Thermal performance of a solar-aided latent heat store used for space heating by heat pump

Solar Energy Vol. 69, No. 1, pp. 15–25, 20002000 Elsevier Science Ltd

Pergamon PII: S0038 – 092X( 00 )00015 – 3 All rights reserved. Printed in Great Britain0038-092X/00/$ - see front matter

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THERMAL PERFORMANCE OF A SOLAR-AIDED LATENT HEAT STOREUSED FOR SPACE HEATING BY HEAT PUMP

†MEHMET ESEN˘Department of Mechanical Education, Fırat University, 23119 Elazıg, Turkey

Received 11 September 1998; revised version accepted 30 November 1999

Communicated by ERICH HAHNE

Abstract—In this study, the cylindrical phase change storage tank linked to a solar powered heat pump systemis investigated experimentally and theoretically. A simulation model defining the transient behaviour of thephase change unit was used. In the tank, the phase change material (PCM) is inside cylindrical tubes and theheat transfer fluid (HTF) flows parallel to it. The heat transfer problem of the model (treated as two-dimensional) was solved numerically by an enthalpy-based finite differences method and validated againstexperimental data. The experiments were performed from November to May in the heating seasons of1992–1993 and 1993–1994 to measure both the mean temperature of water within the tank and the inlet andoutlet water temperature of the tank. The experimentally obtained inlet water temperatures are also taken asinlet water temperature of the simulated model. Thus, theoretical temperature and stored heat energydistribution within the tank have been determined. Solar radiation and space heating loads for the heatingseasons mentioned above are also presented. 2000 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION solar heating system. Their main conclusion wasthat the PCM should be selected on the basis of

Energy storage is much more important where theits melting temperature, rather than its latent heat,

energy source is intermittent such as solar energy.i.e. the melting temperature has a significant

A great disadvantage of this kind of energy showseffect on system performance. Klein and Beck-

up immediately, namely the large discrepancyman (1979) described an extensive computer

between the supply and the demand. The heatsimulation study of a general class of closed-loop

demand is maximum in winter or, in the shortsolar energy system which can be used for a

term, in the evening when the supply of solarvariety of applications including space heating,

energy is minimal or even zero. This makes heatabsorption air conditioning, and certain types of

storage an indispensable element of a solar-po-process heating. The results of this study are

wered heat pump system. One way of increasingpresented as a design method so that they can be

the economic competitiveness of the heat pump isused to estimate the long-term performance of

to integrate it with a thermal energy storagesolar energy systems. Bulkin et al. (1988) sug-

system. The thermal store allows a reduction ingested a mathematical model for designing a solar

the required heat pump size for a given load. Thisheating and hot-water supply system on the basis

reduces the capital cost of the heat pump. Also,of solar absorbers and a heat pump with two

the store reduces the on/off cycling losses of thethermal-storage tanks, taking into account the

system because a smaller-sized heat pump willsystem’s interaction with the outside climate and

run for longer periods at maximum capacitywith the room being served. Ghoneim (1989) has

between cycles to satisfy a given load. Moreover,studied the effect of assumptions in the models of

the store allows the heat pump to operate at lowerearlier studies on both the fraction of the load met

condensing temperatures leading to a higherby solar energy, and the required storage capaci-

steady-state coefficient of performance (COP)ties. Kaygusuz et al. (1991) developed an ex-

(Comaklı et al., 1993a).perimental model to determine the dynamics of

Jurinak and Abdel-Khalik (1978, 1979) havesolar-assisted heat pump, collectors, dryer, and

studied the effects of PCM melting temperatureenergy storage tank used for drying grains.

and latent heat on the performance of an air-basedKaygusuz (1995a) investigated the performanceof a dual-source heat pump system for residentialheating. Also, Kaygusuz (1995b) conducted an

†Fax: 190-424-218-4674; e-mail: [email protected] experimental and a theoretical study to determine

