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Integrated collector-storage solar water heater with extended storage unit Rakesh Kumar*, Marc A. Rosen Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario, Canada L1H 7K4

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 August 2010 Accepted 22 September 2010 Available online 1 October 2010

The integrated collector-storage solar water heater (ICSSWH) is one of the simplest designs of solar water heater. In ICSSWH systems the conversion of solar energy into useful heat is often simple, efﬁcient and cost effective. To broaden the usefulness of ICSSWH systems, especially for overnight applications, numerous design modiﬁcations have been proposed and analyzed in the past. In the present investigation the storage tank of an ICSSWH is coupled with an extended storage section. The total volume of the modiﬁed ICSSWH has two sections. Section A is exposed to incoming solar radiation, while section B is insulated on all sides. An expression is developed for the natural convection ﬂow rate in section A. The inter-related energy balances are written for each section and solved to ascertain the impact of the extended storage unit on the water temperature and the water heater efﬁciency. The volumes of water in the two sections are optimized to achieve a maximum water temperature at a reasonably high efﬁciency. The inﬂuence is investigated of inclination angle of section A on the temperature of water heater and the angle is optimized. It is determined that a volume ratio of 7/3 between sections A and B yields the maximum water temperature and efﬁciency in the modiﬁed solar water heater. The performance of the modiﬁed water heater is also compared with a conventional ICSSWH system under similar conditions. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Solar water heater Collector-storage Modiﬁed storage tank Thermal performance System efﬁciency

1. Introduction The solar water heater is one of the fastest growing technologies in the renewable energy sector. Most solar water heater designs can be categorised into three groups: forced circulation, natural convection and integrated collector-storage. The integrated collector-storage solar water heater (ICSSWH) is relatively simple in design and operation. The costs of ICSSWH systems are also comparatively lower than those for other solar water heater designs [1]. In ICSSWH systems the collection of solar energy and the storage of hot water occur in a single unit. The ICSSWH system operates as an isolated system that involves no moving parts and allows the user to be independent of grid electricity. In addition, due to the large thermal mass associated with the absorber surface these water heaters have an inherent ability to avoid freezing in many conditions. ICSSWH systems require little maintenance, other than seasonal cleaning of the glazing surface, and have ability to provide hot water consistently and reliably for many years. However, ICSSWH systems are often not efﬁcient for overnight applications as their thermal output diminishes sharply as the time

* Corresponding author. Tel.: þ1 905 721 8668; fax: þ1 905 721 3370. E-mail addresses: [email protected] (R. Kumar), [email protected] (M.A. Rosen). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.09.021

increases between the availability of solar energy and its use [2]. The decline in performance can be attributed to the increased heat losses from the absorber surface to surrounding air [3e6]. In the past many strategies have been proposed and analyzed to make integrated collector-storage solar water heaters more viable alternatives. Some of the suggested strategies include incorporation of: night insulation cover [7,8], transparent insulation [9e11], bafﬂe plate [12,13], phase change materials [14,15], and multiple glazing layers [16]. Recently, Kumar and Rosen [17] reported that ICSSWH systems with single glazing and night insulation cover and with double glazing and no night insulation cover yield better thermal outputs than similar systems with a single glass cover, a bafﬂe plate and transparent insulation. Another signiﬁcant area of research to enhance the performance of the ICSSWH is aimed at developing an efﬁcient storage tank (vessel) design. Many storage tank conﬁgurations have been reported in the literature such as cylindrical, rectangular, triangular and trapezoidal. Systems with cylindrical storage tanks are being examined more thoroughly as they may be advantageous due to their ability to endure better the pressure of the main water supply. Other storage tank conﬁgurations are also being investigated. It was reported for a triangular ICSSWH design that the triangular crosssection helps increase the heat transfer rate from absorber surface to water [18,19], while it was found that a trapezoidal shape helps improve thermal stratiﬁcation in the water storage tank [20]. In

