Optimal design of a forced circulation solar water heating system for a residential unit in cold climate using TRNSYS

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Solar Energy 83 (2009) 700–714 www.elsevier.com/locate/solener

Optimal design of a forced circulation solar water heating system for a residential unit in cold climate using TRNSYS Alireza Hobbi *, Kamran Siddiqui Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec, Canada Received 28 March 2007; received in revised form 22 June 2008; accepted 27 October 2008 Available online 17 November 2008 Communicated by: Associate Editor Dr. C. Estrada-Gasca

Abstract An indirect forced circulation solar water heating systems using a flat-plate collector is modeled for domestic hot water requirements of a single-family residential unit in Montreal, Canada. All necessary design parameters are studied and the optimum values are determined using TRNSYS simulation program. The solar fraction of the entire system is used as the optimization parameter. Design parameters of both the system and the collector were optimized that include collector area, fluid type, collector mass flow rate, storage tank volume and height, heat exchanger effectiveness, size and length of connecting pipes, absorber plate material and thickness, number and size of the riser tubes, tube spacing, and the collector’s aspect ratio. The results show that by utilizing solar energy, the designed system could provide 83–97% and 30–62% of the hot water demands in summer and winter, respectively. It is also determined that even a locally made non-selective-coated collector can supply about 54% of the annual water heating energy requirement by solar energy. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Flat-plate collectors; Solar water heating; Forced circulation; TRNSYS

1. Introduction Satisfactory performance and reliability of a solar water heating system requires adequate sizing of its components as well as accurate prediction of the delivered useful energy and outlet water temperature. In cold regions the thermal losses from the solar water heating systems are high, solar irradiance is low, and freezing of the fluid inside the collector is an issue. Therefore, optimization of the system parameters is very important to achieve an adequate performance. The performance of solar water heating systems with flat-plate collectors has extensively been studied theoretically and experimentally over the past several decades. For instance, Hottel and Woertz (1942) established the fundamental quantitative relations among the performance parameters, Bliss (1959) derived the mathematical models *

Corresponding author. Tel.: +1 780 838 5150. E-mail address: [email protected] (A. Hobbi).

0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.10.018

for efficiency factors for a variety of solar collectors; Liu and Jordan (1963) reported a simple procedure to predict the long-term performance of a collector; Whillier and Saluja (1965), Gupta and Garge (1968), and Yeh et al. (2003) studied the effect of several design details on the system performance; San Martin and Fjeld (1975), and Siebers and Viskanta (1977) compared the performance of different configurations of the flat-plate collector; and Hahne (1985) investigated the effect of various parameters on the efficiency and warm-up time of flat-plate collectors. Most of these studies, however, investigated the performance over a short period of time and for simplified operating condition. Different computational tools have been developed to numerically evaluate the long-term performance of solar systems and study the effect of design parameters. TRNSYS 16 (Klein et al., 2004) is extensive software for transient simulation of solar systems (thermal or PV), low energy solar multi-zone buildings, renewable energy systems, fuel cells

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701

Nomenclature Ac CB Cp Dr,i Dr,o F FR 0 F f hf,i Ht IT k L l m_ n t Qu

Collector area, m2 Bond conductance, h m2K/kJ Specific heat of fluid, kJ/kg °C Inside diameter of the pip, m Outside diameter of the pipe, m Fin efficiency factor Collector heat removal factor Collector efficiency factor Solar fraction (annual or monthly) Heat transfer coefficient between the pipe wall and the circulating fluid, W/m2 oC Tank height, m Solar radiation incident rate on the collector surface per unit area, W/m2 Thermal conductivity, W/m2 oC Pipe length, m Collector Length, m Collector flow rate, kg/s Number of riser tubes Thickness, m Useful energy collection rate from the collector, W

and their related equipments. This program has been widely used to study and optimize solar systems. There have been several studies that used TRNSYS to evaluate the effect of different design parameters and operating conditions on the performance of Thermosyphon Solar Water Heating (TSWH) system. For example, Morrison and Braun (1985) studied the characteristics of horizontal and vertical tanks; Shariah and Ecevit (1995) studied the effect of different load temperatures on the performance of the TSWH systems with auxiliary electric heaters; Shariah and Lo¨f (1996) investigated the effect of tank height on the performance and annual solar fraction; Shariah and Lo¨f (1997), and Michaelides and Wilson (1997) studied the effect of an auxiliary electric heater and its location; Shariah et al. (1999) studied the effect of thermal conductivity of the absorber plate, and Shariah et al. (2002) optimized the tilt angle of the collectors. TRNSYS has also been used to optimize the design parameters of TSWH system (Shariah and Shalabi, 1997). Kalogirou and Papamaracou (2000) compared the simulation results from TRNSYS with the experimental values for a TSWH system and found good agreement. Few studies, however, used TRNSYS to study the performance of forced circulation solar water heating systems. For instance, Buckles and Klein (1980) compared performance of different configurations of the forced circulation systems. Michaelides and Wilson (1996) optimized the design criteria of an active SWH system for the hotel application. Wongsuwan and Kumar (2005) studied the performance of forced circulation system experimentally and numerically. The numerical simulations were conduced

Tmain Tset Tin Tout UL Utop Vc W w

Monthly average inlet water temperature, oC Set temperature, °C Collector inlet fluid temperature, °C Collector outlet fluid temperature, °C Collector overall heat loss coefficient, W/m2 oC Collector top heat loss coefficient, W/m2 oC Tank volume, m3 Tube spacing, m Collector width (nW), m

Greek symbols a Solar absorptance u Latitude angle, (°) b Tilt angle, (°) q Density of the fluid, kg/m3 s Solar transmittance e Solar emittance g Collector efficiency Heat exchanger effectiveness eHX Absorber plate thickness, m dp

using TRNSYS and artificial neural network. The results from both numerical models were found to be in good agreement with the experimental values. However majority of the studies, that used TRNSYS for their investigations, were focused on the TSWH systems, which are suitable for warm regions where the winters are mild and therefore liquid freezing is not an issue and the thermal losses from the system is small. In cold regions where the outdoor temperature typically remains below freezing for 4–6 months, thermosyphon system is not an appropriate choice. Although the use of secondary flow loops (such as antifreezes solutions and phase change fluids) with low freezing point is an option for TSWH systems; however, forced circulation systems with a secondary flow that uses an antifreeze fluid would be a suitable configuration for the SWH systems in the cold climates. In addition, the flat-plate collectors are cost effective, easy to fabricate and install, more architecturally adaptive, and requires less operating and maintenance cost that the other kinds of the solar collectors (i.e. evacuatedtube and concentrating). Forced circulation SWH systems have been studied and used over the past decade, but fewer studies (compared to those for TSWH) are reported in the literature on the ‘optimization of various system design parameters’ particularly for the cold regions and small applications. For instance, Furbo et al. (2005) recommended design of large SWH as low flow systems with hot water tanks with external heat exchangers and stratification inlet pipes; Nayak and Amer (2000) evaluated nine dynamic test procedures for evaluation of the flat-plate col-

