Types of heat generation in Ukraine in 2016 and their cost
Январь 31st, 2016
The temperature distributions of the heat storage tank with different obstacles are calculated numerically and presented in zr plane. Temperature distribution of the smooth tank is also presented. The results as follows;
Using the obstacles are improving the thermal stratification inside the tank compared to the smooth tank.
It can be observed that, the obstacle types have gap in the center, have better thermal stratification than obstacle types that have gap near the tank wall.
Obstacle types 7 and 11 have supplied hot water with higher degree to usage rather than other obstacles type and also rather than smooth tank. This is desirable case for thermal stratifications. Other obstacle types have little effect into the thermal stratifications in the tank. The smooth tank has also little thermal stratifications.
While the operation periods of time, the tank has obstacle type 11 has lower average value of temperature in the z=0.2 plane in radial direction than the tank has 7 type of obstacle. The reason of this case is that tank model has obstacle type 11 has cylindrical shaped obstacle in z=0.2. This obstacle prevents the destroying effect of the cold water into the thermal stratifications while the operation period of time increases. So, in tank 11, the temperature of the water going to the heater would decrease while the time period increases. This is also desired situation for heat storage tank in solar energy systems.
T3 has increased in tank 11 and T1 has decreased during the operation times. So, the difference between T3 and T1 would also increase. This is also desired criteria for thermal stratifications. With respect to these arguments, the tank has obstacle type 11 has best thermal stratification between all investigated cases.
The tank has obstacle has improved the solar collector efficiency as well as thermal stratifications. Because, T1 (water return to the solar collector) would decrease when the obstacle is used. So, the increase of the solar collector efficiency can be achieved.
The authors thank to the Erciyes University for FLUENT 6.1.22 code.
The crosssectional view of the used model for numerical analysis is shown in Fig. 1.
Boundary layer equations were used to determine the temperature and velocity distributions in the flow field. The analysis was based on the unsteady, threedimensional continuity, momentum and energy equations.
The assumptions are used as:
— The flow is unsteady, turbulent and threedimensional,
— The thermal conductivity of the tube sheet material does not change with temperature
— The tube material is homogeneous and isotropic.
Three dimensional continuity, momentum and energy equations are solved numerically. The upwind and central difference method used for convections and diffusions, respectively [9].
The aim of using the obstacle is supplying hot water as long as possible in the upper part of the tank to usage. So, high thermal stratification would be achieved by using these obstacles to obtain higher degree of hot water from the tank. The obstacle’s schematic view is shown in figure 2. The details of these obstacle geometries are shown in figure 3. Table 1 indicates that the matches between obstacle type and tank.
d =0.02 m f1 = 0.04 m Vk=0.2 m/s
D= 1 m g = 0.2 m
f = 0.2 m Si = 0.2 m
The hot water entrance velocity is assumed as 0.2 as forced convective regions. The water temperatures are assumed 333, 320 and 285 K for water exit from the tank to usage, water in the tank and water coming from the main lines, respectively.
dl 
1 
T4
V
Figure 1 Crosssectional view of the used tank model Table 1 Obstacle types and tanks matches

The dimensions of the obstacles in figure 3 are shown in Table 2. Table 2 The dimensions of the obstacles

2.1 Physical properties of fluid and boundary conditions
The thermodynamic properties of the water are considered in this study. The velocity and is assumed to be zero at the beginning. The operation pressure in the tank is taken1 atmosphere and the hot water temperature is assumed to be 320 K when the water usage started. The time between the water is started to be used and the water usage was finished is assumed as
calculation region. This time is taken as 30 minutes and the problem solved as unsteady. 
Figure 3 The details of the obstacles in the tank.
E. ANDERSEN, U. JORDAN, L. J. SHAH, S. FURBO Department of Civil Engineering, Technical University of Denmark Building 118, DK2800 Kgs. Lyngby, Denmark Tel.: +45 4525 1901, Fax: +45 4593 1755, ean@byg. dtu. dk, uj@byg. dtu. dk, ljs@byg. dtu. dk, sf@byg. dtu. dk
Since the 1960’ties the influence of the thermal stratification in hot water tanks on the thermal performance of solar heating systems has been studied intensively. It was found, that the thermal performance of a solar heating system is increasing for increasing thermal stratification in the hot water tank.