15

16 M. Esen

the performance of phase-change energy storage purposes, a latent heat thermal energy storagematerials, and the variation of the outlet fluid tank filled by 1090 kg encapsulated PCMtemperature with different values of NTU (the (CaCl .6H O), a heat pump with a water sourced2 2

number of transfer units of the storage unit) for evaporator and an air cooled condenser, a watersolar water-heating systems. circulating pump, and measuring equipment. The

The performance of a solar energy system water cooled solar collectors were installed at anvaries significantly from day to day and from angle of 488 from the horizontal and face duemonth to month making it necessary to examine south. Temperatures were measured with copperits performance over a long term. The main constantan thermocouples. A Kipp and Zonenobjectives of the present study have been: (1) to pyranometer, mounted in the vertical plane of theuse a theoretical model describing the diurnal solar collectors, was used to measure the solartransient behaviour of the phase change energy insolation. Water flow rate was measured bystorage (PCES) unit, (2) to perform computer means of two flowmeters. An automatic datasimulations and experiments in order to determine logging system was used for data acquisition.the distribution of energy, and temperature within Every 25 s all quantities were measured. Solarthe PCES unit, and (3) to determine the monthly insolation, water temperatures, ambient air andspace heating loads, the monthly stored energy, indoor air temperatures were averaged over eachand monthly total solar insolation on collector half-hour period. These averaged quantities andsurfaces, and to present comparisons of these the instantaneous values of the remaining quan-data. tities were recorded every half-hour.

2.2. Operation modes

2. THE EXPERIMENTAL STUDY The two modes of operation were investigatedin this system. The first mode occurs when solar

2.1. Experimental set-up radiation is available for collection and there is aThe experimental set-up described here is at space heating load. During this mode, the hot

Trabzon, Turkey (lat. 418109 N; long. 408209 E). water that receives its energy from the solarFig. 1 shows a sketch of the set-up. The ex- collectors first goes to the energy storage tank. Itperimental apparatus consisted of flat plate solar then releases some of its own energy to the

2collectors having a total area of 30 m , a labora- CaCl .6H O in the storage tank. After this pro-2 22tory building with 75 m floor area for heating cedure it is used as a heat source by the water-

Fig. 1. Solar assisted heat pump system with latent heat storage tank.

Thermal performance of a solar-aided latent heat store used for space heating by heat pump 17

sourced evaporator of the heat pump. Finally, it is difficulty has been removed by the application ofsent to the solar collectors by the water circulating the enthalpy method (Visser, 1986). The relationspump (Storage and Heating Mode). However, between the specific enthalpy and the temperatureduring the night and on cloudy days, when there for different ranges are as follows:is low or no solar radiation and the load is not i(T ) 5 C T for T , T (1)p,s m1zero, the cold water that comes from theevaporator is sent to the tank instead of the r (T 2 T )f m1

]]]]i(T ) 5 C T 1 for T # T # Tp,l m1 m2collectors. The cold water extracts heat energy DTmfrom the PCM in the tank and it flows to the

(2)evaporator for use as a heat source. Thus, at nightand cloudy times, the stored energy in the tank is andused as a heat source for the heat pump.

i(T ) 5 C T 1 r for T . T . (3)p,l f m2The second mode occurs when solar radiationis available for collection and the space heating

These equations will be further simplified byload is zero. In this mode, the hot water is

using a nondimensional enthalpy and temperature.circulated between the collectors and the tank

The nondimensional enthalpy is written as(Storage Mode).

i 2 im1]]H 5 (4)rf

3. THEORETICAL ANALYSISand the nondimensional temperature as

3.1. Modelling of the charging process of the C (T 2 T )p,s m1]]]]u 5 for T , T (5)PCM m1rf

The theoretical treatment of this problem isandsimilar to that described by Esen and Ayhan

(1996) and Esen et al. (1998). Hence, the subject C (T 2 T )p,l m1]]]]u 5 for T $ T . (6)will be discussed very briefly, and for more m1rf

details the reader is referred to the full descriptionConsidering a cylindrical quantity of PCMpresented in the references.