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lectors; Tsilingiris (1996) developed a simple simulation model for large SWH systems; Kikas (1995) studied laminar flow distribution of reverse and direct return circuits in solar collectors; Prapas et al. (1995) studied the thermal behavior of large central SWH; Fanney and Klein (1988) investigated the influence of flow rate and also incorporation of an auxiliary heat exchanger on the performance; Chiou (1982) developed a numerical method to determine the variation of the performance due to non-uniform flow distribution; and Klein and Beckman (1979) presented a general design method for closed-loop SWH systems. The present work is focused on using TRNSYS to analyze a forced circulation solar water heating system for a singlefamily residential unit in Montreal, Canada. A comprehensive study has been conducted to study all design parameters of the system and to determine their optimum values. The monthly and annual solar fractions of the entire system are used as the optimization parameters.

and reported 224 l/day of consumption. Kempton (1987) studied eight single-family dwelling units and found that the hot water usage varies from 44.3 to 126 l/day per person. Based on these studies and by considering additional 10% for the wasted hot water, an averaged hot water consumption of 246 l/day for the dwelling unit is considered in the present study. 2.2. Inlet cold water temperature Monthly average inlet water temperature (Tmain) is a function of outdoor ambient air and main supply water intake temperatures. NAHB (2002) has compiled average monthly inlet water temperature over a year for several North American cities. For Montreal, Tmain varies from 4–5 °C in winter to 11–12 °C in summer. Marcoux and Dumas (2004) measured the actual cold water inlet temperature for Montreal for several days of each month from 1994 to 2004. Because of a significant difference between the values from these two studies, the actual measurements of Marcoux and Dumas (2004) are considered to be more realistic and thus, used in the present study. Their monthly averaged values are given in Table 1.

2. Water heating load In solar heating system design, it is necessary to estimate the long-term (annual and/or monthly) average heating loads. The water heating load or the amount of energy required to warm water from the inlet cold water to a desired temperature, is dependent on several factors such as hot water consumption rate, cold water inlet and desired hot water set temperatures, location and orientation of the building, and system characteristic. This load also includes any heat loss from the storage tank, piping system, the amount of energy that is required to reheat the water that was already heated but not used, and the wasted hot water from sink, shower, dishwasher and laundry machine which is drained without being used. In the present study, these parameters are determined as below.

2.3. Hot water load profile The hourly distribution of hot water consumption in a day can be affected by several factors. It can vary from day to day, from season to season and from family to family. Different cyclic load profiles such as Rand, constant, early morning, early afternoon, late morning, or late afternoon have been considered and studied in the literature. For this study, hot water consumption of 246 l/day is distributed during a day according to the Rand profile (Mutch, 1974) as shown in Fig. 1.

2.1. Household hot water consumption 30 Hot water Consumption (l/h)

The hot water consumption depends on the lifestyle of people, season of the year, time of the day, and geographical parameters. Several studies have estimated the hot water consumption for a single-family dwelling in North America. Babbitt (1960) suggested 227–378.5 l/day for one bath and 378.5–757 l/day for two-bath houses. Becker and Stogsdill (1990) indicated average household consumption of 236 l/day; Gilbert et al. (1985) estimated 250.6 l/day with maximum hourly use of 15.5–33.7 l based on a study of 110 single-family dwellings; and Perlman and Mills (1985) studied 59 homes in Canada and found an average value of 236 l/day, varying from 171 l/day in July to 249 l/day in January. Hiller (1998) monitored 14 homes

25 20 15 10 5 0

0

2

4

6

8

10

12

14

16

18

20

22

24

Time of the Day (h)

Fig. 1. Daily hot water consumption profile (246 l/day).

Table 1 Monthly averaged main cold water temperature in Montreal in (°C) – (Marcoux and Dumas, 2004). Month

January

February

March

April

May

June

July

August

September

October

November

December

Temperature (°C)

3.3

2.9

2.9

5.5

11.2

15.8

20.8

22.3

20.1

15.4

10.4

5.6

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 Flat-plate collector with different areas: To optimize the system, characteristic factors from the standard test data (Fanney and Klein, 1983) have been selected with FR(sa)n = 0.84 and FRUL = 4.67 W/m2 °C. To optimize the collector, a theoretical collector is modeled, and the collector’s monthly and annual efficiencies as well as collector’s characteristic factors are determined and studied over a wide range of design parameters. The collector is considered to be facing south with the tilt (b) equal to Montre´al’s latitude (i.e. u = 45.5°).  Heat Exchanger: Studying different options, a constant effectiveness counter flow heat exchanger is selected.  Fully stratified storage tank (6 nodes): Different tank heights and tank volume–to–collector area ratios are considered. Overall tank heat loss coefficient is assumed to be between 2.5 and 3 kJ/h m2 K.  Forcing function: To apply actual monthly averaged main cold water temperatures and hourly load profile corresponding to 246 l/day of demand, forcing functions from TRNSYS library are used. Cold water temperature is considered to vary every month according to the actual data that are given in Table 1.  Auxiliary electric heater: An auxiliary electric heater connected in series with the storage tank is considered. The electric heater is located before the tempering valve mixing point. Both the tempering valve and auxiliary heater are set to the desired hot water temperature, Tset = 60 °C.  Flow circulation pumps: One pump is considered to circulate flow between heat exchanger and collector, and the other one between heat exchanger and storage tank.

3. System model An indirect forced circulation system with secondary flow loop (i.e. antifreeze fluid) and an external heat exchanger is modeled in this study. The secondary flow, which absorbs and transports the solar energy, is circulating between hot side of a heat exchanger and a collector. The flow is assumed to be a solution of glycol in water with different percentages (in volume) to avoid water from freezing. The secondary fluid exchanges the collected thermal energy to potable water that is circulating between the cold side of the heat exchanger and hot water storage tank. The produced hot water from the tank then passes through an auxiliary electrical heater that warms the water when the produced water is cooler than the desired set temperature or during the overcast days. Contrarily, when the produced water is warmer than the set temperature, a 3-way tempering valve will add cold water to adjust the temperature. An optional in-tank heater was also considered in the original study, but the results are not presented in this paper. Present study is focused on two different sets of simulations for the indirect system. The first set of simulations is conducted to optimize the whole system parameters for a given collector characteristic factors. This is followed by the second set of simulations, which is conducted to optimize the collector parameters to achieve the optimum values of the collector efficiency and characteristic factors. The simulations are conducted using TRNSYS simulation program. The main components of the system are described below and schematically shown in Fig. 2.

Temperature Semsor FLAT-PLATE COLLECTOR (tilted)

703

Hot fluid to the heat exchanger

Pipe length with insulation MAIN COLD WATER INLET

Pipe length with insulation

3-WAY TEMPERING VALVE

on

Cold fluid to the solar collector

off

CONTROLLER

FINAL HOT WATER OUTLET optional in-tank auxiliary heater

EXPANSION TANK Temp. Semsor PUMP-2

COUNTER FLOW HEAT CIRCULATION EXCHANGER PUMP-1

MAIN STORAGE TANK

AUXILIARY HEATER

Fig. 2. Schematic of the indirect forced circulation system model.