The temperature of the storage water heated by the solar collector loop usually varies strongly during the day. In order to reach a good thermal stratification in the tank, different types of pipes, plates, diffusers and other devices have been investigated in the past (e. g. Loehrke, 1979). The aim pursued was to transport the heated water into the tank level of corresponding temperature.
Flexible stratification pipes (manifolds) have been further developed for example by (Gari et al., 1982). Furthermore, a wide variety of non flexible tubes with either open holes and perforated vertical plates inside the pipes (Davidson, 1992) or openings in form of balls (e. g. Leibfried, 2000) or flaps (e. g. described in Krause, 2001) have entered the market during the recent years.
In this paper an investigation of a stratification pipe with openings covered with flaps according to (Krause, 2001) is presented. The flaps are constructed with a soft material which allows the flap to close and open depending on the temperature and pressure differences inside and outside the pipe. Figure 1 shows schematic
illustrations of the pipe. The total height of the pipe is 328 mm, the outer diameter 60 mm, and the flaps are located with a distance of 292 mm in vertical direction (distance between the centre of each opening).
Preliminary laboratory tests by (Shah, 2002) with the same stratification pipe containing 5 openings showed that thermal stratification was well built up for a volume flow rate smaller than 8 l/min and larger than 4 l/min, regardless of the inlet temperature, the temperature level in the tank, and the thermal stratification in the tank. For volume flow rates larger than 8 l/min, however, the number of open flaps increased, so that
water entered the tank at different levels instantaneously. For volume flow rates smaller than 4 l/min laboratory tests indicated that cold water could be sucked in through an opening in a low level due to low pressure differences. The cold water that entered the pipe through these openings from the bottom of the store mixed with the heated water that flew through the pipe and thereby induced mixing in the tank during charging.
More detailed investigations of the flow structure close to the flaps of the stratification pipe are presented in the following for one set of operating conditions. Temperature measurements were carried out and an optical method called Particle Image Velocimetry (PIV) was used to visualize the flow around the flaps.
Experimental Setup
The experimental setup is shown in Fig. 2. The setup consists of a rectangular glass tank with side lengths of 400 x 400 x 900 mm3, a heating and a cooling unit, and standard PIV equipment (Dantec Dynamics). The PIV equipment consists of a laser, a camera and a processing system for analysing the pictures taken by the camera. Information about the PIV equipment is given in Table 1.
Table 1. PIV equipment.

The camera is placed perpendicular to the laser that illuminates a thin slide in the flow.
The inlet consisting of three compound stratification inlet pipes placed in the centre of the tank. The inlet pipe is closed at the top. The outlet is placed in the bottom of the tank in the corner behind the inlet pipe. The temperature is measured in the middle of the pipe below each inlet and in 13 uniformly distributed levels in the tank. Also the in — and outlet temperatures are measured as well as the volume flow rate. The temperatures are measured with thermocouples type TT with an accuracy of 0.5 K. The volume flow rate is measured with an electro magnetic inductive flow meter, type HGQ1 from Brunata HG a/s. The flow meter has an accuracy of about ± 1 %.
CFD code is used to obtain velocity and temperature distributions inside the tank. Three dimensional unsteady solutions are taken by using implicit method in segregated solver. The discretization is achieved by using standard method for pressure and by using first upwind method for momentum, energy, turbulent kinetic energy and turbulent dissipation rate equations. The SIMPLE (semiimplicit method for pressurelinked equations) algorithm was used for flow calculations [10].
Te underrelaxation factors are assumed as 0.3, 0.7, 1, 0.8, 0.8 and 1 for pressure, momentum, energy equations, turbulent kinetic energy (k), turbulent dissipation rate (s) and turbulent viscosity (pt) as, respectively. This factor has assumed as 1 for body force and density.