(Fig. 2c), which is a part of the cylinder, taking aThe energy storage tank (Fig. 2a) consists ofcontrol volume element ( j, k), which is a ringcylindrical tubes packed in the vertical direction.with inner radius R and outer radius R , thenFig. 2b sketches the model for one tube (Esen and k k21

applying an energy balance on that volume ele-Ayhan, 1996; Esen et al., 1998). The storagement results in:material (CaCl .6H O) is inside the tubes and the2 2

HTF flows parallel to it. We assume that the HTF ≠i ≠T ≠TU U U] ] ]rV 5 2 lA 1 lAj,k k k21which is surrounding the cylindrical tubes is j,k≠t ≠R k ≠R k21

situated in theoretical cylinder jackets all around ≠T ≠TU U] ]1lA 2 lA (7)the tubes. The very small spaces between cylindri- j j21j j21≠z ≠zcal jackets were ignored. The packing density is

Eq. (7) is solved by using finite differencethe same everywhere in the tank. The ther-approximations for ≠T /≠R and ≠T /≠z. Substitut-mophysical properties of various phases of theing these finite difference equations into Eq. (7),PCM are different, but are independent of tem-an equation for the enthalpy of a specified ele-perature. The PCM is homogeneous and isotropic.ment can be written in nondimensional form. AnIn the model development, the following effectsenergy balance on the HTF element results in anwere taken into account: the thermal conductivityequation for the temperature distribution of theof the PCM in the axial direction, the thermalHTF element. The resulting set of equations isconductivity for the PCM in the direction normalsolved using the Gauss–Seidel iteration process.to the flow (radial direction) and the local film

temperature difference between the HTF and the3.2. The simulated valuesPCM.

During the phase-change process of the storage The energy balance over the PCM is directlymaterial, a moving boundary occurs. The moving coupled with the energy balance over the wall ofsolid–liquid interface moves continuously with the pipe, and the HTF. The temperature of HTFtime, and the problem cannot be reduced to a flowing from the tank to the heat source on timesimple solution of the Fourier equation. The level (n) is expressed as

18 M. Esen

Fig. 2. Energy storage tank packed in vertical direction with cylindrical tubes (a), the model for one cylinder (b) and cylindricalcontrol volume element ( j, k) (c).

n n21,itfT 5 T (8) The energy content with regard to the initialout,H M11,1

temperature T of the PCM is given byst

The rate of energy flowing from the tank to theM11N12

heat source circuit can be written as nf,itfE 5 E 1 N rr O OH V (11)pcm pcm,st c f j,k j,kN j52 k53t1 n]~P 5 m ? C OT 2 T (9)S Dout,H in,H p,f out,H in,HNt n51 where E is dependent on the range T is inpcm,st st

the solid, the transition, and the liquid range.where P 50 on t 5 t .out,H M,st The energy content with regard to T of allstThe rate of energy lost to the environment fromcylinder walls together is calculated bythe tank is calculated as

N M11t M111 nf,itfn,itf]] E 5 N r C O V (T 2 T ) (12)P 5 A U O O T 2 T . (10)S D w c w p,w j,2 j,2 stenv tank j,1 envN Mt j52n51 j52

Thermal performance of a solar-aided latent heat store used for space heating by heat pump 19

M11and that of all the HTF in the tank by 1 nf,itf]T 5 O T . (19)f,mean j,1M11 M j52nf,itfE 5 N r C O V (T 2 T ) (13)f c f p,f j,1 j,1 stj52 The space heating load calculations were made

on the basis of the average daily load by monthThe energy content of the entire tank is the sumusing the effective UA (overall heat transfer3of Eqs. (11), (12), and (13):area) value for the building and (DD) (numberm

of degree-days per month) (Howell et al., 1982).E 5 E 1 E 1 E (14)tank pcm w f

Thus, the average daily space heating load Qd,shThe percentages in the solid, the transition, and was calculated using the following equation:the liquid range of the PCM are calculated as