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An on/off differential controller that generates the on/off signals operates these pumps. For the controller, lower input temperature is the tank cold side (from tank to heat exchanger), the monitoring temperature is the tank hot side (from tank to load) outlet temperature, and the upper limit is the collector hot water outlet temperature. Upper and Lower dead bands are set to be 10 °C and 5 °C, respectively. The flow rate in the cold side of the heat exchanger is affected by daily hot water consumption pattern. The flow rate in the hot side can vary and it is subjected to the collector’s ‘‘suggested” optimum flow rate per square meter of the collector area.  Connecting pipes (supply and return) between the collector and hot side of the heat exchanger: Different pipe lengths and pipe internal diameters are considered for the first set of simulations. The overall heat loss coefficient is considered to be 3 kJ/h m2 K for both sets of simulations. Connecting pipes between the heat exchanger and storage tank are assumed to be short with negligible losses.  Weather and Meteorological data: It is taken from the Typical Meteorological Year (TMY) data bank of TRNSYS for Montreal. Monthly or annual solar fraction, which is the fraction of the total hot water energy that is supplied by solar system, is calculated using the equation from Buckles and Klein (1980), f ¼ ðQLoad  QAuxiliary Þ=QLoad

ð1Þ

where, QLoad is the total energy removed from the system to support the water heating requirements and QAuxiliary is the total auxiliary energy supplied to the system to support the portion of the total load that is not provide by the solar energy. The solar fraction is a better indicator of the system performance compared to the other parameters such as collector efficiency or heat removal factor, since it manifests the overall performance of the entire system not a component. Monthly or annual collector efficiency, which is the ratio of the useful energy gain to the absorbed solar energy by the collector, is computed using equations from Duffie and Beckman (1991),

ð2Þ

FR or collector heat removal factor, which relates the actual useful energy gain to the useful energy gain if the entire plate was at the inlet fluid temperature was calculated using the equation from Duffie and Beckman (1991), _ p ½1  expðAc U L F 0 =mC _ p Þ=ðAc U L Þ F R ¼ mC

Design parameters

Values

Ac Cp (glycol-water) Vc/Ac Tmain Tset eHX m=A _ c Din/out Lin-out (2L) Uin-out Ht Utank FR(sa)n FRUL u q

8, 6, 4, 3 m2 3.2–4.0 kJ/kg °C 20–300 l/m2 2.9–22.3 °C 60 °C 0.3–1 5–60 kg/h m2 19.94, 25.4, 38.3, 50.5 mm 4–32 m 3 kJ/h m2 K 0.4–2.4 m 2.5–3 kJ/h m2 K 0.84 6.8 kJ/h m2 K 45.5° 1000 kg/m3

Table 3 Range of design parameters for the second sets of the simulations. Design parameters

Range of parameters

dp hf,i Dr,i Dr,o n k (copper) k (aluminum) k (steel) tinsulation kinsulation (Rock Wool) Ub Uside CB ap (selective surface) ep (selective surface) ep (non-selective surface) Glass thickness sg (low iron glass) eg (sa)n V (wind)

0.1–1.5 mm 100–4000 W/m2 K 0.008–0.0254 m 0.00953–0.0289 m 4–24 393 W/m K 221 W/m K 45.3 W/m K 5 cm 0.04 W/m K 0.9 W/m2 K 0.12 W/m2 K 20 h m2 K/kJ 0.97 0.1 0.95 4 mm 0.91 0.88 0.88 4.2 m/s

4. Simulation results and discussion

_ p ðT out  T in Þ=ðAc I T Þ g ¼ Qu =ðAc I T Þ ¼ mC ¼ F R ðsaÞn  F R U L ðT in  T ambient Þ

Table 2 Range of design parameters for the first set of simulations.

ð3Þ

where, IT, UL and F0 are computed from the simulation output using equations from Duffie and Beckman (1991). The other selected design parameters and their ranges are given in Tables 2 and 3 for first and second sets of simulations, respectively.

4.1. Optimization of system parameters 4.1.1. Required collector area The model is studied for four different collector areas (Ac) that are 8, 6, 4, and 3 m2; to estimate the monthly and annual solar fractions and to determine the adequate collector area. The initial value of the hot water tank volume-to-collector area ratio (Vc/Ac) is set equal to 75 l/ m2, which is the base value for the f-chart method (Klein et al., 1976). The collector mass flow rate-to-collector area _ c ) is also initially set equal to 40 kg/h m2, which ratio (m=A is within the recommended range in the literature (e.g. Beckman et al., 1977 or Baughn and Young, 1984).

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A 40% mixture of propylene glycol in water (Cp = 3.8 kJ/ kg °C at 50 °C) is initially considered as the collector fluid. The result of monthly solar fraction (f) for each collector area is depicted in Fig. 3. The results show that for an indirect system with glycol solution, an 8 m2 collector is able to supply 90–99% of the hot water demand from May to September. Results also indicate that for 6 and 4 m2 collectors, f is around 80–93% and 63–76%, respectively, during May to September. The 6-m2 collector is, thus, able to supply around 30–60% of hot water demand during cold months. Comparison of monthly f for different collector areas shows that replacing an 8 m2 with a 6 m2 collector deteriorates the solar fractions by only 6.6–12.6% between May– Sept and by 18.6–26% between October–February, whereas replacing an 8 m2 collector with a 4 m2 one reduces the solar fractions by 31.2–42.7% between May–September and by 59–80% between October and February. Moreover, considering the cost, space requirements, and reliability issues of large collectors (i.e. 8 m2) that suppose to supply 90–99% of the required hot water, a collector with 6 m2 of area that provides 80–93% of the demand in summer can be considered as the adequate size for the present application in Montreal. The results (not shown here) also indicate that the reduction of the monthly solar fraction, for a 6 m2 collector, due to incorporation of heat exchanger and secondary flow indirect system, is only about 5–15% compared to the direct system. This degradation of solar fraction decreases as collector area reduces. 4.1.2. Effect of glycol percentage in solution A glycol-water solution is used as the collector fluid to avoid freezing problems. The specific heat of glycol-water solution varies with temperature and volumetric percentage of glycol in water. Within the operating temperature range of the flat-plate collectors (i.e. 5–110 °C) the specific heat of 20%, 30%, 40%, and 50% ethylene-glycol in water vary from 3780–4022, 3603–3901, 3418–3628, and 3223– 3628 J/k K, respectively. These values for the same percentages of propylene glycol in water vary from 3940–4169, 3807–4109, 3652–3999, and 3474–3879 J/kg K, respectively