R. Kumar, M.A. Rosen / Applied Thermal Engineering 31 (2011) 348e354

another conﬁguration modiﬁcation, the storage tank is considered to have two parts; the part comprising the lower two-thirds is exposed to solar radiation, while the top one-third part is heavily insulated [21,22]. This design was observed to have better heat retention capability than a tank completely exposed to solar radiation. In another study, a storage tank is considered having a modiﬁed-cuboid shape with transparent insulation [23]; an enhanced heat transfer rate and improved stratiﬁcation in the storage tank were observed for this ICSSWH design. In the present investigation, a storage tank is considered consisting of two sections A and B, which share a common side. Section A is a conventional design of built-in-storage solar water heater, while section B is an additional storage unit connected with section A. Heat is transferred from section A to B or vice versa during water heater operation. Natural convection develops in section A due to the effect of buoyancy and is the driving force for inputting heat to section B. An expression is established for natural convection ﬂow rate in section A. Furthermore, to determine the variation in water temperature and efﬁciency, the inter-related energy balances are developed for various nodes of section A and B and solved using a ﬁnite difference technique. The volumes of water in the two sections are optimized to produce maximum heat output from the modiﬁed ICSSWH design. The performance of the proposed solar water heater is compared with a rectangular collector-storage solar water heater. 2. System designs The proposed integrated collector-storage solar water heater with an attached extended storage is shown in Fig. 1. The storage tank can be visualized as having two sections A and B, which share a common surface. Section A is exposed to incoming solar radiation and section B is insulated on all the sides. All surfaces of the storage tank for the proposed ICSSWH are made of 20 gauge galvanised iron sheet. The total volume of water in both sections and the area of the absorber surface are ﬁxed at 100 L and 1 m2, respectively. To suppress bottom and side heat losses, a thick layer of ﬁbreglass insulation is applied on all surfaces of section B as well as all sides and the bottom of section A. Most of the solar radiation striking the glazing of section A is transmitted to the absorber while part is reﬂected back. The absorber absorbs the transmitted solar radiation and transfers it to the water of section A. Due to the combined effect of a temperature gradient and gravity, a natural convection ﬂow develops in section A and causes heat transfer from section A to B. Heat is transferred from section A to B during the day and vice versa

349

Fig. 2. Cross-sectional view of rectangular integrated collector-storage solar water heater.

at night. An identical volume of water per unit collector area is used for comparative performance evaluations with a conventional design of a collector-storage solar water heater (see Fig. 2). 3. Analysis To determine the effect of design, operating and climatic parameters on the thermal performance of the modiﬁed integrated collector-storage solar water heater design in Fig. 1, energy balances are developed for sections A and B. Energy is transferred from section A to B or vice versa by natural convection. To ascertain the heat transfer rate between the two sections, an expression is developed for the natural convection ﬂow rate caused by the buoyancy force. The present development of the natural convection ﬂow rate in section A follows the procedure used by Bansal et al. [24] for estimating the natural convection ﬂow rate between two parallel plates separated by a ﬁxed distances. 3.1. Expression for natural convection ﬂow rate Section A is a conventional rectangular built-in-storage solar water heater design, and is considered identical to a two parallel plate water heater, separated by a ﬁxed distance W. The water heater is inclined an angle q from the horizontal. The following assumptions are made for the development of the natural convection ﬂow rate in section A: 1) The water temperature varies only in the direction of length L. 2) The change in water temperature from the lower side to the upper side is continuous and uniform.

Fig. 1. Cross-sectional view of modiﬁed integrated collector-storage solar water heater.

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3) The water temperature at the upper side of section A is equal to the water temperature at the lower side of section B. 4) All thermophysical properties of water (except density) are taken as constant within the operating range of the water heater. Referring to Fig. 1, the total pressure difference in sections A and B caused by buoyancy can be written as

Dpt ¼ DpA þ DpB

(1)

where DpA and DpB are the pressure differences in section A and B, respectively. The pressure difference in section A (DpA) is calculated as

DpA ¼ gsinq

ZL

fr1 rðyÞgdy

(2)

Here, g is gravitational acceleration, q is the inclination of section A from the horizontal, r1 is the density of water at the lower side, L is the total length of the section A and r(y) is the density of water at a distance y from lower side in the direction of L. The pressure difference in section B (DpB) is written as

