Parametric Study of a Flat Plate Wick Assisted Heat Pipe Solar Collector

Brahim Taoufik e-mail: [email protected]

Mhiri Foued Jemni Abdelmajid e-mail: [email protected] Laboratoire d’Etudes des Syste`mes Thermique et Energe´tique (LESTE), Ecole Nationale d’Ingeńieurs de Monastir, Universite´ de Monastir, Avenue Ibn Jazzar 5019 Monastir, Tunisia

Parametric Study of a Flat Plate Wick Assisted Heat Pipe Solar Collector The use of heat pipes in solar collectors offers several advantages regarding flexibility in operation and application, as they are very efficient in transporting heat even under a small temperature difference. Compared with other systems powered by evacuated tube collectors or flat plate solar collectors using a wickless heat pipe, little attention has been paid to a flat plate solar collectors wick assisted heat pipe. In this paper an analytical model based on energy balance equations assuming a steady state condition was developed to evaluate the thermal efficiency of a flat plate wick assisted heat pipe solar collector. Parameters which affect the collector efficiency are identified, such as tube spacing distance, gap spacing between the absorber plate and the glazing cover, and the emissivity of the absorber plate. The results reflect the contribution and significance of each of these parameters to the collector overall heat loss coefficients. Three heat pipe working fluids are examined and results show that acetone performs better than methanol and ethanol. [DOI: 10.1115/1.4023875] Keywords: plate heat pipe solar collector, wick, model, thermal losses, parameters

1

Introduction

Heat pipe solar collectors outperformed conventional solar collectors because of their efficient heat transport method. They can be either flat plate type or evacuated tube type or concentrating system. The evacuated tube solar collectors perform better when compared to flat plate solar collectors; in particular for high temperature operations, but neither one can be considered “more efficient” than the other. The outcome is dependent on the environmental conditions [1,2]. Flat plate heat pipe solar collectors have been studied by several authors. Most heat pipes developed have a circular section with a wickless structure. Hussein [3–5] investigated theoretically and experimentally flat plate solar collector using wickless, named also as two-phase closed thermosyphon or gravity assisted heat pipe. Transient thermal behavior was analyzed with regard to a range of parameters. The results revealed that the tube’s spacing limited the selection of an absorber plate to one having a high value of thermal conductivity. Also, from the theoretical analysis of laminar film condensation heat transfer inside the inclined wickless heat pipes flat plate solar collector, it was accomplished that the condenser section aspect ratio and the heat pipe inclination angle had a considerable effect on the condensation heat transfer coefficient. Esen [6] presented the results of an experimental investigation of a two-phase closed thermosyphon solar water heater. The results were analyzed with regard to various working fluids (R-134a, R-407c, and R-410a). It was concluded that the working fluid had an effect on the thermal performance of the two-phase closed thermosyphon solar collector. Hybrid flat plate solar collectors were studied by various researchers, Abreu [7–9] focused on the experimental analysis of the thermal behavior of the two-phase closed thermosyphon for compact solar domestic hot water systems with an unusual geometry for the retention of liquid characterized by a semicircular condenser and a straight evaporator. Riffat [10,11] studied the thermal performance of a thin membrane heat pipe solar collector Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received December 15, 2011; final manuscript received November 21, 2012; published online May 31, 2013. Assoc. Editor: Werner Platzer.

Journal of Solar Energy Engineering

and hybrid heat pipe solar collector/CHP system to provide electricity and heating for a building. A porous medium flat plate solar collector also was analyzed by Wu [12] using a numerical method to determine its efficiency. A better efficiency has been found for these collector types compared to the conventional flat plate solar collector. Ismail and Abogderah [13] used heat pipes with internal capillary structure in the evaporator section and methanol as the working fluid. They note that the condenser having a slope greater than the evaporator can improve the collector performance compared to a conventional collector. Joudi [14] investigated the performance of the modified heat pipe compared to a reference gravity assisted heat pipe connected to a common manifold. They noted that the presence of an adiabatic separator caused a remarkable improvement in all heat pipes tested for all lengths and inclination angles and the addition of a screen wick at the evaporator can raise the heat pipe evaporator and adiabatic temperature. The wickless heat pipes show the lowest heat pipes operating temperature among the conventional heat pipe and who is with a separator in the adiabatic section. Most previous studies on the flat plate solar collectors paid more attention to wickless heat pipes, also called a two-phase closed thermosyphon or gravity assisted heat pipe solar collector, to study their performance theoretically and experimentally or comparing them with conventional solar collectors. This paper will discuss a mathematical model that has been developed in order to evaluate the parameters which affect the heat loss coefficients and the collector efficiency of a flat plate solar collector with screen wire wick heat pipes. The methodology that was used will be explained as well as a discussion on the results that were obtained.