705

(ASHRAE, 2005, Chapter 21). The solution densities for both ethylene and propylene glycol at the mentioned temperature range, varies from about 963 to 1079 kg/m3. To study the effect of glycol percentage (i.e., the effect of specific heat variation) on the monthly f and g, the simulations were conducted for different values of Cp varied from 3.2 to 4.0 kJ/kg K for a 6 m2 collector with Vc/Ac = 75 l/m2, and _ c ¼ 40 kg=h:m2 . The solution density is considered to m=A have an average value of 1000 kg/m3 in the concerned range. The variation of the monthly f is depicted in Fig. 4. The results show that the effect of Cp on the monthly and thus annual f is almost insignificant. The simulation results (not shown here) also indicate that Cp also has no significant impact on the collector efficiency (g). Therefore, selecting the percentage or type of glycol solution could be based on the mixture’s freezing point, cost, and corrosion parameters. Considering daily minimum temperature of 17 °C for Montreal, a 40–50% solution of propylene glycol, which is also less toxic than ethylene-glycol would be appropriate for the winter. The results also indicate that the degradation of f values in the indirect system, compared to the direct system, is mainly due to inclusion of the heat exchanger not due to the addition of glycol into the water. 4.1.3. Effect of the collector mass flow rate _ on the annual The effect of collector’s mass flow rate (m) _ c ranging from and monthly f and g was simulated for m=A 5 to 60 kg/h m2. Ac and Vc/Ac were kept constant at 6 m2 and 75 l/m2, respectively. Cp was set equal to 3.8 kJ/ kg °C. The variation of the annual solar fraction with _ c is plotted in Fig. 5. The plot shows that f increases m=A _ c increases from 5 to 20 kg/h m2. It increased rapidly as m=A from 0.49 at 5 kg/h m2 to a maximum value of approximately 0.67 in the range 20–30 kg/h m2. Then f starts to _ c and become decrease with a further increase in m=A _ c ¼ 60 kg=h:m2 . The results approximately 0.62 at m=A from simulations (not shown here) indicate similar trend for g. It was also observed that the maximum values of 1.0 0.9

1.0

0.8 Solar Fraction

Solar Fraction

0.8 0.6 0.4

0.7 0.6 0.5 0.4 0.3

0.2

0.2 Jan Feb Mar Apr May Jun

0.0 Jan Feb Mar Apr May Jun

Jul Aug Sep Oct Nov Dec

Fig. 3. Variation of the monthly solar fraction for different collector areas; 8 m2 (), 6 m2 (j), 4 m2 (N), 3 m2 (d).

Jul Aug Sep Oct Nov Dec

Fig. 4. Variation of the monthly solar fraction for different specific heats (Cp) in kJ/kg °C; Cp = 4 (j), Cp = 3.8 (4), Cp = 3.7 (*), Cp = 3.5 (s), Cp = 3.2 (e).

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Annual Solar Fraction

0.65 0.60

0.55 0.50 0.45 5

10

20

30 40 • 2 m/Ac (kg/hr.m )

50

60

Fig. 5. Variation of the annual solar fractions versus the collector flow rate-to-area ratio (m_/Ac).

the monthly f (i.e. 0.93–0.95) occur in July, which are about 42% greater than annual fraction and the minimum values (i.e. 0.22–0.3) occur in November, which are 54–58% less than the annual fraction. The results indicate that the operation of the system at the optimal m_ increases the collector’s useful solar energy gain (Qu) that in turn improves f _ c and g. The results also indicates that as long as the m=A ratio is around 20–40 kg/h m2, the flow rate can be kept constant throughout the year and the monthly variation of flow rate has no significant effect on the overall solar fraction and collector efficiency. The highest and the lowest monthly g are found to be 41% (in October and April) and 36% (in November and December). The optimum values are found to be in good agreement with the previous results for the TSWH systems, e.g. 50 kg/h m2 (Beckman et al., 1977) and 18–48 kg/h m2 (Baughn and Young, 1984). 4.1.4. Effect of the tank volume The effect of tank volume on the system performance is studied for various tank volume–to–collector area ratios (Vc/Ac) for a 6 m2 collector with 30 kg/h m2 flow rate. The results showing the impact of the variation of Vc/Ac on the annual f is presented in Fig. 6. The results show that

the annual f increases rapidly as Vc/Ac increases from 20 to 40 l/m2. For Vc/Ac values between 40 and 100, the increase in solar fraction is gradual. For Vc/Ac > 100 l/m2, the annual f starts to descend, which is likely due to an increase in heat losses form the storage tank, as the tank become larger. It is observed that with the increase of tank volume, the rate of the removed energy from the tank to supply the load increases, and the required auxiliary energy decreases. The recommended values are determined to be around 55– 65 l/m2 for this study, which is in the moderate range and the annual f for this range is about 2% less than the maximum annual f observed around 100 l/m2. For each Vc/ Ac, it was found that the maximum values of the monthly f (i.e. 0.84–0.94) occurring in July, which are about 43–46% greater than annual fraction, and the minimum values (i.e. 0.24–0.3) occurring in November, which are 56–58% less than annual fraction. For a tank within the recommended range, i.e. with Vc/Ac = 55–65 l/m2, the highest and the lowest monthly f is found to be 0.95 in July and 0.3 in November, respectively. The recommended range for Vc/ Ac is found to be in agreement with the other types of solar water heating systems, for instance, 60 l/m2 for the thermosyphon system (Shariah and Lo¨f, 1996), and 50–75 l/ m2 for the active system (Duffie and Beckman, 1991).

4.1.5. Effect of the tank height The effect of tank height (Ht) on the system performance _ c ¼ 30 kg=h:m2 is studied for a 6 m2 collector with m=A 2 and Vc/Ac = 65 l/m over a range of Ht from 0.4 to 2.4 (m). Fig. 7 presents the variation of the annual f with Ht. The results show that the annual f increases with Ht from 0.4 to 1.2 m, remains almost constant for Ht between 1.2 and 1.8 m, and slightly increases with a further increase in Ht. The results suggest that any tank with Ht in the range of 1.2–1.8 m is desirable. The preferred value of 1.2 m is comparable to the previous studies such as Shariah and Shalabi (1997) and Shariah and Lo¨f (1996) who suggested the tank height of 1 m for the thermosyphon systems. It was also observed that for any Ht, the maximum values

0.70

0.68

Annual Solar Fraction

Annual Solar Fraction

0.68 0.65 0.63 0.60 0.58

0.66

0.64

0.62

0.55 20 30 40 45 50 55 60 65 70 75 80 100 200 300 2

Vc/Ac (lit/m )

Fig. 6. Variation of the annual solar fraction versus the tank volume–to– collector area ratio (Vc/Ac).

0.60 0.4

0.6

0.8

1.0 1.2 Ht (m)

1.6

1.8

2.4

Fig. 7. Variation of the annual solar fraction versus the tank height (Ht).

