Collector Efficiency in Downward-type Internal-recycle Solar Air Heaters with Attached Fins

The internal-recycle operation effect on collector efficiency in downward-type rectangular solar air heaters with attached fins is theoretically investigated. It is found that considerable collector efficiency is obtainable if the collector has attached fins and the operation is carried out with internal recycling. The recycling operation increases the fluid velocity to decrease the heat transfer resistance, compensating for the undesirable effect of decreasing the heat transfer driving force (temperature difference) due to remixing. The attached fins provide an enlarged heat transfer area. The order of performance in a device of same size is: double pass with recycle and fins > double pass with recycle but without fins > single pass without recycle and fins. Nomenclature: c A = surface area of the absorbing plate = BL (m 2) f A = total surface area of fins (m 2) B = the width of absorber surface area = nw 1 (m) C p = specific heat of air at constant pressure (J/kg⋅ K) e D = equivalent diameter of the channel (m) E = further improvement of collector efficiency, defined by Equation (41) F 1 , F 2 = collector efficiency factors for subchannels 1 and 2, respectively OPEN ACCESS Energies 2013, 6 5131 H = height of the air tunnel in the solar collector, or the distance between glass cover and absorbing plate (m) h = convective heat-transfer coefficient for fluid flowing over the plate of duct (K W/m 2) h p-c = convection coefficient between the plate and glass (K W/m 2) h p-R = radiant heat-transfer coefficient between two parallel plates (K W/m 2) a c r h − , = radiation coefficient from the glass to the air (K W/m 2) h r , p-c = radiation coefficient from the plate to the glass (K W/m 2) w h = convective feat-transfer coefficient between glass cover and ambient (K W/m 2) I = improvement of collector efficiency in the recycle device without fins, Equation (39) f I = improvement of collector efficiency in the recycle device with attached fins, Equation (40) 0 I = solar radiation incident (2 W/m) k = thermal conductivity of air (K W/m 2) s k = thermal conductivity of absorbing plate and fins (K W/m 2) L = collector length (m) m  = mass-flow rate of air (kg/s) n = fin number Nu = Nusselt number u Q = useful gain …


Introduction
Solar air heaters in which energy is transferred from a distant radiant energy source directly into air [1,2], can be employed for drying, supplying fresh air to hospitals, and paint spraying operations [3].The flat-plate solar air heater is a simple device consisting of one or more glasses or transparent material covers situated above an absorbing plate with the air flowing either over or under the absorbing plates [4][5][6].
Solar air collector efficiency can be improved by enhancing the free and force convection effects [7,8], increasing the transfer area [9] and creating turbulence inside the flow channel with baffles [10], or with corrugated surfaces [11].It was pointed out that applying the recycling effect to heat-and mass exchangers can effectively enhance performance due to the increase in fluid velocity, resulting in convective heat or mass transfer enhancement [12][13][14][15][16][17].This work investigates collector efficiency in a downward-type internal-recycle flat-plate solar air heater with fins attached on the absorbing plate for improved performance.

Theoretical Analysis
A downward-type internal-recycle solar air heater with n fins attached on the absorbing plate is considered with a flow channel of width B, length L, and height H, as shown in Figure 1.An insulated plate with negligible thickness is placed vertical to the absorbing plate and bottom plate at the centerline to divide the flow channel into subchannels 1 and 2 of equal width B/2.A pump is installed for recycling the exiting fluid with reflux ratio R from the end of subchannel 1 into subchannel 2.
During operation, before entering subchannel 1, the inlet airflow with mass flow rate m  and temperature fi T will mix with the airflow exiting from subchannel 2 with mass flow rate m  R and temperature ' f T .The following assumptions are made in this analysis: (1) the absorbing-plate, bottom-plate and bulk-fluid temperatures are functions of the flow direction (z) only; (2) both glass covers and fluid do not absorb radiant energy; (3) except for the glass covers all parts of the outside solar air collector surface, as well as the thin plate for separating both subchannels, are well thermally insulated; (4) the physical properties of the fluid and materials are constant; and (5) steady state operation exists.

Temperature Distribution for the Fluid in Subchannel 1
The steady-state energy balance for differential sections of the absorbing plate, bottom plate and flowing fluid are, respectively: where: in which A f (=2 L nw 2 ) and A c (=BL) are the surface areas of n fins and absorbing plate, respectively, while 1 , f η denotes the fin efficiency in subchannel 1, i.e., [18]: and: Solving Equations ( 1) and ( 2) for (T P − T f1 ) and (T R − T f1 ), we have: Substituting Equations ( 7) and ( 8) into Equation ( 3), one has: where: in which F 1 is called the collector efficiency factor of subchannel 1, which is essentially constant for any design and fluid rate [3] and U t is the loss coefficient from the solar collector top to the ambient air.If U t is assumed to be constant along the flow direction, Equation ( 9) can be easily integrated for the boundary condition: The result is: Equation ( 12) is the temperature distribution of the bulk fluid along the flow direction (z) of subchannel 1.Thus, the fluid temperature at the outlet of subchannel 1 is readily obtained from Equation ( 12) by substituting the condition: The result is: where A c = BL = L nw 1 , surface area of the absorbing plate.Similarly, the differential energy-balance equation for the fluid in subchannel 2 is readily obtained using the same procedure performed for subchannel 1 except for the boundary conditions of where the collector efficiency factor of subchannel 2 is defined as:

Mixed Inlet Temperature
If Equation ( 13) is divided by Equation ( 14), one has: Taking energy balance at the inlet with fi T as the reference temperature, this gives: or: Substitution of Equation ( 18) is substituted into Equation ( 16) to eliminate ' f T resulting in the mixed inlet temperature as:

Outlet Temperature and Collector Efficiency
Once the mixed inlet temperature is calculated from Equation (19), the outlet temperature fo T in the downward-type internal-recycle solar air heaters with fins attached is readily obtained from Equation (13).The collector efficiency cf η may be defined with the useful gain of energy Q u divided by the insolation c A I 0 , as:

Mean Fluid and Absorbing Plate Temperatures
The mean fluid and absorbing-plate temperatures are needed for calculating the heat-transfer coefficients.The mean-fluid temperature may be taken approximately as: Substitution of Equation ( 20) is substituted into Equation ( 21) to eliminate fo T giving fm T in terms of cf η as: The collector efficiency may also be defined using: and the mean absorbing-plate temperature can be expressed in terms of cf η as:

Heat Transfer Coefficients
The convective heat-transfer coefficient h w for air flowing over the outside surface of the glass cover depends primarily on the wind velocity V. McAdams [14] obtained the experimental result as: An empirical equation for the loss coefficient from the top of the solar collector to the ambient U t was developed by Klein [19] following the basic procedure of Hottel and Woertz [20] for the horizontal collector with one glass cover shown in Figure 1: (26) and Equation (26) can also be expressed in terms of thermal resistances for this single glass cover system from the collector plate to the ambient air as follows: if the wind heat transfer coefficient w h of ±10% uncertainty existed and the amount of change in the value of t U was calculated within ±2% in the present study.
The radiation coefficient between the two air-duct surfaces may be estimated by assuming a mean radiant temperature equal to the mean fluid temperature [3], i.e.: In a solar air heater and collector-storage walls study it is necessary to know the forced convection heat-transfer coefficient between two flat plates.The following correlations [21] for air may be derived from Kay's data for fully developed turbulent flow with one side heated and the other side insulated:

= =
(30) The characteristic length is the equivalent diameter of the duct: eq,2 eq,1 and the average air velocities in subchannels 1 and 2 are: Thus, from Equations ( 31)-(33), one obtains the Reynolds numbers for the rectangular ducts as: T , is obtained.The following flow sheet may be helpful to simply expressing the calculation procedure.Given:

Effects of Operating Parameters on Collector Efficiency
The outlet air temperature decreases when the air flow rate m  increases and the collector efficiency increases, as indicated in Figures 2-5.On the other hand, the outlet air temperature fo T increases with the inlet air temperature fi T , resulting in a decrease in collector efficiency cf η .Of course, both the outlet air temperature and collector efficiency increase when the incident solar radiation I 0 increases.

Improvement in Performance by Recycling
The improvements (I f and I) in collector efficiencies ( cf η and c η ) using downward-type internal-recycle collectors with and without fins attached, respectively, are best illustrated by calculating the percentage increase in collector efficiency based on c η obtained in a single-pass device of same size without recycling and fins attached, i.e.: The theoretical values of f I for the system of present interest with the given values of c η [17], were calculated using Equation (37), and the results are listed in Table 2.The predicted values for I without attached fins were already calculated in a previous work [22].The results are also presented in , respectively.The contribution of increasing fluid velocity by applying the internal-recycle operation may be more effective than the undesirable effect of lowering the temperature difference by remixing.

Effect of Fin Attached on Performance
The improvements I in collector efficiency obtained in a downward-type internal-recycle recycled solar air heater of the same size but without fins attached [22], are also listed in Table 2 %) is obtained when employing the device with fins attached, instead of using the same device but without fins employed in the previous work [22].The further enhancement in collector efficiency E by attaching fins on the absorbing plate may be illustrated, based on a device of the same size but without fins, as: Equation (39) may be rewritten using Equations (37) and (38) as: Some values for E were calculated from Table 2, with the results listed in Table 3.As shown in this table further collector efficiency enhancement in the device with fins attached increases with the inlet air temperature fi T , while efficiency decreases when the reflux ratio R and/or the air flow rate m  increases.