The convergence factors are used as 103 for continuity, momentum, turbulent kinetic energy and turbulent dissipation rate equations. This value is taken 106 for energy equations [10].
The best obstacle type and angle for supplying higher thermal stratification has been found numerically between all investigated cases. The aim is supply hot water as long as possible with high thermal stratification between the temperatures T4 (cold water enter to the tank from main lines) and T2 (hot water supplied by solar collector). In order to obtain this higher stratification, different kind of obstacles as cylindrical, semicylindrical and conic are inserted to the tank. These obstacles are placed in the tank with suitable angles and coordinates to decrease contact area between cold and hot water in the tank. T4 flow fibers don’t have to destroy hot water gradient. However, the hot water entering the tank (T2) would destroy the stratification. Therefore, hot water velocity is taken as 0.02 m/s for natural circulation. The flow rate of the hot water from tank to usage would be equal to the cold water entering to the tank from the main lines. The cold water velocity from the main lines is assumed as 1 m/s.
There would be vortexes in the tank. Because two different fluids are mixed in the tank and they are hitting each other towards to the wall and obstacle surfaces. Therefore, calculations are carried out by using wall functions method and standard ks turbulent models with FLUENT [10].
Higher percentage of the cold water entering to the tank would be directed towards to cold water exit channel (T1) from the tank. Because the cold water enters and exit pipes in radial direction are in the same axis as symmetrical condition. So, the cold water can not produce a lot of vortex inside the tank and destroying effects into thermal stratification inside the tank would be decreased. The water is wanted to be hot as possible as for usage. In order to achieve this, the hot water exit channel (T3) is generally located at the top of the tank.
The numerical analysis of the effect of the different type of obstacles into the thermal stratifications in the hot water storage tank in solar energy system has presented. The geometrical details of the obstacle types are defined under the theoretical model caption. The present study is initial works that aimed to find the best obstacle type between all investigated cases to analyze in experimental setup later.
Nearly 30 different types of obstacles are considered in this work but, 12 of them is present here. The temperature difference distributions of the tank with and without obstacle, which is given in figure 3 and 4, are presented in figure 5.
Smooth tank is considered firstly to compare the thermal stratification inside the tank with obstacles. There is a little thermal stratification at the top of the smooth tank. So, the temperature difference between thermal stratifications is far from desired values in smooth tank. The temperature distribution of the smooth tank case is depicted in figure 413. The hot water (T2) and cold water (T4) has contact in all axial crosssectional area when they enter the tank. The rotations of the hot and cold water velocity vectors occur. Because they hit each other towards to the tank wall. The hot water stratification has been destroyed by cold water in this condition. In order to keep higher thermal stratification, the axial contact area between cold and hot water must be decreased and cold water mustn’t be directed towards upper part of the tank. Therefore, the obstacles in different shapes as cylindrical, semicylindrical and conic are placed in the tank to get minimum axial contact area.
The thermal stratification area and thickness are higher in tank with obstacles rather than tank without obstacles. The thermal stratifications are shown in figure 4 for storage tank with 12 different type of obstacle and 1 smooth tank. Figure 5 represent the temperature difference according to the tank numbers to determine the best tank models in order to obtain higher thermal stratification. T3T4 and ((T2T1HT3 — T1)) must have higher and ((T2T3) and (T1T4)) must have lower value to obtain good thermal stratifications. With respect to all these argument, obstacle type 7 and 11 has supplied higher thermal stratification.
T3 and T1 temperature distributions according to the tank model are illustrated in figure 6. T3T1 (temperature difference between water exit to the usage and water going to the storage tank) must be considered for choosing the tank model has better performance of thermal stratification. This temperature difference must be higher to obtain higher thermal stratification. Obstacle type 11 has higher value of T3T1. It can be said that obstacle type 11 can supply highest thermal stratification between all investigated cases. The best indicators to evaluate the effect of the obstacles into the thermal stratifications are T3 and T1. T3 and T1 must be higher and lower as soon as possible, respectively. T3 and T1 values are very close in smooth tank.