UAfollows. In the solid range:]Q 5 14(DD) . (20)d,sh m ND

100]]Per 5 OOV for ( j, k)s j,kV The effective UA value for the building is thepcm,c j k

sum of the products of the overall heat transfernf,itfso that H , 0 (15)j,k coefficients (U ) and buildings areas (A ) for thet t

building’s various exterior surfaces: slab (floor,in the transition range:ceiling), walls, windows, and roof. The values of

100 UA for window, wall, floor and ceiling area are]]Per 5 OOV for ( j, k) 21t j,k 315, 96, 187.5 and 150 W K , respectively. SoVpcm,c j k

the effective UA value for the heated building isC DT 21p,l mnf,itf nearly equal to 0.75 kW K . The number of]]]so that 0 # H # 1 1 (16)j,k rf degree-days is the monthly total of all the nega-tive differences between each average daily out-and in the liquid range:door temperature and 18.38C. The total heatingperiod in a day is 14 h.100

]]Per 5 OOV for ( j, k)l j,k Except for these calculated values, temperaturesVpcm,c j kT , T and T are also measured ex-in,H out,H f,meanC DTp,l mnf,itf perimentally.]]]so that H . 1 1 . (17)j,k rf

Finally, the mean temperature of the pipe wall 4. RESULTS AND DISCUSSIONis given by

To acquire the theoretical results, the simula-M11 tion program prepared by Esen (1994) was used.1 nf,itf]T 5 O T (18)w,mean j,2 The properties of PCM (CaCl .6H O), the HTF,M 2 2j52

and other parameters used in this work are listedand the mean temperature of the HTF by in Table 1.

Table 1. The properties of PCM, the HTF, and other parameters used in this work23Density of PCM (CaCl .6H O) 1710 kg m2 2

21 21Specific heat of PCM (solid phase) 1460 J kg K21 21Specific heat of PCM (liquid phase) 2130 J kg K21 21Thermal conductivity of PCM (solid phase) 1.088 W m K21 21Thermal conductivity of PCM (liquid phase) 0.539 W m K

21 21Thermal conductivity of PCM (transition phase) 0.7 W m KMelting temperature of PCM (lower) 29.78CMelting temperature of PCM (upper) 29.858C

21Latent heat of fusion 187.49 kJ kg23Density of HTF 1000 kg m

21 21Specific heat of HTF 4200 J kg KShape of tank (L /R ) 4.923t,inn

3Inside volume of tank 4.25 m2Inside surface area of tank 13 m

22 21Thermal loss of tank 0.55 W m KEnvironment temperature of tank 188C

23Density of cylinder wall material 1200 kg m21 21Specific heat of cylinder wall material 500 J kg K

21 21Thermal conductivity of cylinder wall material 0.055 W m K

20 M. Esen

3Fig. 3. Variation of T , T , T , Per , Per , and Per with time (T 5188C, V 54.25 m , L 53.2 m, N 5110).out,H w,mean f,mean s l t st tank c c

Fig. 3 shows the variation of T , T , than the values of T . In addition, Esenout,H w,mean w,mean

~T , Per , Per and Per with time. Each curve (1994) determined that, as the value of mf,mean s l t in,H

has been generated for constant values of R , increases, the values of T , T , T andc,inn out,H f,mean w,mean

~m and T . As seen from the figure, as the E increase too.in,H in,H pcm

values of Per and Per become zero when the The variation of P , P , E , E , E ands t env out,H tank f w

whole PCM melts (i.e. at which time maximum E with time is given in Fig. 4. As can be seenpcm

energy is stored in the PCM), the value of Per from the figure, the values of E , E , E andl w f tank

becomes 100%. The value of E almost remains P as well as the value of E almost continuespcm env pcm

the same from this point (see Fig. 4). The total of as constant; because the values of T , Tw,mean f,mean

percentages of PCM by volume always become and T do not increase more when the PCMout,H