DpB ¼ ðr2 r3 Þgh2

(3)

where r2 and r3 are the densities of water in the lower and upper sides in section B, and h2 is the height of section B. The variation in density of water with temperature can be written as [24]

rT ¼ r0 ð1 bTÞ

(4)

where r0 and rT are the densities of water at temperature 0 C and T (in C), respectively, and b is the volumetric expansion coefﬁcient of water. Furthermore, the total pressure drop due to friction in the sections A and B can be written as

Dps ¼ DpAc þ DpBs

Dps ¼ DpAc 1 þ rp

(5) (6)

where Dps is the total pressure drop in the water heater, DpA-c is the pressure drop in section A, DpB-s is the pressure drop in section B, and rp is the ratio of pressure drop in section B to that in section A. For the development of the natural convection ﬂow rate in section A, the total pressure difference (Dpt) caused by buoyancy should be greater than the total pressure drop (Dps). In stationary conditions, we have

Dpt ¼ DpAc 1 þ rp

ZL

L 2

where T1 and T2 are the water temperatures at the lower and upper sides of section A, and L is the length of section A. By combining Eqs. (8) and (9), we obtain

L gbr0 sinqðT2 T1 Þ þ g br0 h2 ðT3 T2 Þ ¼ DpAc 1 þ rp 2

0

(8) where T1 and T2 are the temperatures of water in the lower and upper sides of section A and T3 is the temperature at the top side of section B. Also, h2 is the height of section B and T(y) is the temperature of water at a distance y from lower side of section A. The temperature variation along the length of section A is assumed uniform; therefore the value of integration of Eq. (8) can be written as

(10)

The relation between the developed natural convection mass _ and the supplied useful heat (Q_ u ) to section A is ﬂow rate (m) written as

(11)

where Q_ in and Q_ L are the rates of input heat gain and total heat loss _ is the developed natural convection ﬂow rate in in section A, and m section A. By combining Eqs. (10) and (11), we obtain

_ Q in Q_ L L gbr0 sinq þ g br0 h2 ðT3 T2 Þ ¼ DpAc 1 þ rp _ mcw 2 (12) The heat transfer rate due to buoyancy from section A is equal to the heat gain by section B. We can express this equality as follows:

_ w ðT2 T1 Þ ¼ mc _ w ðT3 T2 Þ mc

(13)

Combining Eqs. (11), (12) and (13), we determine

gr0 b Q_ in Q_ L sinq h2 DpAc þ ¼ _ w 1 þ rp 2 L L mc

(14)

A relation for the pressure drop per unit length and the depth of section A can be written as [24]

DpAc L

¼

12vrv1 W2

(15)

where DpA-c is the pressure drop in section A, W is the depth of section A, n is kinematic viscosity, v1 is the velocity of water, and r is the density of water. _ can be expressed as Also, the developed mass ﬂow rate m

_ ¼ rv1 B1 W m

(16)

where B1 and W are the breadth and depth of section A, r is the density of water, and v1 is the velocity. Finally, combining Eqs. (14), (15) and (16), we obtain

_ ¼ m

fTðyÞ T1 gdy þ gbr0 h2 ðT3 T2 Þ ¼ DpAc 1 þ rp

(9)

0

(7)

Combining Eqs. (2), (4) and (7) yields

g br0 sinq

fTðyÞ T1 gdy ¼ ðT2 T1 Þ

_ w ðT2 T1 Þ ¼ Q_ u ¼ Q_ in Q_ L mc

0

ZL

" # 1 g r0 b Q_ in Q_ L B1 W 3 sinq h2 2 þ 2 L 12vcw 1 þ rp

(17)

This expression for the natural convection ﬂow rate in section A of proposed integrated collector-storage solar water heater is the cause of heat transfer from section A to B during day time. It can be seen in this relation that one of the most inﬂuential parameters on the developed ﬂow rate is the depth W of section A. In the night time, reverse convection heat transfer occurs from section B to A, but at a slower rate, as the effect of temperature gradient and gravity weaken. Also this reverse heat transfer rate depends on the temperatures of water in the two sections, are very close, and the common crosssectional area.