2

Mathematical Formulation

The specific characterization of this type of collector is that heat pipes sealed on the absorber plate have a porous structure filled with an amount of methanol. Each of them will transfer the energy absorbed in the evaporator section to the condenser section where the condensate returns by the assistance of the porous structure and gravity (see Fig. 1). The enlarged view of the evaporator cross section is shown in Fig. 2.

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Fig. 1

Fig. 2

Heat pipe solar collector

Evaporator cross section (enlarged)

Various assumptions were made to facilitate the theoretical analysis: (i) (ii) (iii) (iv) (v) (vi) (vii)

steady-state condition the flat fin thickness is rather small to neglect the transverse temperature gradient the internal heat transfer coefficients in the heat pipes are constant along the evaporator and condenser the temperature gradient over the heat pipe perimeter may be neglected the end face area of the extreme collector blocks is relatively small; this allows neglecting the end heat losses the saturation temperature in the heat pipe was assumed constant the bond resistance between the fin and heat pipe is neglected

031016-2 / Vol. 135, AUGUST 2013

The temperature distribution over a fin flat plate in one collector element is described by the following equation [15,16]: T 4 Tg4 d2 T ks kp dp 2 ¼ Iabs þ ðT Ta Þ þ hpg T Tg þ r 1 1 dx ds þ 1 eg ep (1) With the boundary conditions dT ¼ 0; dx x¼0

Tjx¼Lp ¼ Te

(1a)

Transactions of the ASME


hpg is the heat transfer coefficient between the two parallel surfaces (glass cover, absorber plate), determined from the criteria relation of Hollands [17] for tiled angles u from 0 to 75 deg hpg ¼ Nu

ka L

1708ðsinð1:8uÞÞ1:6 Nu ¼ 1 þ 1:44 1 Ra cosðuÞ "

13 #þ RacosðuÞ þ 1 5830

# 1

1708 Ra cosðuÞ

The substitution of relation (3) into (1e) gives the transcendental algebraic equation for T of the form [16]

(1d)

Generally, with fixed Ta and Tg , Eqs. (1) and (1a) are solved using the finite difference technique to determine the distribution along a fin. In practice, the following condition is mainly fulfilled [16]: Tjx¼0 Te T Tg ;

T ¼

ð Lp T 0

dx Lp

(1e)

Considering this condition,

kp dp

ks ds (3c)

(1c)

þ

a Pr ¼ aa

Ub ¼

where hr,pg represent the radiation heat transfer coefficient from the absorber plate to the glass cover and is given by T2 þ Tg2 T þ Tg (3d) hr;pg ¼ r 1 1 þ 1 eg ep

and _ gbDT L3 Ra ¼ ; a a a

and

(1b)

where "

1 Ut ¼ 1=ðhpg þ hr;pg Þ þ 1=ðhw þ hr;ga Þ

d2 T ks ¼ Iabs þ ðT Ta Þ dx2 ds 2 3 2 2 þ T T T þ T g 6 7 g 7 T Tg þ6 4hpg þ r 5 1 1 þ 1 eg ep

(2)

Considering the boundary conditions, with hpg fixed and the expression of T (Eq. (1e)), the analytic solution of Eq. (1) has the following form [16]: coshðmxÞ TðxÞ ¼ Tg þ Tr þ Te Tg Tr coshðmLp Þ

(3)

tanh mLp 1 Tg þ Tr þ Te Tg Tr T ¼ Lp m

(4)