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of the monthly f (i.e. 0.9–0.96) occur in July, which are about 42–44% greater than the annual fraction, and the minimum values of the monthly f (i.e. 0.28–0.3) occur in November, which are 56–58% less than the annual fraction. The monthly and annual g (not shown here) are found to be between 0.36 and 0.41 for the studied range. 4.1.6. Effect of the heat exchanger effectiveness The variation of monthly and annual f is studied for different heat exchanger effectiveness (eHX) varying from 0.3 to 1.0. The simulation first conducted for both parallel and counter flow heat exchangers. It was concluded that a counter flow heat exchanger presents better solar fractions. Fig. 8 shows the impact of the effectiveness of a counter flow heat exchanger on the annual solar fraction. The results show that the f increases with eHX up to effectiveness values around 0.7–0.8. A further increase in eHX resulted in a slight decrease in f. As eHX increases up to 0.8, f increases as a result of the increase in the useful energy gain from the collector, the energy rate from the tank to the load, and the energy rate from the heat exchanger to the tank, but also as a result of decrease in the required auxiliary energy. Contrarily, as eHX increases further from 0.8 the useful energy gain from the collector, energy rate from the tank to the load, and energy rate from heat exchanger to the tank decreases, and required auxiliary energy increases. This causes reduction of f. It was also found that the maximum values of the monthly f (i.e. 0.87– 0.95) occur in July, which are about 42–46% greater than annual fraction, and the minimum values of the monthly f (i.e. 0.27–0.3) occur in November, which are 55% less than the annual ones. A counter flow heat exchanger with eHX around 0.7 (most of the commercial heat exchangers) would be suitable for this application. 4.1.7. Effect of supply and return pipes The effect of the total length (2L) and inside diameter (ID) of the supply and return pipes between the collector and heat exchanger is studied for different pipe lengths

707

(sum of the supply and return pipes is 2L), varying from 6 to 32 m, and for four different pipe inside diameters: 19.94, 25.4, 38.3, and 50.05 mm. Variation of the annual f with the 2L and ID is depicted in Fig. 9. The plot shows that for a given ID the annual f decreases as the pipe length increases. This is, mainly due to an increase in the heat losses as the pipe length increases. However, the higher heat losses from the inlet pipe to the collector, reduces the inlet temperature to the collector resulting in an improvement of the efficiency. It is also seen that due to larger heat losses, f decrease as the pipe diameter increases, whereas g increase as the diameter increases because of smaller pressure drop and lower inlet temperatures. The plot also shows that the change in f with pipe length is larger for pipes with large ID and the change in f with pipe diameter increases with the pipe length. For example, when the total length is 6 m, the change in f with pipe diameter is almost negligible and for 32 m, the solar fraction decreased by about 10% as ID increased from 19.95 to 50.5 mm. The results indicate that a pipe with 19.94 or 25.4 mm ID and total length less than 10 (m) would perform better. It was also observed that for the studied pipe diameters and pipe lengths, the maximum values of the monthly f (i.e. 0.89– 0.96) occur in July, which are 43% greater than the annual fraction, and the minimum values (i.e. 0.26–0.3) occur in November that are 55–57% less than the annual fraction. Shariah and Shalabi (1997) proposed the pipe inside diameter greater than or equal to 12 mm for the thermosyphon system, which is similar to the suggested values in the present study for the forced system. 4.2. Optimization of the collector’s parameter The second sets of simulations are conducted to study the effect of collector design parameters on the monthly and annual f, g, F0 , UL and FR. The theoretical relation between f, g, F0 , UL, FR and collector’s design parameters is presented in Duffie and Beckman (1991). A theoretical flat-plate collector is modeled for the same forced circula-

0.68

0.68 Annual Solar Fraction

Annual Solar Fraction

0.67 0.66

0.63

0.61

0.66 0.65 0.64 0.63 0.62 0.61 0.60

0.58

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

εHX

Fig. 8. Variation of the annual solar fractions versus the heat exchanger effectiveness (eHX).

6

16

24

32

Total Length, 2L (m) Fig. 9. Variation of the annual solar fractions versus the total length of the connecting pipes (2L) for different pipe diameters; ID = 19.94 mm (d), ID = 25.4 mm (j), ID = 38.3 mm (N), ID = 50.5 mm ().

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tion (indirect) system. It is assumed that the absorber plate is coated with a selective coating (e.g. Black-Chrome or Black-Copper), glazing is a single plate low iron glass, and both back and sides of the collector are insulated with Rock Wool insulation with density of 24 kg/m3. Moreover, the wind velocity is considered to be 15 km/h, which is the recorded maximum wind velocity in Montre´al. In this section, the system parameters that were optimized in the previous section are used as constants i.e., Ac = 6 m2, m_ ¼ 180 kg=h, Vc = 390 l, Ht = 1.2 m, Cp = 3.8 kJ/ kg °C, 2L = 6 m. Likewise, Tset is 60 °C, daily consumption rate is 246 l/day, and Tmain values are taken from Table 1. The other design parameter and their ranges are presented in Table 3.

observed that the minimum monthly values of f occur in November (i.e. 0.3, 0.29, and 0.26, for Cu, Al, and St, respectively), which is 56% smaller than their annual values. Maximum values of f occur in July (i.e. 0.96, 0.95, and 0.89, for Cu, Al, and St, respectively), which is 44% greater than their annual values. Monthly values of g are found to be around 0.35–0.39. Shariah et al. (1999) reported 4–7% and 12–19% improvement of annual f and the characteristic factors, respectively, when they changed the absorber plate material from steel to aluminum. They also suggested using aluminum instead of copper as the absorber plate material. These are consistent with our results.

4.2.1. Effect of the absorber plate material Variation of f and g are studied for three different absorber plate materials: Copper, Aluminum, and Steel with 1 mm thickness. The 6 m2 collector is 2  3 m. The internal diameter of the collector tubes (Dr,i) and the number of riser tubes (n) are set equal to 24.5 mm and 10, respectively. The values of the annual f, g, F0 , and FR for these three plate materials are presented in Fig. 10. From the results it can be seen that f , g, FR, and F0 decrease with a decrease in thermal conductivity (k). It was also observed that the variation of the characteristic factors is significant for the smaller values of the thermal conductivity but it becomes insignificant as k increases. For instance, by changing the plate material from copper to aluminum, f , g, F0 , and FR, are reduced, respectively, by only 1.5%, 1.2%, 1.2%, and 1.2%. By changing the copper plate to steel, f , g, F’, and FR are reduced by 9%, 10.6%, 10.3% and 10%, respectively. The above results indicate that the fabrication of commercial collectors with copper absorber plate, which is heavier and more expensive, is not necessary and an aluminum absorber plate can perform similar to that of copper. The overall heat loss coefficient (UL), for the studied materials, is found to be in range of 12.80–12.87 kJ/h m2 K, which indicates that k has small effect on the UL. It was also