100% at a given time. Also, in the previous study becomes completely liquid. As shown in the(Esen and Ayhan, 1996) it was seen that, as the figure, the energy content of the tank always

~values of m and T increase at a given time, becomes equal to the total of the values of thein,H in,H

the stored energy in the PCM increases too. When E , E and E . Since the value of the P ispcm w f out,H

the PCM completely melts, the values T and the rate of energy flowing from the tank to thein,H

T approach each other. Throughout the charg- heat-source (to the solar collectors), it begins fromout,H

ing process, the values of T become bigger a negative value, then it approaches zero when thef,mean

21 21Fig. 4. Variation of P (kJ h ), P (MJ h ), E (MJ), E (MJ), E (kJ) and E (MJ) with time (T 5188C, V 54.25env out,H tank f w pcm st tank3m , L 53.2 m, N 5110).c c

Thermal performance of a solar-aided latent heat store used for space heating by heat pump 21

Fig. 5. Variation of T , T , T , T , T and T with time of day.in,H out,H out,H,ex f,mean f,mean,ex w,mean

outlet water temperature of the tank begins to which extracts the heat of water in the tankincrease; because the value of the T ap- becomes maximum towards evening, and theout,H

proaches the value of the T . value of E decreases when the value of Tin,H pcm f,mean

The variations of the theoretical and the ex- is smaller than the melting temperature of theperimental temperatures with the time of day are PCM (see also Fig. 6).depicted in Fig. 5. As seen in the figure, the Fig. 6 shows the variation of I , E , P ,i pcm env

measured and the calculated values of T and P , Per , Per and Per with time of day. Theout,H out,H s l t

T are very near each other. As the theoretical total of Per , Per and Per is always 100% at af,mean s l t

values are calculated, the measured values of T given time. This result is the same as seen in Fig.in,H

were taken as the theoretical values of T . Solar 3. So long as the value of T increases, Pin,H f,mean env

radiation is maximum at around solar noon, and increases too. The moment the value of Tf,mean

after it begins decreasing from this point, the begins decreasing, P decreases too, because theenv

temperatures T , T and T decrease temperature difference (T 2T ) decreases.in,H w,mean out,H f,mean env

too, respectively. The stored energy in the PCM As soon as T becomes higher than T , theout,H in,H

21 22 21 21Fig. 6. Variation of I 310 (W m ), E (MJ), P (kJ h ), P (MJ h ), Per (%), Per (%) and Per (%) with time ofi pcm env out,H s l t

day.

22 M. Esen

charging period is finished and the discharging filled with PCM) made of PVC (polyvinyl chlo-period begins. Because of insufficient insolation, ride) are not as good as some metals (e.g. copper,the PCM cannot completely melt, and thus maxi- aluminium, steel, etc.). Therefore, more appro-mum energy storage of PCM cannot be provided. priate pipe wall materials, shapes and dimensionsThis case shows that the PCM containers (pipes should be selected. The aim of modelling latent

Fig. 7. The variations of I, Q, (E /Q) and (E /I) during the months of the heating season in 1992–1993 and 1993–1994.pcm pcm

Thermal performance of a solar-aided latent heat store used for space heating by heat pump 23

heat stores is essentially an appropriate selection season. It is clear that if the space heating had notof the parameters mentioned above (Esen and been carried out, more load would have been metAyhan, 1996; Esen et al., 1998). by the stored energy. However, the amount of