Estimating hpg and hloss, m can be calculated from Eq. (3b). The temperature distribution along a fin, at fixed Te and Tg , is obtained by finding the root of the algebraic Eq. (4) using a simple root procedure (Newton–Raphson method). The values of Te and Tg are determined using heat balance relationships for the heat pipe evaporator and the glass covering one finned heat pipe as shown in Fig. 2. The heat balance relation for the heat pipe evaporator is of the form (5) he Le ðTe Tsat Þp d Iabs Le 2Lp þ d þ Qloss ¼ 0 The first term on the left represents the heat gained by the heat pipe through convection, the second term represents the total solar radiation absorbed by the collector. Qloss is the amount of heat lost by heat transfer (by convection, radiation, and conduction through the heat insulation layer to the surrounding air) from the heat receiving surface of one glasscovered finned heat pipe which can be expressed as follows: T4 Tg4 2Lp Le Qloss ¼ 2Lp Le hpg T Tg þ Ub ðT Ta Þ þ r 1 1 þ 1 eg ep Te4 Tg4 þr (5a) dLe þ Ub Le dðTe Ta Þ 1 1 þ 1 eg ee

where Tr ¼

1 hloss

Iabs þ

ks Ta Tg ds

(3a)

and 0

hloss

1 2 2 T þ Tg T þ Tg C k B Cþ s; ¼B @hpg þ r A ds 1 1 þ 1 eg ep

hloss m2 ¼ kp dp (3b)

Iabs ¼ I(apsg)e is the solar radiation absorbed on the tiled collector, and (apsg)e is the effective absorptance-transmittance product evaluated from the correlation given in [15]. hloss is the global heat losses transfer coefficient between the cover and the fin plate. We can define the top and back heat losses coefficients Ut and Ub, respectively, as (Fig. 2) Journal of Solar Energy Engineering

The third term is the radiation loss from the heat pipe to the glass cover; we assume here that the heat pipe emissivity ee is equal to that of the absorber plate ep. The heat balance relationship for the glass covering one finned heat pipe is given by h i 4 hw Tg Ta þ r eg Tg4 T1 2Lp þ d Le ag I 2Lp þ d Te4 Tg4 T4 Tg4 2Lp Le hpg T Tg r 2Lp Le r dLe ¼ 0 1 1 1 1 þ 1 þ 1 eg ep eg ep (6) The first term on the left is the heat lost by convection between the glass cover and the surrounding air due to wind velocity, the second is the heat lost by radiation between the glass cover and the surrounding air, the third is the solar heat absorbed by the glass cover, the fourth is the heat loss by convection, the and fifth AUGUST 2013, Vol. 135 / 031016-3


and six terms are heat lost radiation from the absorbed plate and the heat pipe tube to the glass cover. If we introduce the expression of Qloss, Eq. (6) can be written as h i 4 hw Tg Ta þ r eg Tg4 T1 2Lp þ d Le ag I 2Lp þ d þ Ub 2Lp Le ðT Ta Þ þ Ub Le d ðTe Ta Þ Qloss ¼ 0

manifold wall and the cooling liquid. The heat gained by the flowing fluid from one condenser section of the heat pipe can be expressed as Qc;i ¼

(7)

The resolution of Eqs. (5) and (7) requires the knowledge of convective heat transfer coefficients hw, he, and the sky temperature T1. The wind heat transfer coefficient has the expression [18] hw ¼ 5:7 þ 3:8Vw

T1 ¼ 0:0552 Ta1:5

Nucl ¼

Qc ¼

The first term in Eq. (8) is the energy transferred from the plate toward the tube edge per tube unit length. The second term is the energy transferred by the glass cover to the half of the tube per tube unit length; this can be written respectively by qtot ¼ qfin þ qtube

(8a)

where

¼ 2mkp dp Te Tg Tr tanhðmLp Þ

(8b)

and

N X

3

T 4 Tg4 7 d6 7 g Þ r e I h ðT T qtube ¼ 6 abs pg e 5 1 1 24 þ 1 eg ep

(8c)

Eventually this useful energy must be transferred to the fluid passing through the manifold via the condenser section of the heat pipe, subject of many thermal resistances. Indeed, for a single heat pipe, the heat transferred from the evaporator outer surface to the condenser outer surfaces may be written as qtot;i Le ¼

ðTe Tc Þ Re þ Rc

(9)

This heat will be transferred to the cooling liquid by heat conduction through the manifold wall, and heat convection between the 031016-4 / Vol. 135, AUGUST 2013

(10a)

mC _ P;l ðTiniþ1 Tini Þ ¼ mC _ P;l ðTout Tin Þ

(10b)

i¼1

The theoretical efficiency of the solar collector is usually defined as the ration of the extracted heat in the manifold to the incident solar radiation on the absorber g¼