1052 EuroSun2004 
Figure 43 
1.5 ■ 1.4 ■ 1.3 0.9 0.8 0.7 0.6 °.5 0.4 0.3 0.2 0.1 0 
1.5 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 
SHAPE * MERGEFORMAT
Temperature distributions of obstacle type 11 and 7 for operation periods of 5, 10, 15, 20, 25 and 30 minutes are shown in figure 7 and 8 in z plane, respectively. These two different obstacles have different temperature for z=0.0, 0.1, 0.2 and 0.3 m during the 30 minutes operation period. Obstacle type 11 reach the maximum temperature in z=0.3 m for all operation period but, obstacle 7 can reach the maximum temperature in z= 0.6. The temperature values are nearly the same in between z=0.4 and z=1.5 as in figure 7 and 8. So, these two obstacle type nearly has the same temperature inside the tank in all points.
Figure 9 represent the T3 and T1 distributions in z plane versus operation time for obstacle types 11 and 7. These temperature presented here for 6 different time periods as t=5, 10, 15,
20, 25 a 30 minute as seen in figure 9. T3 values are nearly the same for these two obstacle type but, Ti has lower value in obstacle type 11 after the 10 minute of operation period. So, type 11 has higher temperature difference between T3 and T1 after 10 minute in obstacle typell rather than obstacle type 7. The case is desired for higher thermal stratification. In the
light of these parameters, obstacle type 11 has supplied the best thermal stratification for system has natural circulation inside between all investigated obstacles.
1. Conclusions
The numerical analysis of the effect of the using different kind of obstacles in the heat storage tank to obtain higher thermal stratification has been presented. The temperature distributions in the heat storage tank with different obstacles are also presented in zr plane. Temperature distribution of the smooth tank is also presented.
The results from these analyses as;
The tank with obstacles has better thermal stratifications rather than smooth tank.
The obstacle types have gap in the center, have better thermal stratification than obstacle types that have gap near the tank wall.
Tank models 7 and 11 have higher thermal stratification. So, these obstacles have supplied hot water in higher degree to use and also have water to the heater tank in lower degree. This is desirable case for thermal stratifications. It is seen that other obstacle have little effect into the thermal stratifications.
In z=0.2 plane, the average temperature values in radial direction is being lower in obstacle type 11 compared to the obstacle type 7 while the time period increases. Because tank model 11 has cylindrical shaped obstacle in z=0.2. This obstacle prevents the destroying effect of the cold water into the thermal stratification while the operation period of time. So, the temperature of the water going to the heater would decrease while the time period increases in tank 11. This is also desirable condition for heat storage tank.
T3 (water temperature for usage) has increased in tank 11 and T1 (water is going to the heater) has decreased while the increase of operation times. So, obstacle type 11 has the highest temperature difference between T3 and T1. This is the desired criteria for thermal stratifications. In the light of all these considerations, the tank, has obstacle type 11, is the best tank type for thermal stratification in between investigated cases.
Using obstacle has improved the solar collector efficiency as well as thermal stratifications. Because, T1 (water return to the solar collector) would decrease when the obstacle is used. So,
the solar collector efficiency would also increase.
Acknowledgement
The authors thank to the Erciyes University for FLUENT 6.1.22 code. References
1. Alizadeh S., An Experimental and Numerical Study of Thermal Stratification in a Horizontal Cylindrical Solar Storage Tank, Solar Energy, Vol.66, No.6, pp.409421, 1999.
2. AlNimr M. A., Temperature Distribution inside Electrical Hot Water Storage Tanks, Applied Energy, Vol.48, pp.353362, 1994.
3. Misra R. S., Thermal Stratification with Thermo siphon Effects in Solar Water Heating Systems, Energy Conversion Management, Vol.35, No.3, pp.193203, 1994.
4. Helwa N. H., Mobarak A. M., Effect of Hot Water Consumption on Temperature Distribution in a Horizontal Solar Water Storage Tank, Applied Energy, Vol.52, pp.185194, 1995.