Fig. 7a and b presents the variations of I and Q stored energy is higher than the load in spite ofduring the months of the heating season in 1992– energy consumed for heating in March. The1993 and 1993–1994, respectively. In 1992– monthly average outdoor temperatures for1993, the Q becomes maximum in January, November to May in 1993–1994 are 8.6, 10, 9.2,whereas the I becomes maximum in May. In 6.1, 8.6, 14.3 and 16.48C, respectively. The ratios1993–1994, the Q is maximum in February. For of E /Q in 1993–1994 are bigger than those inpcm

both heating seasons, the values of insolation 1992–1993. This can perhaps be due to twobecome smaller than the load values in reasons: (1) the average outdoor temperatures inNovember, December, January and February. In 1993–1994 are higher compared to the values inthese months, both the heating and the storage 1992–1993, (2) using smaller pipe radius inwere practised on sunny and warm days. The 1993–1994. It is evident that PCM cylinders withstored energy in the PCM was released at night. smaller radii will melt at a shorter time and theseOn sunny but cold days only storage was per- cylinders can store much more heat energy com-formed, and this stored energy was used for pared to PCM cylinders with thicker radii.heating during the night. However, on warm days The variations of ratios of E /I during thepcm

and when solar radiation and a space heating load months of the heating season in 1992–1993 andis available, an air-sourced heat pump and/or a 1993–1994 for the storage mode and the storagewater-to-air heat exchanger can be used. and heating mode are shown in Fig. 7e and f,

Fig. 7c depicts the variation of the ratio of respectively. As seen in Fig. 7e and f, the storedE /Q during the months of the heating season energy is lower than the values of insolation forpcm

in 1992–1993 for the storage mode and the all the months in both seasons, because somestorage and heating mode. Whereas the heat pump stored energy in the tank is lost to the environ-in the storage mode does not run, both heating ment. On the other hand, some energy in the tankand storage are carried out in the storage and is stored in the HTF and the pipe walls. The lostheating mode. Naturally, the ratios of E /Q energy occurs both from the tank and from thepcm

were smaller in the storage and heating mode solar collectors.compared to the ratios in the storage mode. Asseen in the figure, the stored energy meets 60% ofthe load in addition to the energy consumed for

5. CONCLUSIONspace heating in March. While the whole load isalmost met by the stored energy in April, the ratio To study the thermal performance of the solar-of E /Q nearly becomes 2.5 in May. As the aided latent heat storage tank in the charging andpcm

ratios of E /Q are very low from November to discharging process, a theoretical model waspcm

February for the storage and heating mode, either developed, and an experimental system con-the water-sourced (solar-aided) heat pump to- structed by Comakli et al. (1993b) was used together with an auxiliary heater should be run, or validate it. A comparison between mathematicalonly storage is performed during daytime, and the results of the model with experimental datawater-sourced (store-aided) heat pump together showed reasonable agreement. The followingwith an auxiliary heater should be run at night. conclusions can be drawn from the results of thisThe monthly average outdoor temperatures for study.November to May in 1992–1993 are 11.5, 7, 5.5, 1. To show accuracy of the model developed in4.5, 9, 11 and 15.58C, respectively. Although the this study, there is a lot of evidence.average outdoor temperature in February is lower • The total of percentages of the PCM bythan that in January, the heating load in February volume in the solid, the transition and theis smaller than that in January. This is affected by liquid range is always (at a given time)the fact that February has only 28 days. 100%.

Fig. 7d exhibits the variation of the ratio of • The total of E , E and E is alwayspcm w f

E /Q during the months of the heating season equal to E .pcm tank

in 1993–1994 for the storage mode and the 2. Because the outlet water temperature of thestorage and heating mode. The stored energy tank is low (or constant) at the beginning ofalmost meets half of the load in addition to energy the experiments, the heating cannot be per-consumed for heating in the first 4 months of the formed well. To improve this situation, a

24 M. Esen

H nondimensional enthalpyshorter length of pipes as well as a shorterI monthly total solar insolation on tilted collector

inside height of the tank should be selected. surfaces (MJ)3. The thickness of the pipe walls should be thin I instantaneous solar radiation on tilted collectori