Qc IAc

(10c)

Equation (9) introduces the thermal resistance of the heat pipe (see Fig. 3). The circuit can be simplified by eliminating the resistances which have little significance, like the resistances in the adiabatic regions and the axial vapor resistance since a saturation temperature is assumed along the axial length of the heat pipe. Therefore, only radial resistances are taken into account [20]. Within the evaporator section, the thermal resistances which account for temperature drops are container wall resistance Rp,e, wick conduction resistances Rw,e, and the liquid-vapor interface resistance at the evaporator Ri,e. These resistances can be expressed respectively as follows:

Rp;e Ri;e

2

hcl Dh ks

Dh is the hydraulic diameter which depends on the geometry of the manifold [11]. The useful heat gained by the outlet manifold fluid is therefore equal to the summation of heat rejected from the condenser section of a number N of heat pipe.

(7b)

Using the Newton method, the minimization of Eqs. (5) and (7) allows us to find Te and Tg which are used to calculate the temperature distribution T(x) along the fin plate. Knowing the plate temperature distribution, it is possible to calculate the useful energy transferred to the heat pipe (qtot) per unit length of heat pipe [19] 2 3 4 4 Te Tg 7 dT d6 7 þ 6Iabs hpg ðTe Tg Þ r qtot ¼ 2kp dp 5 1 1 dx x¼Lp 2 4 þ 1 eg ep (8)

(10)

hcl is the convective heat transfer coefficient of the cooling fluid which depends on the velocity of fluid and the condenser cross section area, it can be expressed using the annular flow model [10]

(7a)

The evaporator heat transfer coefficient he ¼ (ReAe)1 depends on heat pipe resistance in the evaporator section and the outer heat pipe area. The expression of the sky temperature has the form [18]

qfin

Ac ðTc Tini Þ _ p;l ðTiniþ1 Tini Þ ¼ qtot;i Le ¼ mC ds 1 þ ks hcl

ln do;w =di;w Rw;e ¼ ; 2pLe keff rffiffiffiffiffiffiffiffiffiffiffiffi 2 Rv Tsat Rv Tsat ¼ 2 2p hfg Psat ðdi =2ÞLe lnðd=di Þ ¼ ; 2pLe kp

(11)

Psat ¼ 3.8 105 Pa is the vapor saturation pressure which corresponds to the vapor saturation temperature of the working fluid (Tsat ¼ 337 K). The effective thermal conductivity of the wick structure (screen wire mesh) saturated with the working fluid is calculated as follows [21]: keff ¼

kl ½ðkl þ kw Þ ð1 cÞðkl kw Þ ½ðkl þ kw Þ þ ð1 cÞðkl þ kw Þ

(11a)

Stainless steel with three layer was used for the wick structure because it is compatible with the three fluids tested. The other characteristics and geometry of the wick in the heat pipe are summarized in Table 1. The equivalent thermal resistance in the evaporator section is then Transactions of the ASME


Fig. 3

Heat pipe thermal resistances [20]

Table 1 Heat pipe wick design properties [20] Property Mesh number Effective capillary radius Porosity

Value

Expression

50 Mesh/in. ¼ 1968.5 Mesh/m 2.54 104 m 0.6289

N rce ¼ 1=2 N 1 c 1 pS N dw 4 dw2 c3 K¼ 122ð1 cÞ2

7.74 1010 m

Permeability

Width of apparatus: ww ¼ 2.3226 104 m Wick thickness: tw ¼ 0.0014 m

Table 2

Geometry

Wire diameter: dw ¼ 0.00023 m Crimping factor: S ¼ 1.05

Basic dimensions specifications of the different components of the collector

Collector

Length: 1.96

Width: 1.0 m

Depth: 0.1 m

Glass cover

Material: window glass Air gap: L ¼ 0.05 m

Dimension: 1.550 0.96 0.004 m

Collector effective area: (Ac) ¼ 1.488 m2

Absorber plate

Material: copper Thickness: 0.001 m 6 copper heat pipe Evaporator length: 1.550 m

Length: 1.550 m Conductivity: kp ¼ 385 W/(m K) Outer diameter: 0.0127 m Adiabatic length: 0.04 m