5. Hariharan K., Badrinarayana K., Temperature Stratification in Hot Water Storage Tanks, Energy, Vol.16, No.7, pp.977982, 1991.
6. Hahne E., Chen Y., Numerical Study of Flow and Heat Transfer Characteristics in Hot Water Stores, Solar Energy, Vol.64, No.13, pp.918, 1998.
7. Mo Y., Miyatake O., Numerical Analysis of the Transient Turbulent Flow Field in a Thermally Stratified Thermal Storage Water Tank, Numerical Heat Transfer, Part A, Vol.30, pp.649667, 1996.
8. Eames P. C., Norton B., The Effect of Tank Geometry on Thermally Stratified Sensible Heat Storage Subject to Low Reynolds Number Flows, Int. J. of Heat Transfer, Vol.41, No.14, pp.21312142, 1998
9. P. V. Suhas, Numerical Heat Transfer and Fluid Flow, pp. 79109, Hemisphere Pub. Co., New York, 1980.
10. FLUENT 6.1.22 user’s guide. Fluent Incorporated, Centerra Resource Park, 10, Cavendish Court, Lebanon, NH 03766, USA, 2001.
Nomenclatures
Vk Hot water velocity from tank to tank
V§ Cold water velocity from mainlines to tank
D Tank diameter
H Tank height
f1 The distances between cold water enter and exit point and bottom of the tank
d Pipe diameter
Si The distance between the point hot water enter and tank ceiling
d1 The gap diameter in the center of the obstacle
l Channel length
T Temperature
T3 Usage water temperature
T 1 Temperature of the water going to the heater
T 2 Temperature of the water coming from the heater
T4 Temperature of the water coming from the mainlines.
t Time
Necdet ALTUNTOP1, Mevlut ARSLAN1, Veysel OZCEYHAN1,
1 Dept. of Mechanical Engineering, Erciyes University, 38039 Kayseri, Turkey
Abstract: The numerical analysis of the effects of water flow rate into the thermal stratifications in the cylindrical hot water storage tank has been presented. The obstacle, has dimensions f/H=0.133 and g/D=0,2 and has a gap at the center of, has also replaced in the tank. This obstacle has supplied the thermal stratification between cold (at the bottom) and hot (at the top) water. Because it prevents mixing of two fluids. The flow rate has changed for both tanks with and without obstacles in order to analyze the effect of the volume flow rate. The temperature distributions are also presented for both types. The temperature distributions of the cold water in, hot water out and the temperature differences of the water going to and coming from the collector have been presented into the graph. The temperature distributions of both tank types have been compared to supply as high as possible hot water to usage and as low as possible to heater. At result, The best thermal stratification has obtained with Vk=0,8 m/s. The tank type has obstacle has better performance into thermal stratification compared to the smooth tank.
Water has widely used in domestic and international area fro solar energy storage as sensible heat. In storage units, when the hot water is being used, the cold water comes instead of the hot water from the main lines and these two waters would be mixed in the tank and the water temperature would decrease drastically. In this study, the obstacle has placed to prevent this disadvantages and the effect of the volume flow arte into the thermal stratification has also investigated.
There is some previous analysis about these subjects as; ALIZADEH, has investigated the thermal behavior of a horizontal cylindrical storage tank both experimentally and numerically. He used one dimensional the Turbulent Mixing Model and Displacement Mixing Model in numerical calculations. He has used some models to prevent unsteady behavior of the vertical temperature distributions [1].
ALNIMR has solved and presented some mathematical models to determine the effect of the different design parameters on the thermal stratification within the tank and the time required by tank to supply water within a specified outlet temperature [2].
MISRA has analyzed the thermal stratification both theoretically and experimentally in hot water storage tank for the thermo siphon effect in solar water heating systems. He has given the analytical expressions to obtain temperature distributions in the tank. He has also given the diagrams depends on the time to present conductive heat transfer between the layers in the storage tank [3].
HELVA ad MOBARAK have investigated the effect of the amount of the hot water using into the temperature distribution in solar water heating storage tank [4].