R. Kumar, M.A. Rosen / Applied Thermal Engineering 31 (2011) 348e354

3.2. Energy balance for section A

Tw ¼

Section A is identical to a rectangular built-in-storage solar water heater. Transient energy balances based on the ﬁrst law of thermodynamics are written for the absorber surface and water. Energy balances for the absorber surface and water are written as

mp cp

dTp ¼ ðasÞe It Ap Ut Tp Ta Ap hpwA Tp TwA Ap dt (18)

mwA cw

dTwA ¼ hqwA Tp TwA Ap UbeA ðTwA Ta ÞAbeA Q_ dt (19)

where Q_ represents the rate of heat transfer from section A to B or vice versa, and can be expressed as

_ w ðTwA TwB Þ þ K2 hBA ABA ðTwA TwB Þ Q_ ¼ K1 mc

(20)

In Eq. (20), we introduce two parameters K1 and K2; the value of K1 is either 1 or zero, while value of K2 is 0 and 1, depending on the direction of heat ﬂow in two sections. The following conditions relating to the parameters K1 and K2 apply during the operation of water heater: K1 ¼ 1 and K2 ¼ 0 if TwA TwB (a condition representing heat ﬂow from section A to B). K1 ¼ 0 and K2 ¼ 1 if TwA < TwB (a condition representing heat ﬂow from section B to A). Here, Tp is the temperature of the absorber surface, TwA and TwB are the temperatures of the water in sections A and B, respectively, Ta is the temperature of ambient air, hpwA is the heat transfer coefﬁcient from the absorber surface to water, UbeA is the bottom heat transfer coefﬁcient, Ut is the top heat transfer coefﬁcient from the absorber surface to ambient air, hBA is the convective heat transfer from sections B to A (during night time), It is the incident solar irradiance on the glazing, (as)e is the effective trans_ is mittanceeabsorptance product for the absorber surface, and m the natural convection ﬂow rate. Also, Ap is the absorber surface area, AbeA is the area of bottom and sides of section A, ABA is the common area of sections A and B, mwA is the mass of water in section A, mp is the mass of the absorber surface, and cp and cw are the speciﬁc heats of the absorber plate and the water, respectively. The left hand sides of Eqs. (18) and (19) respectively represent the changes with time in energy contents of the absorber surface and the water. 3.3. Energy balance for section B An energy balance for section B is written as

mwB cw

dTwB _ f cw ðTwB Tin Þ ¼ Q_ UbeB ðTwB Ta ÞAbeB m dt (21)

Here, Q_ is the energy transfer rate between sections A and B, UbeB is the heat transfer coefﬁcient from the water to ambient air, AbeB is the total surface area of section B excluding the common surface area of A and B, Ta is the ambient temperature, Tin is the inlet _f water temperature to storage tank from the main water line, and m _ f is is the ﬂow rate of water withdrawal. If there is no withdrawal m equal to zero. The left hand side of Eq. (21) represents the change with time in energy content of the water in section B. The average temperature of water in water heater is denoted by Tw at any instant and is calculated by

351

ðTwA þ TwB Þ 2

(22)

In the beginning of the heating operation the temperatures of water in two sections are same. As solar radiation begins to strike the absorber, the temperature of water in section A increases and a natural convection ﬂow develops in section A. Due to this natural ﬂow, the temperature of water in section B approaches that of section A. After a long time, the temperatures of water in two sections tend toward the average temperature Tw. During the charging of the water heater the temperature of the water in section A is slightly higher than the average temperature Tw and in the night the temperature of water in section B is slightly higher than Tw. The values of the average water temperature changes with the water temperatures in the two sections. The water temperatures in two sections of the water heater are inﬂuenced by the water mass in each section, the input heat supply, the common cross-section area of the two sections and the inclination of section A from the horizontal. The values of the temperatures in sections A and B are calculated by inter-related Eqs. (18)e(21) and then substituting Eq. (22) to determine the average temperature in the water heater.