Tube’s spacing: wt ¼ 0.160 m

Material: glass wool Material: aluminum Liquid inside: water

Conductivity: kS ¼ 0.034 W/(m K) Dimension: 0.97 0.17 0.04 m

Heat pipes Insulation Manifold

Re ¼ Rp;e þ Rw;e þ Ri;e

(11b)

and the equivalent thermal resistance in the condenser region is Rc ¼ Rc;e þ Rw;c þ Ri;c

(12)

where Rp;c Ri;c

ln do;w =di;w Rw;c ¼ ; 2pLc keff rffiffiffiffiffiffiffiffiffiffiffiffi 2 Rv Tsat Rv Tsat ¼ 2 2p hfg Psat ðdi =2ÞLc lnðd=di Þ ¼ ; 2pLc kp

(12a)

During the operation of heat pipes, there are some performance limits on these devices. The wick structure is carefully chosen to overcome these limits. The important limits are the viscous limit, Journal of Solar Energy Engineering

Inner diameter: 0.0117 m Condenser length: 0.170 m Thickness: 0.05 m Mass flow rate: m_ ¼ 0:02 kg=s

capillary limit, sonic limit, boiling limit, and entrainment limit [21]. The viscous limit is reached when the vapor flow is governed by viscous forces due to the very low operating temperature and low vapor densities. The capillary pumping limit is reached when the total pressure drop in the heat pipe is equal or superior to the maximum capillary pressure difference, then the maximum axial heat transport capability is reached. This will lead to an interruption of the condensate back flow to the evaporator, which will then dry out or burn out. Another condition occurs when the velocity in the adiabatic section becomes sonic. At this point the flow is shocked, and the maximum flow rate is attained. Clearly the heat transported through the heat pipe cannot be increased further beyond this point, which is commonly called the sonic limit. For high gas velocities, the interface between the gas and liquid also becomes highly agitated and disturbance waves appear. These waves are torn from the surface giving rise to drop entrainment in the gas AUGUST 2013, Vol. 135 / 031016-5


Table 3 Collector parameters and heat pipe limits Collector parameters Plate absorbance: ap ¼ 0.9 Plate emissivity: ep ¼ 0.95 Cover transmittance: sg ¼ 0.81 Cover emissivity: eg ¼ 0.89 Limits (W)/fluid types

Methanol

Capillary limit: Viscous limit: Entrainment limit: Sonic limit: Boiling limit:

48.1 2.07106 873.4 6.98104 884.01

Table 4

Cover absorptivity ag ¼ 0.08 Inclination angle to horizon: u ¼ 45 deg Ambient temperature: Ta ¼ 298 K Wind velocity: Vw¼ 0 m/s Ethanol Acetone 1.08104 3.15105 2.21104 5.10104 970.66

9.98103 1.41105 3.42104 8.33104 1.74103

Energy heat balance verification Collector (Ac ¼ 1.488 m2)

Solar energy gain (W) (IAc)

Heat loss (W) Qloss

Heat gain in water (W) Qc

Relative error ½ðIAc Þ ðQloss þ Qc Þ=ðIAc Þ

370.7 381.8 393.0

503.2 754.0 1004.4

0.0211 0.0458 0.0608

892.8 1190.4 1488

core and this limit is called the entrainment limit. For high radial heat fluxes to the evaporator nucleate boiling can occur. If the vapor bubbles do not expel from the capillary structure a vapor layer will effectively insulate the heated evaporator which gets overheated (burned out), this limit is called the boiling limit. For all the fluids tested and while calculating heat pipe limits, it was found that these limits are not reached (Table 3). For example, with a methanol heat pipe it was found that heat pipes had a heat transport factor of around 48 W corresponding to its capillary limit. The designed heat transfer limit is sufficient enough to transfer the heat gained by the heat pipe tube, as the maximum heat gained by the heat pipe tube for I ¼ 1200 W/m2 was around qtube Le ¼ 18.7 w only.