HARIHARAN and BADRINARAYANA have analyzed the thermal stratifications numerically
and experimentally in the hot water storage tank. They have studied the effect of surrounding and operating conditions into the thermal stratifications. They have observed that stratification improves with increasing AT and water flow rates [5].
HAHNE and CHEN have studied numerically about the flow and heat transfer characteristics in a cylindrical hot water store. They have used the storage efficiency to obtain thermal stratification. They have found that the increase of the Richardson and Peclect number has an effect that increases the storage efficiency [6].
Mo and MIYATAKE have carried out the transient numerical analysis for the thermal stratifications in the storage tanks. They have used turbulence model (ks model). They have presented the effect of exchange cold water with hot water into the thermal stratifications [7].
EAMES and NORTON have investigated the effect of the tank geometry into the thermal stratification for sensible heat storage for low Reynolds number. They have presented the effect of inlet and outlet port locations on store performance [8].
In this study, the effect of the using different volume flow rate of the water for obtaining higher thermal stratifications has been analyzed numerically. One obstacle is placed in the cylindrical tank to get the best performance for thermal stratifications inside the tank between all investigated volume flow rates. The water has been used as fluid. The flow type has assumed as turbulent. There would be vortexes in the tank. Because two different fluids are mixed in the tank and they are hitting each other towards to the wall and obstacle surfaces. Therefore, calculations are carried out by using wall functions method and standard ks turbulent model.
The main difference of this work is that the thermal stratification is supplied by using the obstacle. This obstacle has prevented to mixing of two different fluids to supply higher thermal stratification. The used obstacle has hole at the center. The different volume flow rate is used to analyze the effect of using this obstacle. The previous works has two dimensional calculations but, this present study has carried out by three dimensional.
Samuel L. Abreu1, Juan Pablo de L. C. Salazar1, Sergio Colle1
1LABSOLAR — Solar Energy Laboratory / Federal University of Santa Catarina —
Florianopolis — SC — Brazil
Wilson Reguse2
2Centrais Eletricas de Santa Catarina — CELESC (Santa Catarina state utility)
samuel@emc. ufsc. br, phone +55 4 8 331 9379, fax + 55 4 8 3317615
Introduction
A particular characteristic of the electric energy consumption in Brazil is the widespread use of electric showerheads and the resulting peak demand between 18h and 21 h. Over 90% of the residences in Brazil have electric showerheads. Studies have shown that electric showerheads represent approximately 23% of a household’s energy consumption and this fraction increases to around 35% of the total demand during the peak hours for lowincome consumers (Prado and Gongalves, 1998). Electric showerheads are very cheap, usual prices lie under US$30 in Brazil, have a nominal power between 4kW and 8kW and are very efficient in terms of energy conversion. All these aspects contribute to the large scale use of electric showerheads for water heating among lowincome consumers. Furthermore, showering is the only use of hotwater by this class of consumers in Brazil. Therefore, Compact Domestic Solar HotWater Systems — CDSHWS, cheaper and easy to install when compared to conventional solar hotwater systems, may be an economically attractive alternative to supply large scale hotwater usage, with the benefit of reducing the peak demand on the utility grid.
Utilities in Brazil are obliged by regulation laws to supply electric energy to low — income consumers. However, the associated costs of energy generation and distributions are heavily affected by the power of the electric showerheads, making investments in almost all cases economically unviable. Januzzi and Schipper (1991) estimate that the marginal expansion costs lie around US$ 1,500.00 per kilowatt. (falta ref para inserir). This scenario leads to the conclusion that the utility can account for the large scale installation of CSDHWS in its investment policy. In other words, the utility can share the cost of the solar heaters, which lies around US$ 300,00, with low — income electricity consumers.
In a previous work, Salazar et al. (2003) optimized seven parameters of a CSDHWS using peak demand and total cost as constraints. The optimized parameters were: collector aperture area, storage tank volume, heater power, electric showerhead power, setpoint temperature of the storage tank, mixing valve temperature and collector slope. The chosen optimization procedure was successful, but the lack of information on hotwater consumption profiles is a limitation on the reliability of the predictions.