3.4. Efﬁciency of water heater The efﬁciency of water heater can be written as

Zt1 _ f cw ðTw Tin Þdt m mw cw Twf Ta1 þ

h¼

0

Zt

(23)

It dt 0

Here, Ta1 and Twf are the average temperatures of water at the beginning of the heating processes and at the time of ﬁnal withdrawal. Also, t1 is the time for the water withdrawal from the water heater excluding ﬁnal withdrawal, and mw is the total mass of water in sections A and B. The numerator of Eq. (23) represents the quantity of useful heat produced during operation of the water heater, whereas the denominator represents the amount of solar radiation incident over the glass cover during the corresponding time. The energy balances in Eqs. (18)e(21) are solved using a forward time step marching ﬁnite difference technique. In this technique the quantity (dT/dt) is replaced by (Tiþ1Ti)/Dt, where Ti and Tiþ1 are the values of temperature T just before and after the time step Dt. The values of Dt are restricted by stability solution considerations so as to satisfy Eqs. (18)e(21), and is taken to be 10 s in order to meet stability requirements. Various heat transfer coefﬁcients are used in Eqs. (18)e(21). The heat transfer coefﬁcients from the absorber surface to the glazing and also from the glazing to the ambient air include both convective and radiative parts, while the heat transfer coefﬁcient from the sides and bottom insulation is conductive. Heat transfer across the common area of A and B is by natural convection. These heat transfer coefﬁcients are determined using standard relations provided in Holman [25] and Dufﬁe and Beckman [26]. The values of all heat transfer coefﬁcients are taken to exhibit transient variations. The most important heat transfer process for this investigation is between the absorber surface and the water (section A). Natural convection is considered the mode of heat transfer in this instance. Faujii and Imura [27] developed the following correlation for the

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estimation of Nusselt number from an inclined heating surface to water:

Nue ¼ 0:56ðGre Pre cosfÞ1=4 ; 105 < Gre Pre cosf < 1011

(24)

Here, f is the angle of the absorber surface relative to the vertical. The above relation is valid when a hot surface is facing downwards. In applying the above relation, all values are calculated (except the volumetric coefﬁcient of expansion) at the reference temperature Te, deﬁned as

Te ¼ Tp 0:25 Tp TwA

(25)

where Tp and TwA are the temperatures of the absorber surface and the water in section A. At the reference temperature (denoted by subscript e), the Grashof number (Gre) and Prandtl number (Pre) are calculated by using following relations:

g b Tp TwA L3c Gre ¼ v2 Pre ¼

v

a

(26)

(27)

where Lc is the characteristic length, and n and a are the kinematic viscosity and thermal diffusivity of water. 4. Results and discussion All calculations for a typical day are made for the climatic conditions of Toronto. ICSSWH systems are useful for seasonal applications in Toronto (April to October), as the exposure of these water heaters to the freezing conditions of Toronto for longer periods might cause damage to the water heater due to water expansion in freezing situations. The month considered for numerical simulation is July in order to permit assessment of the period when the maximum heat is produced from the solar water heater. The hourly variations of solar irradiance and ambient temperature for July in Toronto are plotted in Fig. 3 [28]. Simultaneously the values of solar irradiance are also calculated and plotted corresponding to tilt angles of 15 , 30 , 45 and 60 , to observe the effect of tilt angle. For the performance evaluation, the water heater is south facing and inclined at an angle of 30 . A comparison of performance is also made of the modiﬁed ICSSWH system (Fig. 1) with an ICSSWH system with a conventional rectangular design (Fig. 2). In the comparative study the volumes of water are taken 100 L per square meter of absorber area in both the designs. In Figs. 4 and 7 the

Fig. 3. Hourly variation in solar radiation and ambient temperature.

