Developing of New Structure of Flat Plate Solar Water Heater and Method for Calculation and Design

Single pane glazed flat solar heaters found rather wide application for domestic hot water supply. However, the practice of use shows some discrepancy between estimated and observed data: in one case the temperature of hot water does not conform to the expected pattern, in other case doubts arise about correctness of their sizes, in some cases the quantity of heated water is not enough, etc. Because of such divergence of opinions, it is becoming necessary to think about correctness of existing methods of sizing and designing of flat plate solar water heaters. This article attempts to develop a new structure and improved method for calculation and design of flat plate solar water heaters. Analysis proved relatively higher energy and cost effectiveness of the new structure of flat plate solar water heater.


Introduction
The algorithm of performance of flat plate solar water heater consists of following steps (1) Evaluation of optical losses and penetration rate of solar radiation through glazed cover. (2) Absorption of penetrated solar radiation by absorber sheet and rising the flat plate absorber's and consequently the hot tunnel and hotbox air temperatures. Nevertheless, as indicates H. P. Garg [1], usually the absorber plate temperature is unknown and is difficult to calculate or measure because it is a function of several parameters. To solve this problem the authors of this paper used a new approach allowing determining mentioned temperatures. (3) Transferring of hot tunnel's air heat to the water, flowing in the water metallic meander tube, laid in the hot tunnel. (4) Storing of hot water in a tank and consume it, when there is need. Descripted mechanism impels to use the mane principals of heat transfer and solar irradiant to developing a new, more energy efficient structure and method for calculation and design of suggested flat plate solar water heater.  1-aluminum frame, 2-thermal insulation layer, 3-copper or aluminum absorber sheet, 4-tap water inlet tube, 5-hot water outlet tube, 6-180 o bend water meander tube, 7-glass cover

New Structure and Operation of a Flat Plate Solar Water Heater
The new structure of flat plate solar water heater consists of powder coated aluminum frame (hotbox) (1) the bottom and sidewalls of which are covered by mineral wool thermal insulation layer (2). For absorbing solar rays and converting them into heat on the insulation layer (2) a copper or aluminum absorber sheet (3) and glass cover (7) are installed. On the absorber sheet a narrow air tunnel with length about l=1 m and height h tun. =0.05 m is created. In the tunnel a copper, 180° bend water meander tube (6) with, exterior diameter d ext. =0.024 m is laid. Through the inlet of tube (4) enters tap water and hot water exits through the outlet tube (5). Water meander tube and interior surface of the water heater are covered with dark color. The inside surface and inside air absorb penetrated solar energy Q sol.in and are heated up to an appropriate conditional temperature t cond. , °C. Then the solar energy Q sol.in transfers to the water, flowing in water 180° bend meander tube and heats it up to a final temperature t w.fin. The required quantity and temperature of hot water are provided by the heliosystem consisted of solar plate water heater units, arranged parallel and in series.

Accounting of Simultaneous Impact of Solar Radiation and Ambient Temperature on Functionality of Flat Plate Solar Water Heater
All types of solar water heaters simultaneously are sensitive to intensity of solar irradiance I, W/m 2 and temperature of ambience (outside air t out ). For this reason, in cold climatic conditions, the ambient temperature t out and as well the inside temperature of the hot tunnel, at nighttime and in the early morning are the same and negative. Therefore, for correct determination of absorbed solar heat Q sol.in and radiation conditional temperature t cond in tunnels, should be analyzed the daily unstable changes of solar irradiance I, W/m 2 , and temperature of ambience (outside air t out ), which take place simultaneously. Daily changes of outside temperature of given area are shown by the following cosine harmonic function [2]: Curve 1-daily course of outside air variable temperature; Curve 2-daily average temperature of outside air.
where: t out -running outside temperature during a day, °C, A t -amplitude of daily temperature change (temperature fluctuation range), Т=24 hour -daily period of oscillation of the outside temperature, Z t -instant time of a day when given temperature occurs, Z t.max. -instant time of the day, when outside air temperature reaches to its highest value.
The diagram of Fig. 2 represents the course of daily change of wintertime outside temperature in Yerevan city [2].
Based on guide of construction climatology of Armenia [2] the wintertime daily course of irradiance changes for Yerevan city represents the Fig. 3. From Fig. 3 it is evident that the effective sunrise takes place at 9:30 o'clock in the morning. The Fig. 2 displays that at the same 9:30 o'clock the temperature of outside air rises up to t out= -10°C, which is too low for water heating. That is why it is more probable that flat solar heater starts operating in water heating regime at 10:00 o'clock, after sunrise, when intensity of solar radiation reaches to I=655 W/m 2 (see Fig. 3) and ambient temperature becomes t out= -7°C. The mentioned combination of irradiance I=655 W/m 2 and outside temperature t out =-7°C conditions thermal characteristics of flat plate solar water heater.