3

Results

A program code was developed to simulate the heat pipe solar collector behavior, where we consider the air thermal characteristics between the glass cover and absorber plate as functions of the mean plate temperature. The basic specific dimensions of the heat

Fig. 4 Mean fin plate temperature and water outlet temperature compared with experimental data

031016-6 / Vol. 135, AUGUST 2013

pipes collector under investigation are summarized in Table 2. Methanol heat pipe limits with the collector optical and atmospheric parameters are summarized in Table 3. In order to validate the numerical results given by the developed code, two methods are used. A numerical method, by verifying the energy heat balance calculated since heat is always conserved (see Table 4) and an experimental method, by comparing the mean fin plate temperature T and the outlet water temperature Tout with the experimental data carried out by Atig [22] in LESTE for different incident solar radiation. The simulation is carried out with the parameters value given in Table 2, where a methanol heat pipe solar collector is constructed and tested. A good agreement between the experimental and the numerical results is shown (Fig. 4). Figure 5 shows an example of the fin plate temperature distribution TP, generally difficult to calculate in traditional solar collectors models. The temperature reaches a maximum value in the middle distance of the absorber plate and the minimum temperature is the evaporator temperature. Figure 6 shows that both the collector and the fin efficiency are affected by tube spacing distance specially the fin efficiency defined as gfin ¼ tanhðmLP Þ= mLp . This is because the collector

Fig. 5 Fin plate temperature distribution example



Fig. 6 The effect of tube spacing distance on the performance of the collector

Fig. 8 The effect of the number of H.P on collector efficiency

Fig. 7 The effect of tube spacing distance on the performance of the collector for three absorber plate thermal conductivities

Fig. 9 The effect of plate emissivity on the performance of the collector

heat losses increase due to the large area subject to convection and radiation. Indeed, an increase of the glass temperature is observed when the tube’s distance increases; a double glazing therefore is to plan to limit the losses. The effect of the absorber plate thermal conductivity with tube spacing distance on the collector and the fin efficiencies are shown in Fig. 7. The collector and the fin efficiencies are strongly affected at the low plate’s thermal conductivities values. This is may be due to the relatively small amount of heat required to the heat pipe which affects the collector performance. Aluminum can be chosen as an absorber plate but for a specific tube’s spacing distance. The results revealed by Hussien [3–5], which indicate that the tube’s spacing limited the selection of an absorber plate to one having a high value of thermal conductivity, is also valid for a wick assisted heat pipe. The effect of the number of heat pipes on collector efficiency is shown in Fig. 8 for different working fluids at fixed tube’s distance. One can see that the increase of the HP number of up to the value of about 10 gives a substantial improvement in the collector efficiency. A little further improvement is shown above this value. This is because the heat loss in the manifold (condenser region) increases limiting the increase of the collector performance. In other words, the water temperature passing across the manifold increase gradually from one heat pipe to the next when the number of HP increases. Consequently, the heat transfer by conduction through the manifold wall and by convection between

the manifold wall and the cooling liquid will increase, also limiting the collector performance. Figure 9 shows the effect of the plate emissivity on the collector and the fin efficiencies. A remarkable decrease in the fin efficiency can be observed when the plate emissivity ep increases, also, the collector efficiency is reduced by about 14% when ep increases from 0.1 to 0.95. This is because the overall heat loss coefficient increases. The radiation is the dominant mode of heat transfer between the absorber plate and cover in the absence of a selective surface. When a selective surface having an emittance of 0.1 is used, convection is the dominant heat transfer mode since low emissivity coating can significantly reduce radiative heat losses of glass panes (see Fig. 10). The air gap spacing between the absorber plate and the glazing is a factor that contributes to the decreasing of the collector’s efficiency (Fig. 11). The heat loss coefficients decrease as the air gap spacing increases due to the decreasing of the heat loss coefficient between the glass cover and the absorber plate hpg. Optimizing this gap reduces the convective heat losses from the absorber plate to the glazing cover. An optimal gap of about 6 cm is suitable for the three fluids tested because the collector efficiency is at maximum and the heat loss coefficients are at minimum (Fig. 12). The optimum ratio Le/Lc (evaporator length to condenser length) also can be obtained from plotting useful heat gained by the water passing across the manifold versus Le/Lc as shown in Fig. 13. From different values of solar radiation, and for the three


AUGUST 2013, Vol. 135 / 031016-7


Fig. 13 The optimum value of Le/Lc Fig. 10 The effect of plate emissivity on heat loss coefficients and glass cover temperature