4.2.2. Effect of the absorber plate thickness The effect of the absorber plate thickness (dp) on the system performance is studied over a range of dp varying from 0.1 to 1.5 mm. The collector is a 2  3 m aluminum plate. Initially, Dr,i is set to 24.5 mm, and the number of the riser tubes (n) is to 10. The variations of the annual f as well as the collector characteristic factors with dp are presented in Fig. 11. The results show that f and the collector characteristics factors are improved by increasing the plate thickness. The plots show that the improvement of these factors is significant as dp increases from 0.1 to 0.4 mm. However, when dp > 0.4, the influence of dp on these parameters is weak. Results show that the f , g, F0 , and FR increased by 15.7%, 17.3%, 16% and 15.3%, respectively, as dp increased from 0.1 to 0.5 mm. Whereas, when dp increased from 0.5 to 1 mm, f , g, F0 , and FR increased by 2.3%, 2.6%, 2.6%, and 2.5%, respectively. It was also observed that the influence of dp, for the studied range, is small on the UL. As dp increased from 0.1 to 1.5 mm, UL decreased from 12.92 to 12.80 kJ/h m2 K. It was found that the minimum monthly values of f (i.e. 0.23–0.29), and g (i.e. 0.31–0.35) occur in November, which are 56% and 9.5% smaller than their annual values, respectively. The maximum values of f (i.e. 0.89–0.96) occur in July, which are 46% greater than their 0.9

0.9

0.8 ƒ, η, F' and FR

ƒ,η, F' and FR

0.8 0.7 0.6 0.5

0.7 0.6 0.5 0.4

0.4

0.3

0.3 45.3 (Steel)

221 (Aluminum)

393 (Copper)

k (W/mK)

Fig. 10. Variation of the annual solar fraction, f (d), collector efficiency, g (), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the thermal conductivity of the plate (k).

0.2

0.1

0.2

0.4

0.5 0.8 δ p (mm)

1.0

1.2

1.5

Fig. 11. Variation of the annual solar fraction, f (d), collector efficiency, g (), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the absorber plate thickness (dp).

A. Hobbi, K. Siddiqui / Solar Energy 83 (2009) 700–714

respective annual values. The maximum values of g are about 0.35–0.39. The difference between the maximum and minimum values of the remaining studied parameters with their respective annual values was negligible. It is concluded that the plate thickness in the range of 0.6 to 0.8 mm is sufficient for the residential applications and thicker plates seems to be not economical. The thickness of 0.8 mm is selected for the subsequent parametric analysis. 4.2.3. Effect of the riser tube diameter For the same 6 m2 collector with aluminum absorber plate of 0.8 mm thickness, the effect of riser tube diameter (Dr,i) is studied over a variety of available commercial copper tube sizes, which are 8, 8.64, 13.84, 16.92, 19.94, and 25.4 mm. The number of riser tubes is assumed to be 10. The effect of Dr,i on the annual f , g, F0 , and FR is shown in Fig. 12. The results show that f , g, F0 , and FR improve as Dr,i increases; however, this increment is about 5% between an 8 mm and a 25.4 mm diameter tube, and it is less than 2.5% between a 13.84 and 25.4 mm diameter tubes. It can be concluded that Dr,i in this range has no significant influence on the solar fraction and other collector characteristic factors. Therefore, considering scaling problems inside the tubes, cost, fabrication difficulties, and capacity to carry the maximum flow rate, tubes with 13.84 mm to 19.94 mm inside diameters would be more feasible. This optimum diameter range is in agreement with the values reported in Shariah and Shalabi (1997) for TSWH. Results (not shown here) indicate that for Dr,i less than 8 mm, f is very small yet the pressure drop is high; thus, they are not recommended. It was also found that the impact of Dr,i is negligible on UL. As Dr,i increases from 8 to 25.4 mm, UL decreases from 12.84 to 12.81 kJ/h m2 K. It was also observed that the minimum monthly values of f (i.e. 0.28–0.29) occur in November, which is about 56% smaller than their annual values. The maximum values of f (i.e. 0.92–0.95) occur in July that is about 45% greater

709

than their annual values. The difference between the maximum and minimum values of the remaining studied parameters with their respective annual values was small. Monthly values of g varied from 0.33 to 0.39. 4.2.4. Effect of the number of riser tubes The number of riser tubes (n) is one of the important parameters in design of a flat-plate collector. For a fixed collector width (w), an increase in n reduces the distance between the riser tubes and vise versa since w = n  W. To study the effect of n, the 6 m2 collector (l = 3 m, w = 2 m) with aluminum absorber plate (dp=0.8 mm) is considered. The tubes are considered to be of diameter Dr,i = 13.84 mm. The number of risers varied from n = 4 to n = 24 and the corresponding tube distance varied from W = 50 cm to W = 8.33 cm. The variation of the annual f , g, F’ and FR with n is presented in Fig. 13. The results show that the annual f , g, F0 , and FR increase with n. However, the percentage increase of these parameters is higher as n increases from 4 to 9. For n > 9, the percentage increase of these parameters becomes relatively small and after n = 14 becomes insignificant. For instance, the increase in the annual f and FR is about 43% and 34%, respectively, as n increased from 4 to 8; whereas, f and FR are increased by only 7.7% and 8.6%, respectively, as n increased from 9 to 16. It was found that the reduction of the overall heat loss coefficient by increasing the number of tubes is insignificant. As n increased from 4 to 24, the UL reduced from 13 to 12.74 kJ/h m2 K. It was also observed that the minimum monthly values of f (i.e. 0.17–0.33) occur in November, which is 54–60% smaller than the annual f, and the maximum values of f (i.e. 0.64–0.99) occur in July, which are about 48% greater than the annual fraction. The difference between the maximum and minimum values of the remaining studied parameters with their respective annual values was small. Shariah and Shalabi (1997) showed that f reaches to its maximum for n around 8 but stays almost the same as n increases.

0.9

1.0 0.9

0.8 ƒ, η, F' and FR

ƒ, η, F' and FR

0.8

0.7 0.6 0.5

0.7 0.6 0.5 0.4

0.4 0.3

0.3

8.00

8.64

13.84 16.92 D r,i (mm)

19.94

25.40

Fig. 12. Variation of the annual solar fraction, f (d), collector efficiency, g (*), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the riser tube diameter (Dr,i).

0.2 4

6

8

9

10

12 n

14

16

18

20

22

24

Fig. 13. Variation of the annual solar fraction, f (d), collector efficiency, g (*), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the number of riser tubes (n).