Fig. 4. Hourly variation in water temperature for modiﬁed solar water heater together with rectangular shape (R) ICSSWH system.

temperature of water refers to the average temperature of the water in section A and B. The water temperatures, efﬁciencies and natural convection ﬂow rates are calculated for various volume ratios for the two sections (VA/VB), where VA and VB denote the volumes of water in sections A and B, respectively. The following volume ratios are considered in the numerical simulation: 0.11 (10/ 90), 0.43 (30/70), 1 (50/50), 2.33 (70/30) and 4 (80/20). The inﬂuence of angle of inclination on the water temperature and the natural convection ﬂow rate is also calculated. In Figs. 4 and 5, the volumes of water in the two sections of the proposed water heater are optimized to achieve highest water temperature and efﬁciency. The water volumes ratio (VA/VB) is varied to optimize volume ratio in the two sections, keeping the total volume of water at 100 L. The volume ratio (VA/VB) is varied from 0.11 (10/90) to 4 (80/20). Simultaneously the water temperature and efﬁciency of the rectangular ICSSWH (Fig. 2) is also plotted in Figs. 4 and 5 and it is represented by R. The highest water temperature is observed corresponding to a volume ratio of 2.33 (70/30) and it is about 5e6 C higher than the corresponding water temperature in a rectangular ICSSWH system. In Fig. 5 the efﬁciency is presented for similar water volume ratios along with the efﬁciency of the rectangular ICSSWH design. The efﬁciency of the modiﬁed water heater varies from 42.3% to 53.7% as the volume ratio changes from 0.11 to 4. The maximum efﬁciency is obtained corresponding to a volume ratio 2.33 (70/30), for the volume ratios considered, and this is the case of maximum water temperature (Fig. 4) in the modiﬁed ICSSWH. Therefore, the proposed design of solar water heater delivers the maximum thermal output when the water volume is distributed 70% in section A and 30% in section B. For lower volume ratio values (0.11, 0.43, 1) than 2.33 (70/30), greater heat losses occur in the water

Fig. 5. Efﬁciency of water heater corresponding to different water volume ratios together with rectangular shape (R) ICSSWH.

R. Kumar, M.A. Rosen / Applied Thermal Engineering 31 (2011) 348e354

353

Fig. 8. Hourly variation in ﬂow rate corresponding to various tilt angles. Fig. 6. Hourly variation in natural convection ﬂow rate for several volume ratios.

heater due to higher operating temperature in section A. For a higher volume ratio than the 2.33 (70/30), such as 4 or more, section A has a higher water volume per unit absorber area and this characteristic slows the heating in section A and inﬂuences negatively the developed natural convection ﬂow rate and consequently the efﬁciency of water heater. On a comparative level, the efﬁciency of modiﬁed design of water heater corresponding to ratio 2.33 (70/30) is about 5% greater than that for the rectangular design of ICSSWH. Fig. 6 shows the developed natural convection ﬂow rate in section A during the charging of the water heater. The variation in the developed ﬂow rate is demonstrated for the same volume ratios considered in Figs. 4 and 5. The volumes of water in the two sections change to evaluate the inﬂuence of different volume ratios on the developed natural convection ﬂow rate, however the total volume of water in the two sections is ﬁxed at 100 L. The ﬂow rate increases as the volume ratio increases; this variation is more rapid as the volume ratio changes from 0.11 to 2.33 and less rapid for higher ratios. Note that, although the ﬂow rate increases as the volume ratio increases from the optimized value (2.33), this characteristic does not improve the thermal output of the water heater (Figs. 4 and 5). This observation can be understood by noting that the water temperature and water heater efﬁciency are explicit functions of the volume ratio in the two sections, the input heat supply, the total heat losses, the amount of water per unit surface area and its inclination with horizontal, and the water withdrawal rate from the water heater. While the developed natural convection ﬂow rate rises with increasing volume of water in section A and with the depth of storage tank (as it is proportional to W3/2), this

Fig. 7. Hourly variation in the temperature of water corresponding to various tilt angles.