Fig. 11 The effect of plate-cover distance on the performance of the collector

Fig. 14 Collector efficiency curve for different working fluid

Fig. 15 Collector efficiency curve compared with earlier works

Fig. 12 The effects of plate-cover distance on overall heat loss and heat loss coefficients

fluids tested, the useful heat reaches a maximum within an interval of about 8 to 10. Note that a value of 8.25 is given by Azad [23] who used the ethanol as a working fluid with no wick in the condenser region. 031016-8 / Vol. 135, AUGUST 2013

Figure 14 shows the efficiency plot for the collector. The efficiency varies linearly with ðTw Ta Þ=I, where Tw ¼ ðTin þ Tout Þ=2 is the average water temperature. The results indicate that acetone performs better than the other fluids like methanol or ethanol. In Fig. 15 the collector curve approaches the numerical result carried out by Façao and Olivera [24,25] for the methanol heat pipe while taking the same collector specific dimensions. The results are also compared with the thermal performance of a thin membrane heat pipe solar collector carried by Riffat [10]. Transactions of the ASME


4

Conclusions

A theoretical analysis is performed on the flat plate heat pipe collector with a single glass cover using an assisted wick heat pipe. These collector types are paid less attention in literature. The results are first compared with experimental data of the prototype heat pipe designed and parametric study is performed to evaluate the thermal efficiency of the collector. It can be concluded that the emissivity of the absorber plate has a significant impact on the top heat loss coefficient and consequently on the efficiency of the collector. The increase of the heat pipe number and consequently the incident surface area does not compensate for a significant increase of the collector efficiency because the heat loss in the manifold increases. Results showed a collector’s efficiency of 70% and an overall heat loss coefficient of 3.7 W/(m2K) with a methanol heat pipe which approaches the result carried by Façao [24]. Three different fluids are compared and the result show that acetone performs better. Finally, the model is capable to predict some performance characteristics of the solar system which may contribute to improved wick assisted heat pipe solar collector’s designs.

Nomenclature A¼ Cp ¼ d¼ di ¼ dw ¼ g¼ h¼ hfg ¼ I¼ Iabs ¼ K¼ L¼ LP ¼ m¼ m_ ¼ N¼ Nu ¼ Pr ¼ q¼ Q¼ R¼ Ra ¼ Rv ¼ rce ¼ T¼ T ¼ Tr ¼ Tin ¼ Tout ¼ Tw ¼ U¼ V¼ wt ¼ ww ¼ x¼

area, m2 specific heat, J/(kg K) outer tube diameter, m interior tube diameter, m wire diameter, m acceleration due to gravity, m/s2 heat transfer coefficient, W/(m2K) latent heat, J/kg global solar radiation intensity, W/m2 solar radiation absorbed, W/m2 permeability, m2 distance between a receiving plate and glass, m flat fin half width, m metal coefficient mass flow rate, kg/s wire number, 1/in. or 1/m Nusselt number Prandtl number heat flux per unit length, W/m2 heat flow rate, W thermal resistance, K/W Raleigh number vapor constant, 488 J/(kg K) effective capillary radius, m temperature, K mean fin plate temperature, K reduced temperature, K inlet water temperature, K outlet water temperature, K average stored water temperature, K overall heat transfer coefficient, W/(m2 K) velocity, m/s tubes’ distance, m wick wire width, m coordinate

Greek Symbols a¼ aa ¼ b¼ e¼ u¼ c¼ g¼ s¼ ¼

absorptivity air thermal diffusivity, m2/s gas volume expansion coefficient emissive coefficient inclination angle to horizon, deg porosity efficiency transmittance kinematic viscosity, m2/s


d¼ l¼ k¼ kw ¼ r¼ 1¼

fin plate thickness, m fluid absolute viscosity, kg/(m s) thermal conductivity, W/(m K) thermal conductivity of the wick, W/(m K) Stefan–Boltzmann constant, 5.67 108 W/(m2 K4) sky

Subscripts and Superscripts a¼ abs ¼ b¼ c¼ coll ¼ e¼ eff ¼ f in ¼ g¼ i¼ l¼ lat ¼ loss ¼ n¼ p¼ r¼ s¼ sat ¼ t, top ¼ tot ¼ tube ¼ w¼ þ¼

air, ambient absorbed back, bottom, edge collector, condenser gained by collector evaporator effective fin plate glass cover inner, interface liquid lateral losses number absorber plate radiation, reduced insulation layer saturation top total tube wind, water, wick max

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