22surfaces (W m )so that the energy stored in pipes walls21i specific enthalpy of PCM (kJ kg )becomes minimum. If lots of pipes with small itf final iteration level

radii are used, the total volume of pipe walls L length of cylinder (m)c

M number of axial elementsincreases; therefore, the whole PCM melting~m mass flow rate of HTF flowing from heat source toin,Htime becomes longer compared to the melting 21tank (kg s )

time in the tank which contains fewer pipes nf final time level inside subroutineN number of radial elementswith big radius (Esen, 1994). Consequently,N number of cylinderscthe thickness of the pipe walls should beN number of timesteps inside the subroutine programtthinner if a lot of pipes with small radius are ND number of days in a month

used. P rate of energy lost to environment (W)env

Per percentage of PCM in the liquid range by volumel4. Note that energy released to the heating space(%)by heat pump is not only the energy extracted P rate of energy flowing from the tank to heat sourceout,H

from the PCM, since the energy (electric (W)Per percentage of PCM in the solid range by volumeenergy) consumed to run the heat pump is s

(%)added to it. The ratio of E /Q is stillpcm Per percentage of PCM in the transition range bytinsufficient especially in the first 4 months of volume (%)

Q monthly total space heating load (MJ)the season. Therefore, availability of seasonalQ average daily space heating load (MJ)d,shstorage should be investigated for Trabzon R radial distance (m)

(placed on the Black Sea side). R inner radius of PCM cylinders (m)c,inn

R outer radius of PCM cylinders (m)5. The choice of modes should be done by c,out21r latent heat of fusion (kJ kg )fchecking the temperature T automatically.in,H R inner radius of the tank (m)t,inn6. Other storage materials and storage types T temperature (8C)

T theoretical mean temperature of HTF in the tankshould be investigated. f,mean

(8C)7. The PCM used in the experiments of thisT experimental mean temperature of HTF in the tankf,mean,exstudy was not changed during two seasons. (8C)T temperature of the HTF flowing from the heatThus the most appropriate number of heat in,H

source to the tank (8C)cycles should be determined. When the num-T lower melting temperature of the PCM (8C)m1ber reaches the value determined, PCM used T upper melting temperature of the PCM (8C)m2

T theoretical temperature of HTF flowing from thein the tank should be renewed. out,H

tank to the heat source (8C)8. The heating space should be insulated veryT experimental temperature of HTF flowing from theout,H,exwell according to standards of ASHRAE, tank to the heat source (8C)T initial temperature of the tank (PCM, HTF, cylin-TSE etc. st

der walls) (8C)9. On cloudy but warm days, a solar assistedT theoretical mean temperature of cylinder walls (8C)w,meanheat pump together with air-sourced t time (h)t initial time in main program (h)evaporator can be more efficient. M,st

22 21U thermal loss of storage tank (W m K )10. The performance of a solar assisted storage 22 21U overall thermal loss coefficient (W m K )t3tank used by a heat pump system should be V control element volume (m )j,k

3examined over the long term. V one PCM cylinder volume (m )pcm,c3V inside volume of the tank (m )tank

z axial distance (m)DT transition range width (8C)mNOMENCLATURE

2A area (m ) Greek letters2A floor area (m )t u nondimensional temperature221 21A inside surface area of the tank (m )tank l thermal conductivity (W m K )21 21C specific heat (J kg K )p l thermal conductivity of PCM in liquid phase (W21 21 l

21 21C specific heat of HTF (J kg K )p,f m K )21 21C specific heat of PCM in liquid phase (J kg K )p,l l thermal conductivity of PCM in solid phase (Ws21 21

21 21C specific heat of PCM in solid phase (J kg K )p,s m K )21 21C specific heat of cylinder wall material (J kg K ) l thermal conductivity of PCM in transition phasep,w t

21 21(DD) number of degree-days per month (W m K )m

E energy content of HTF (J) l thermal conductivity of cylinder wall material (Wf w21 21E energy content of PCM (J) m K )pcm

23E initial energy content of PCM (J) r PCM density (kg m )pcm,st23E energy content of the tank (J) r HTF density (kg m )tank f

23E energy content of cylinder walls (J) r density of cylinder wall material (kg m )w w

Thermal performance of a solar-aided latent heat store used for space heating by heat pump 25

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