effect slows the heating process. As more water is exposed per unit absorber area in section A, the overall impact of slow heating at higher volume ratios inﬂuences the heat transfer between two sections and subsequently the water temperature and the water heater efﬁciency. In the Fig. 7 the tilt of section A of the modiﬁed ICSSWH is varied to maximize thermal output in Toronto. For this variation, the volume of water in the two sections is taken equal to the earlier optimized value of 2.33 (70/30) based on the considered ratios of 0.11, 0.43, 1, 2.33 and 4. The water volume ratio for the two sections is set to the optimized value (2.33), but the total volume of water in two sections is constant at 100 L. The water temperature corresponding to tilt angles of 15 , 30 , 45 and 60 are plotted in Fig. 7 and the comparable values of solar irradiance on the absorber surface are illustrated in Fig. 3. The maximum water temperature is achieved in the water heater corresponding to a tilt angle 30 based on the considered angles and this is also the case of maximum solar irradiance incident on the absorber surface (Fig. 3). As the tilt angle increases from 15 to 45 , a continuous increase is observed in the developed natural convection ﬂow rate (Fig. 8); however the amount of solar irradiance on the absorber surface is decreased as the tilt angle increases beyond 30 (Fig. 3). The combined effect of the increased natural convection ﬂow rate and the reduced amount of solar irradiance is a reduced thermal output from the water heater. Therefore, the tilt angle for section A based on the chosen angles to produce maximum heat from the proposed design of solar water heater for the climatic conditions of Toronto is 30 . 5. Conclusions The integrated collector-storage solar water heater (ICSSWH) is considered a simple design of solar water heater. Building on various past modiﬁcations in the design and shape of storage vessel of ICSSWH systems aimed at improving efﬁciency for round the clock operation, the conﬁguration of storage tank is modiﬁed here by adding an extended storage unit to the conventional rectangular shape. A numerical simulation is performed of the modiﬁed design of the ICSSWH, dividing the total volume into two sections A and B. The volumes of water in two sections are optimized to maximize the thermal output from the water heater. A comparison of the performance of the modiﬁed design with that of a rectangular design of ICSSWH supports the beneﬁts and signiﬁcance of new design. The highest water temperature and efﬁciency are observed corresponding to the case in which the total water storage volume is distributed such that 70% is in section A and 30% in section B. Also, an efﬁciency improvement of about 5% is observed for the new design over a corresponding rectangular ICSSWH. The tilt of section A is optimized at 30 to obtain a maximum heat output for

354

R. Kumar, M.A. Rosen / Applied Thermal Engineering 31 (2011) 348e354

the climatic conditions of Toronto. Although this investigation focuses on the thermal performance of integrated solar water heaters with extended storage units, the enhanced performance (about 5%) is signiﬁcant and is expected to make this design more economically viable. Since the total volume of the storage tank is constant in the performance evaluation of the two designs and only the tank shape varies, the cost of the design modiﬁcation is likely not signiﬁcant. Overall, the modiﬁed ICSSWH system design appears to be able to generate more thermal output than the conventional rectangular shaped ICSSWH system at reasonable high efﬁciencies, and thus merits further investigation. Acknowledgements The authors gratefully acknowledge the ﬁnancial support provided by the Natural Sciences and Engineering Research Council of Canada. Nomenclature

B1 C G h It L Lc m _ m mw _ m Q_ in Q_ L

T U v1 W

breadth of section A (m) speciﬁc heat (J/kg C) gravitational acceleration (m/s2) heat transfer coefﬁcient (W/m2 C) total solar irradiance (W/m2) length of section A (m) characteristic length (m) mass (kg) mass ﬂow rate (kg/s) total mass of water in section A and B (kg) natural convection ﬂow rate (kg/s) input heat rate to section A (W) total heat loss rate from section A (W) temperature ( C) heat transfer coefﬁcient (W/m2 C) velocity (m/s) depth of section A (m)

Greek letters a thermal diffusivity of water (m2/s) b coefﬁcient of volumetric expansion of water (1/ C) h energy efﬁciency (%) q inclination of section A with horizontal n kinematic viscosity (m2/s) effective absorptanceetransmittance product (as)e f inclination of section A relative to vertical Subscripts a ambient beA bottom plus edges of section A beB bottom plus edges of section B in inlet water temperature p absorber plate pwA absorber plate to water in section A wA water of section A wB water of section B

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