | Inlet air temperature, K |
| : | Mean of the plate and glass temperatures , K |
| : | Outlet air temperature, K |
| : | Mean plate temperature, K |
| : | Sky temperature, K |
| : | Overall loss coefficient, Wm−2 K−1 |
| : | Width of the duct, m. |
| : | Collector slope, deg |
| : | Gap between the absorber plate and glass cover, m |
| : | Air temperature rise , K |
| : | Change in thermal efficiency |
| : | Emissivity |
| : | Thermal efficiency = |
| : | Effective efficiency,(38) |
| : | Dynamic viscosity, Pa s |
| : | Kinematic viscosity of air at temperature , m2s−1 |
| : | Density of air, kg m−3 |
| : | Transmittance-absorptance product. |
| : | Duct bottom surface |
| : | Glass |
| : | Mean |
| : | Plate. |