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4.2.5. Effect of the tube spacing and collector’s aspect ratio The dimensions of the collector can be confined by architectural geometry of the building, thus, affecting the aspect ratio (R) of the collector. For a constant Ac, a change in R can be attained by either changing the tube spacing (W) when the tube number (n) is fixed, or by altering n when W is maintained constant. Considering Ac = l  w = l  n  W, the aspect ratio can be defined as R = l/w = l/(nW) = Ac/(nW)2. The collector is of the same specification as in the previous section. In the first case, n is kept constant equal to 14 (a number within the optimum range) and R is varied from 0.2 to 5 by changing W from 39.1 to 7.8 cm, respectively. The results for this case are depicted in Fig. 14. The results show that for a constant n, the annual f , g, F0 , and FR increased with an increase in R (i.e. either increase of tube length or decrease of tube spacing). The percentage increase is large for aspect ratios less than 1, but for R > 1.2, the percentage increase becomes small. For instance, the annual solar fraction is increased by 34% as R increase from 0.2 to 1.2, whereas it increased by only 5.7% as R increased from 1.2 to 5. For the studied range of aspect ratios, UL is varied only between 12.8 and 13.1 kJ/h m2 K. It was also found that the minimum monthly values of f (i.e. 0.21–0.33) occur in November, which are 54–58% smaller than the annual fraction. The maximum values of f (i.e. 0.75–0.99) occur in July, which are about 40–48% greater than the annual values. The difference between the maximum and minimum values of the remaining studied parameters with their respective annual values was negligible. From the above results it can also be concluded that as long as R is between 1.25 and 2 (i.e. tube spacing is between 15.6 and 12 cm) the system has the lower heat loss and thus better performance. Similarly, Ghamari and Worth (1992) determined the optimum tube spacing to be around 13–16 cm, and Shariah and Shalabi (1997) suggested it to be around 8–15 cm. For the second case W is kept constant at 14.3 cm (within the determined optimum range) and the aspect ratio is diverged by changing n. Since smaller aspect ratios

(below 0.8) have insufficient performance and higher aspect ratios have lager UL, the simulation is conducted for the R values between 0.5 and 18. The results for the second case are depicted in Fig. 15. The results show that for a constant W, an increase in R has almost negligible effect on the annual f , g, F0 , and FR. Therefore, when n and W are within the optimum values and Ac is constant, a reduction in n will not affect the performance of the system, appreciably, as long as tube length increases. In other word, system performance and collector efficiency increases by either increasing l (i.e. increasing R) or by reducing n when Ac and W are kept constant. Increasing R in this case, increases the flow velocity inside tubes that, in turn, improves the heat transfer rate inside the tubes. Even though the collector flow rate is very small (0.0083 kg/ s m2) and results showed that the difference between the solar fraction for a collector with n = 4, l = 10.3 m (R = 18), and a collector with n = 14, l = 3 m (R = 1.5) is only 2%, a narrow and long collector with less tubes causes high pressure drops, high friction losses, and also higher heat losses from the surface area of the collector edges which, in practice, reduces the performance dramatically. For example increasing m_ from 30 to 50 kg/h m2 causes 5% reduction in the annual f and 3% reduction in g for R = 12 or 18. Considering results from Section 4.2.4, collectors with n less than 4 or R grater than 9 are not recommended. In other word, if R needs to be increased, W has to be reduced from the optimum value corresponding to R = 1.5. Selecting an adequate aspect ratio needs a balance between all of the parameters, and a reasonable pressure drop inside each tube as well as economical considerations. In this case, as R varied between 0.5 and 18, UL varied from 12.77 to 13.2 kJ/h m2 K. It was also observed that the minimum monthly values of f , and g occur in November, which are respectively 55% and 7.8% smaller than their annual values. The maximum values of f occur in July, which are about 42% greater than their respective annual values. The difference between the maximum and minimum values of the remaining studied parameters with their

1.0

1.0

0.9

0.9 0.8 ƒ, η, F' and FR

ƒ, η, F' and FR

0.8 0.7 0.6 0.5 0.4

0.6 0.5 0.4

0.3 0.2

0.7

0.2 0.5

0.8 1.0 1.2 1.5

1.8 2.0 2.5 3.0

4.0 5.0

R

Fig. 14. Variation of the annual solar fraction, f (d), collector efficiency, g (*), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the collector aspect ratio (R) when n is constant.

0.3

0.5

0.8

1

1.2

1.5

1.8 2.5 R

4

8

10

12

18

Fig. 15. Variation of the annual solar fraction, f (d), collector efficiency, g (*), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the collector aspect ratio (R) when W is constant.

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Table 4 Optimum values of the design parameters for the modeled indirect forced circulation system.

1.0 0.9 0.8 ƒ, η, F' and FR

711

0.7 0.6 0.5 0.4 0.3 0.2 0.1 50

100 300 500 800 1200 1500 2000 2500 3500 4500 h f.i (W/m²K)

Fig. 16. Variation of the annual solar fraction, f (d), collector efficiency, g (*), collector efficiency factor, F’ (j), and collector heat removal factor, FR (N) versus the heat transfer coefficient inside the tube (hf,i) when ep = 0.1 and (1/CB) = 0.05.

respective annual values was negligible. These results are in good agreement with theoretical studies of Yeh et al. (2003) stated that a proper increase of aspect ratio increases the collector efficiency. 4.2.6. Effect of heat transfer coefficient inside the tubes The effect of heat transfer coefficient inside the tubes (hf,i) was studied for the collector with 6 m2 area, 0.8 mm thick aluminum absorber plate, 13.84 mm ID riser tubes, 14.3 cm tube spacing and R = 1.5. The hf,i was varied from 100 and 300 W/m2 K for laminar flows and 1000–1500 W/ m2 K for turbulent flows (Duffie and Beckman, 1991). The plate is considered to have a selective coating with a good contact between the plate and the tubes (i.e. 1/ CB = 0.05 h.m2 K/kJ). The variation of the annual f, g, F0 , and FR are presented in Fig. 16. The results show that the annual f , g, F0 , and FR increased with an increase in hf,i. Plot also shows that the percentage increase is large for smaller value of hf,i i.e. when the flow is in laminar range. For hf,i above 1000 W/m2 K i.e. in the turbulent regime, the percentage increase becomes smaller. It was also found (not shown in here) that the overall heat loss coefficient decreased slightly as hf,i increased (i.e. from 13.05 to 12.78 kJ/h m2 K). 5. Optimized design The optimum values of the design parameters obtained in Sections 4.1 and 4.2 for a forced circulation solar water heating system in Montreal, are summarized in Table 4. To evaluate the performance of the optimized system, the simulations were conducted using the optimized parameters listed in Table 4. The monthly and annual values of f , g, F0 , FR, and UL for the optimized system are presented in Table 5. The results show that for a single-family dwelling in Montreal, the optimized system can fulfill 83–97% of the hot water demand during May to September and 30–68% of the demand between October and February. On the

Parameters

Value

Ac Cp dp k (aluminum) tinsulation 2L Dr,i eHX n W _ c m=A Vc/Ac Ht ap ep Glass thickness sg eg

6 m2 3.8 kJ/kg K 0.6–0.8 mm 221 W/m K 5 cm 6–16 m 13.8–19.9 mm 0.7 9–14 12–15.6 cm 30 kg/h m2 55–65 l/m2 1.2 m 0.97 0.1 4 mm 0.91 0.88

Table 5 Monthly and annual values of f , g, F’, FR and UL based on the optimum design parameters. f

g

F’

FR

UL

January February March April May June July August September October November December