Determination of Thermal Characteristics of Flat Plate Solar Water Heater
In the early morning, before sunrise, there is not solar irradiance, penetrating into hotbox. As a result, the internal surface and ambient temperatures of hotbox are equal to outside air temperature t out that in wintertime cold climate of Armenia makes t out =-19°C. In the morning, after sunrise, solar radiation penetrates through glass cover and is absorbed by dark colored absorber sheet. The following production allows quantifying solar energy Q sol.in , W, that penetrates into narrow hot tunnel: where: F-surface of glazed cover, m 2 , I-solar radiation intensity, for 40° northern latitude (Armenia), P=0.95-solar rays absorption rate by dark colored inside surface of the narrow hot tunnel [3].
The Fig. 3 shows that from 10:00 o'clock to 15:00 o'clock the intensity of solar radiation fluctuates and at 12:30 o'clock rises up to I=850, W/m 2 and the average intensity of solar radiation at that period stays on the level I=750, W/m 2 .
Daily average intensity of solar radiation equals to I av. =450 W/m 2 [2] that is typical for 40° northern latitude.
Because of partial reflection of incident solar rays from glass cover and dust level on its surface, the penetration rate of radiation through single pane glass cover makes 64 0. = χ [3]. Sizes of hot tunnel of the flat plate solar water heater are assumed as follows: the length a=1 m, the width b=0.24 m (equal to the diameter of 180° bend of water tube) and height of narrow air tunnel h air.tun. =0.05 m, the surface of the transparent glass cover is F=0.24 m 2 .
According to formula (2) the following quantity of solar energy Q sol.in , W, penetrated into the hotbox is determined by the following production: As a result the absorber sheet and air in the tunnel acquire so called radiation conditional temperature t cond. , °C, which is determined by the following formula [4]: where: in α -Convective heat exchange rate on internal surface of the narrow hot tunnel, W/(m 2 °C).

Evaluation of Convective Heat Exchange Rate on Internal Surface of the Narrow Hot Tunnel
Formula (3) shows that for finding absorber sheet temperature the value of convective heat exchange rate on internal surface of hot tunnel in α is needed. For this purpose, the following formula from similarity theory is used [5,6]: where: Nu-dimensionless Nusselt criterion (number), where: Gr -dimensionless criterion (number) of Grasshof. Pr -Prandtl number. For air Pr=0.7.
The following expression presents the Grasshof number: where: g -Acceleration due to gravitation force, g=9.8 m/s 2 , β =0.0032-rate of cubical expansion of air in the range of temperatures 0 to 100°C [7], l -characteristic dimension of hot tunnel, m, ν -kinematic viscosity of air, 00001416 0. = ν m 2 /s.

Water Final Temperature in Water Tube
Assuming that whole the heat 6 .
W passes to the water, flowing in water meander tube the final temperature of water t w.fin can be determined by the help of the following formula: where: t w.in -initial temperature of tap water, t w.in= 10°C, g w -water flow rate in the tube, kg/s, c w -specific heat of water c w = 4180 J/(kg°C). If daily demand of hot water makes, for instance, G w =120 kg/day or g w =G w / 7 h=120/7=17.1 kg/h, the final temperature of water t w.fin. , according to (7) The water heating up to t w.fin. =14.81°C indicates that in the hot tunnel the air temperature is higher, than t w.fin =14.81°C. This fact proves the radiation temperature t r.ab.sh of absorber sheet, on the surface of which takes place free convection: where: t out =-7°C-outside air temperature at 09:30 in the morning, 12 =

Determination of Water Tube Diameter
The inferior diameter of water tube calculates the following formula: where: ω=0.015 m/s -velocity of movement of the water in tube, ρ w =1000 kg/m 3 -density of water.
Substitute of above data for values in formula (9) The exterior diameter of water tube in 3 mm is bigger, than the inferior diameter d tub.inf. =0.02 m. That is to say d tub.ext. =0.023 m or 23 mm.

Determination of Required Length of Water Meander Tube
For complete transferring of the absorbed Q sol.in= 95.6 W of solar energy to the water, the tube should have appropriate length l tub , m, which can be determined by the following equation: where: t w.av -average temperature of the water, in the meander tube, A-thermal resistance to the heat transfer from air of hot tunnel to the water in the tube, m °C / W.
The average temperature of the water represents the following fraction:  (11) The thermal resistance A to heat transfer from hot tunnel air to the water in cylindrical meander tube is calculated by the following expression [ (11) and (12) in the formula (10) and making some simplifications, the following equation is obtained: For determining the required length l tub , m of water tube, the formula (13) is converted into the following equation: For transferring completely the penetrated solar energy to the water, flowing in water tubes, the required length of water meander tube, calculated by (14) will obtain:

Design of Heliosystem with Flat Plate Solar Water Heater Units
Considered flat plate solar water heater unit consists of hotbox's frame with sizes a=1 m, b=0.24 m and height h .air.tun =0.05 m. In air tunnel of each unit a water heating tube with length l tub. =4 m and diameter d tub.ext. =0.023 m is laid, which provides g w =17.1 kg/h warm water with temperature t w.fin. =14.81°C. The solar units are connected each to other in form of modules and arrays. The modules are parallel installed separate units. Each of them by inlet of its water tube is connected to a tap water main pipeline, which supplies water with initial temperature t w.in. =10°C. The outlets of water tubes are connected to the warm water collector. With the help of parallel arranged units it is possible to increase the quantity of warm water of the same t w.fin. =14.81°C temperature. The number of parallel installed modules n par.mod depends on required hourly or daily quantity of hot water, which is determined by the following fraction: where: G w -daily required total quantity of hot water, kg/day g w -hourly quantity of water, heated in a flat plate unit, kg/h. If there is necessity to get elevated temperatures of water the units should be connected each to other in series. For instance, in the second flat plate unit, connected with previous one in series, the inlet temperature of water is the outlet temperature of the previous unit t w.fin. =14.3°C. Such calculation can be realized by using the formula (7) where: t w.fin.gl. -global final temperature of water at the outlet of the last unit, connected in series, t w.fin.1 -final temperature of water at the outlet of the first unit, n -number of all units, connected in series.
unit . each t ∆ -Elevation of water temperature in each next unit, connected in series.
For instance, if n=8 units are connected in series, at the outlet of the first unit the temperature of water is t w.fin =14.81°C and in each of (n-1)=7 units, connected each to other in series the temperature growth will make: 7x4.81°C =33.67°C. Therefore, the global final temperature of water at the outlet of the last 8 th unit will make 14.81+33.67=48.48°C. In case of need of higher temperatures, the number of units, connected in series should be respectively increased.
If there is need for increasing of hot water quantity, can be used the heliosystem with parallel arranged units as shown in Fig. 4.
If there is need for increasing of hot water temperature, can be used the heliosystem with connections of units in series as shown in Fig. 5. The number of unites connected in series is determined by the formula as follows: For selecting the maximum number of solar water heater units that can be connected in series, should be taken into account hydraulic losses in the system [9] At present, are widely used flat plate solar water heaters, the scheme of which displays the Fig. 6 [10]. 1-flat plate solar water heating units, 2-water heating meander tube with length 9.06m, 3-hot water collecting pipeline, 4-thermal insulation, 5-water tank, 6-heat exchanger, 7-cold water supplying pipeline, 8-valves 1-flat plate solar water heating units, 2-water heating meander tubes, 3-hot water collecting pipeline, 4-water tank thermal insulation, 5-water tank, 6heat exchanger, 7-cold water supplying pipeline, 8-valves

Energy Efficiency and Cost Effectiveness of Flat Plate Solar Water Heater New Structure
For evaluating efficiency of suggested flat plate solar water heater, it is important to determine its initial cost. Because a sample of new flat plate solar water heater is not produced yet, there are not practically proved data on initial cost. That is why an attempt has been done to determine new solar heater initial cost by using Armenia market costs of materials and manufactured goods in accordance with main parts of flat plate solar water heater. The costs of different parts of the heater, assessed by materials and labor costs in Armenian market are the followings:  cost of 1 m 2 of glass cover-6$/m 2 . Cost of glass cover for the water heater -6$/m 2 x 0.237 m 2 =$1.43 labor cost of arrangement of the glass cover-$10. Total cost of installation of glass cover -$11.43 According to the above assessments, the initial (capital) cost of one unit of developed flat plate solar water heater makes: $25+$6+$6.1+$1.0+65.8+20+11.43=$135.3.
There would be also 10% of trivial expenses, which make about $13.53. Therefore, the total capital cost of one unit of the developed flat plate solar water heater makes $148.8.
The structure and operation of the heliosystem shows the Fig. 7 Substitute above values for quantities of formula (18) will obtain Q saved.year =5500 kWh/year of yearly saving of energy.
By replacing of gas heating boiler by suggested heliosystem, it is possible to save fuel gas during a year in the quantity, determined by the following calculation: The comparison with existing flat plat solar water heaters [11] the payback period of suggested structure of flat plate solar heater is about twice shorter.

The suggested new method includes new approaches
for selection of values of solar radiation and ambient temperature taking into account their simultaneous impact on the main characteristics of flat plate solar water heater. 2. The developed simplified method allows calculating all required thermo-physical and constructive characteristics needed for designing rather productive and efficient flat plate solar water heaters. 3. The detailed analysis of suggested method and obtained results prove rather efficient functionality of solar water heater in very cold climatic conditions with very low outside temperatures. 4. The suggested flat plate solar water heater produces 410 l/day of hot water and can be applied for heat supply to domestic and industrial consumers, which need hot water with temperatures up to 100°C. 5. Farther improvement of hot tunnels' structures can increase energy efficiency of flat solar heaters. 6. Although the payback period of new flat plate solar water heater is almost twice shorter compared to existing ones, but it is steel not enough efficient. Therefore, farther simplifying of structure is needed.