Colle et al. (2003) carried out the economical optimization of the CSDHWS storage tank insulation thickness. The optimization showed that life cycle cost savings are sensitive to insulation costs, when preheating of the storage tank during the morning early hours is required in order to avoid the expected peak demand. This optimization concern should be taken into account, in order to minimize the cost of CSDHWSs.
To study the effects of CSDHWSs on the peak demand, ninety lowincome consumers from a housing unit were chosen to have their showerhead electric energy consumption monitored. Sixty consumers were equipped with CSDHWSs, while the remaining consumers served as a reference case. The electric energy
consumption of the showerheads was continuously measured, providing the profiles from which the results of this paper are derived.
The thermodynamic properties of the water are considered in this study. The velocity and is assumed to be zero at the beginning. The operation pressure in the tank is taken 1 atmosphere and the hot water temperature is assumed to be 320 K when the water usage started. The time between the water is started to be used and the water usage was finished is assumed as calculation region. This time is taken as 30 minute and the problem solved as unsteady.
The velocity and temperature distributions inside the tank have obtained by using the computer code [12]. Three dimensional unsteady solutions are taken by using implicit method in segregated solver. The discretization is achieved by using standard method for pressure and by using first upwind method for momentum, energy, turbulent kinetic energy and turbulent dissipation rate equations. The SIMPLE (semiimplicit method for pressurelinked equations) algorithm was used for flow calculations.
The convergence is very important in numerical calculation by using the code. Solutions were assumed to converge when the following convergence criterion is satisfied by every dependent
variable at every grid point in the computational domain
pnew — pold
¥
Where (^) in general could be any dependent variable. In this study, ^=10’3 for continuity, momentum. Turbulent kinetic energy and turbulent dissipation rate equations. This value is 10^6 or energy equations.
To underrelaxation factors are assumed as 0.3, 0.7, 1, 0.8, 0.8 and 1 for pressure, momentum, energy equations, turbulent kinetic energy (k), turbulent dissipation rate (s) and turbulent viscosity (pt) as, respectively. This factor has assumed as 1 for body force and density.
The CSDHWS works in a single phase thermosyphon mode, consisted of a single glazed flatplate collector and a horizontal storage tank equipped with a resistor located immediately above the collector, as shown in Fig. 1. The system can be easily accommodated on the rooftop and integrated with existing piping (see Fig. 2). An additional electric showerhead, with continuously adjustable power, provides extra heat input. Therefore, auxiliary energy can be added to the system either in the storage tank or in the electric showerhead, but in the present analysis only the electric showerhead was used. The system is also equipped with a thermostatic mixing valve at the storage tank outlet pipe, which prevents scalding. The compact system is only used for showering purposes. Table 1 shows the technical characteristics of the system. The solar collector was tested according to European flatplate collector test standards (MullerSteinhagen, 2002).
Table 1. Technical characteristics of the compact solar hotwater system

Figure 1. Compact solar hotwater system scheme 
hundred consumers from a housing unit for lowincome families (monthly income from US$250.00 to US$500.00) were interviewed using a questionnaire based on a model suggested by Vine et al. (1986). Ninety families were selected according to the similarity with a standard hotwater consumption profile and sixty of them received a CSDHWS. The groups are named as follows:
(i) Group A — sixty consumers with CSDHWSs.
(ii) Group B — thirty consumers without CSDHWSs.
Fig. 2 shows the systems installed on the rooftops. The buildings were financed by Caixa Economica Federal (Federal Brazilian Savings Bank) under a leasing contract.
Figure 2. Compact solar domestic hotwater systems on the roof of the buildings 
The power of the electric showerheads of all ninety consumers was averaged over five minute intervals. The consumers without the CSDWHS were used to characterize the typical energy consumption profile of a group of lowincome consumers. The comparison between the two groups was used to estimate the solar fraction provided by the solar systems.