0.42 0.62 0.75 0.72 0.83 0.91 0.97 0.85 0.90 0.68 0.30 0.34

0.39 0.39 0.41 0.41 0.41 0.40 0.39 0.38 0.39 0.41 0.36 0.37

0.89 0.88 0.88 0.88 0.88 0.87 0.87 0.88 0.88 0.88 0.89 0.89

0.85 0.84 0.84 0.84 0.83 0.83 0.83 0.83 0.84 0.84 0.85 0.85

12.01 12.54 12.89 12.99 13.37 13.60 13.63 13.34 13.04 12.46 11.75 11.78

Annual

0.68

0.40

0.88

0.84

12.78

annual basis, it can fulfill 68% of the hot water demand. The results also show that the best performance of the system is in July in which the monthly solar fraction is 0.97 and the worst performance is in November when the solar fraction is reduced to 0.30. The monthly values of g, F0 , and FR vary between 0.37–0.41, 0.87–0.89 and 0.83–0.85, respectively. For the present simulations the collector plate is considered to be coated with a selective coating (ep = 0.1), which minimizes the plate emittance and thus, improves the collector’s performance. However, the application of selective coating on the collector plate requires somehow costly and advanced techniques, such as electroplating, anodization, evaporation, and sputtering (Kalogirou, 2004), which may not be available in many regions. Therefore, to get a more conservative estimate of the performance of a system which incorporates a collector that can be simply fabricated and utilized, simulations were conducted with the non-selective coating such as high

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Table 6 Monthly and annual values of f , g, F’, FR and UL based on the optimum design parameters using a non-selective coating. f

g

F’

FR

UL

January February March April May June July August September October November December

0.31 0.47 0.59 0.57 0.67 0.74 0.79 0.69 0.73 0.53 0.23 0.25

0.29 0.29 0.31 0.32 0.32 0.31 0.31 0.29 0.31 0.31 0.28 0.26

0.84 0.84 0.83 0.83 0.82 0.82 0.81 0.82 0.82 0.83 0.84 0.84

0.79 0.78 0.77 0.77 0.76 0.75 0.75 0.75 0.76 0.77 0.78 0.79

19.76 20.55 21.50 22.19 23.30 23.96 24.35 23.86 23.13 21.84 20.31 19.69

Annual

0.54

0.30

0.83

0.77

22.04

temperature matt black paint (ep = 0.95) that can be easily applied on the plate, using the parameters in Table 4. The monthly and annual values of f , g, F0 , FR, and UL for this case are tabulated in Table 6. Comparison of results in Tables 5 and 6 shows that by replacing a selective coating with non-selective one, the annual values of f , g, F0 , and FR, are degraded by 21%, 23%, 6%, and 9%, respectively, whereas, UL increased by 72%. With non-selective coating, the system could meet 67–79% of hot water demand from May to September, and 23–47% of the hot water demand from November to February. This indicates that even a locally made flat-plate solar collector (without using any advanced manufacturing methods) can provide 54% of water heating energy requirement annually, provided that the design parameters are in the optimum range. 6. Conclusion

 An indirect forced circulation solar water heating system with flat-plate collector that provides hot water requirements of a single-family house in Montreal is modeled. Two sets of simulations were conducted. The first set was conducted to determine the optimum values of the system parameters and the second set was conducted to determine the optimum values of the collector design parameters. The annual solar fraction was considered as the optimization parameter. From the simulation results it was concluded that:  A 6 m2 collector, with superior values of FR (sa)n and FRUL, is appropriate for this application.  Degradation of the solar fractions from direct to indirect system is mainly due to the incorporation of the additional heat exchanger but less affected by replacement of water with glycol solution as the concentration of glycol solution has no significant influence on the system performance. The reduction of solar fractions is about 6–15.5%. Percentage of the glycol solution in water has small effect on the solar fractions.

 Both the solar fraction and the collector efficiency increases rapidly as the collector flow rate increases. After reaching the optimum value at a flow rate around 30 kg/h m2, the solar fraction and the collector efficiency decreases with a further increase in the flow rate.  The solar fraction increases with the tank volume up to 80 l/m2. Tanks larger than this size have higher heat loss from the tank to the surroundings that reduces the system performance. The optimum volume is found to be in the range of 55–65 l/m2.  The solar fraction increases with the tank height. The percentage increase is sharp when the tank changes from the horizontal tank to the vertical one. The percent increase of the solar fraction with the tank height is small for tank height greater than 1.2 m.  The solar fraction increases with an increase in the heat exchanger effectiveness up to values around 0.7–0.8. It decreases slightly with a further increase in the effectiveness. A counter flow heat exchanger with eHX around 0.7 is considered to be suitable for the proposed application.  The annual solar fraction decreases as the length and diameter of the pipes connecting the collector to the heat exchanger increases. Contrarily, the collector efficiency increases with an increase in pipe length and diameter. Pipe diameters of 25.4 or 38.3 mm with total pipe length (2L) less than 10 m are considered appropriate for the present application.  The annual f , g, F0 , and FR increase with an increase in the thermal conductivity of the absorber plate. Replacing absorber plate material from copper to steel has very significant effect on the collector and system performance but changing it from copper to aluminum has not significant effect.  The annual f , g, F0 , and FR increase with an increase in the absorber plate thickness. The percentage increase in the system performance is large as the thickness increases up to 0.6 mm. Further increase of the plate thickness slightly improves the system performance. Plate thickness around 0.8 mm is found to be adequate for this application.  The percentage increase in the annual f , g, F0 , and FR is small for the riser tubes diameters (Dr,i) greater than 8 mm. Considering less pumping requirements, fabrication troubles, erosion, and cost; the pipe diameter of 13.84 mm found to be appropriate for our application.  For a constant collector width, as the number of riser tubes increases, the annual f , g, F0 , and FR improves. Dependency of these factors on the tube number is strong when the tube number is small. When the tubes are more than 14, the influence of the tube number on the collector and the system performance becomes relatively weak.  For a constant tube number as the aspect ratio increases (either the tube length increases or the tube distance decreases) f , g, F0 , and FR increase continuously. The percentage increase of these parameters for aspect ratios less than 1 is large, and for aspect ratios greater than 1.2, is small. When the tube spacing is kept constant, altering

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aspect ratio will change the tube number and the tube length. However, if the tube diameter and spacing are within the obtained optimum values, reduction in the tube number, as the aspect ratio and tube length increases, has negligible effect on the system performance. Aspect ratios around 1.5 found to be suitable for our application.  Increase in the heat transfer coefficient has very significant effect on the system performance when the flow inside the tube is in the laminar regime. For a fully turbulent flow the percentage increase in the annual f , g, F0 , and FR is small with an increase in the heat transfer coefficient.  The optimized system can fulfill 83–97% of the hot water demand during May to September and 30–68% of the demand during October to February with an annual value of 68%.  Replacing selective coating with a non-selective coat (e.g. normal matt black paint) reduces the annual solar fraction and collector efficiency by 21% and 23%, respectively. However, they could still fulfill about 54% of the annual water heating energy requirements by solar energy in a cold climate like Montreal.

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