Conclusions
The performance in a downward-type solar air heater with internal recycling was investigated in the previous work [22].In the present study the absorbing plate of this device was attached with fins for further improved performance.
In addition to the recycling operation, further enhancement in collector efficiency is obtainable if operation is carried out with fins attached on the absorbing plate.Further enhancement in collector efficiency E based on the device without fins, reaches 51.48% for I 0 = 1100 W/m 2 , K 298 = fi T , kg/s 01 0. m =  and R = 1.Further enhancement in collector efficiency E decreases when the air flow rate and/or the reflux ratio increase.Therefore, employing fins on the absorbing plate is ineffective when the performance is operated under a large reflux ratio with high air flow rate.
The improvements in collector efficiencies, I f and I, in the recycled devices with and without attached fins, increase with increasing reflux ratio, especially when operating at a lower air flow rate.It is shown in Table 2 and Figures 2-5 that the desirable effect of increasing the fluid velocity using the recycle operation compensates for the undesirable effect of decreasing the driving force (temperature difference) for heat transfer due to the remixing at the inlet.We can see in Table 2 that about 140% improvement I f in collector efficiency is obtained by employing the recycled solar air heater with attached fins based on comparison with the single-pass device of same size operated without recycling and fins.The order of performances in the devices of same size is: double pass with recycle and fins > double pass with recycle but without fins > single pass without recycle and fins.

= 1 w 2 wε
area of the absorbing plate = BL (m 2 ) f A = total surface area of fins (m 2 ) B = the width of absorber surface area = nw 1 (m) C p = specific heat of air at constant pressure (J/kg⋅ K) e D = equivalent diameter of the channel (m) E = further improvement of collector efficiency, defined by Equation (41) F 1 , F 2 = collector efficiency factors for subchannels 1 and 2, respectively OPEN ACCESS H = height of the air tunnel in the solar collector, or the distance between glass cover and absorbing plate (m) h = convective heat-transfer coefficient for fluid flowing over the plate of duct ( K W/m 2 ) h p-c = convection coefficient between the plate and glass ( K W/m 2 ) h p-R = radiant heat-transfer coefficient between two parallel plates ( radiation coefficient from the glass to the air ( K W/m 2 ) h r , p-c = radiation coefficient from the plate to the glass ( K W/m 2 ) w h = convective feat-transfer coefficient between glass cover and ambient ( K W/m 2 ) I = improvement of collector efficiency in the recycle device without fins, Equation (39) f I = improvement of collector efficiency in the recycle device with attached fins, k = thermal conductivity of air ( K W/m 2 ) s k = thermal conductivity of absorbing plate and fins ( K W/m 2 ) L = collector length (m) m  = mass-flow rate of air ( kg/s ) n = fin number Nu = Nusselt number u Q = useful gain of energy carried away by air per unit time ( W ) R = reflux ratio Re = Reynolds number of flow channel T = temperature ( K ) t = fin thickness t U = loss coefficient from the top of solar collector to the ambient( K W/m 2 ) ν = Average air velocity in the flow channel ( m/s ) V = wind velocity ( m/s ) = distance between fins (m) = height of fin (m) z = axis along the flow direction (m) Greek Letters c η = collector efficiency of a solar air collector with recycle but without fins c η = collector efficiency of a single-pass solar air collector without recycle and fins cf η = collector efficiency of a solar air collector with recycle and fins f η = fin efficiency σ = the Stefan-Boltzmann constant ( = emissivity of glass cover p ε = emissivity of absorbing plate R ε = emissivity of bottom plate g τ = transmittance of glass cover p α = absorptivity of the absorbing plate φ = modified factor for attached fins, defined by Equation (4) Subscripts a = ambient f = fluid i = inlet m = mean value o = outlet at subchannel 1 (z = L) p = absorbing plate R = bottom plate 1,2 = subchannel 1, subchannel 2 Superscripts 0 = mixed ′ = Outlet at the first pass or inlet at subchannel 2 (z = L)

Figure 1 .
Figure 1.Downward-type solar air collector with internal recycle and fins attached.
. The most significant optical property affecting solar collector efficiency is the transmittance-absorptance product, i.e., the numerical value 83125 study.As an illustration showing the expected sensibility to the potential uncertainties, the transmittanceabsorptance product of % and the amount of changes of the value of fo T was calculated by the procedure performed in Equation (36) and less than 0.5% in the present study with T fi = 288 K,

Table 2
for comparison.Operating with recycling substantially improves the collector efficiency with or without fins attached, as confirmed from this table and Figures2-5.The improvements increase with increasing reflux ratio R, especially when operating at lower air flow rate m  with higher inlet air for comparison.Considerable further collector efficiency enhancement is achieved if fins are attached to the absorbing plate to increase the heat transfer area.Taking the case of

Table 3 .
Further enhancement of performance for: (a)