Experimental investigation of phase change material melting in rectangular enclosures with horizontal partial fins

International Journal of Heat and Mass Transfer 78 (2014) 839–851

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Experimental investigation of phase change material melting in rectangular enclosures with horizontal partial fins Babak Kamkari ⇑, Hossein Shokouhmand School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 13 April 2014 Received in revised form 5 July 2014 Accepted 21 July 2014 Available online 8 August 2014 Keywords: Phase change material Melting enhancement Partial fin Fin effectiveness

a b s t r a c t This paper presents an experimental investigation of phase change material (PCM) melting in a transparent rectangular enclosure with and without horizontal partial fins. The enclosure was heated isothermally from one side while the other walls were thermally insulated. Experiments were performed with wall temperatures of 55, 60 and 70 °C (3:6  108 6 Ra 6 8:3  108 ) for finned and unfinned enclosures. Visualization of the melting process and the temperature field were performed directly. Both qualitative and quantitative information about the melting phenomena were obtained using digital photographs of the instantaneous melt front evolutions and temperature recordings at the vertical mid-plane of the enclosure. Temperature histories revealed that the thermally stratified region became smaller as the number of fins increased. Experimental data were used to calculate melt fractions, heat transfer rates and Nusselt numbers during the melting process. Furthermore, two correlation equations were developed using the dimensionless parameters to predict the Nusselt number and melt fraction. Also, in order to evaluate the improved thermal performance of the enclosure in the presence of partial fins, two other parameters were defined, melting enhancement ratio and overall fin effectiveness. Experimental results indicated that increasing the number of fins decreased the melting time and increased the total heat transfer rate while the surface-averaged Nusselt number reduced. Melting enhancement ratio and overall fin effectiveness increased with increasing the number of fins and decreased with raising the wall temperature. Melting enhancement ratios decreased with time after reaching some maximum values indicating that partial fins are more beneficial during the initial time of the melting. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Thermal energy can be stored in a material as sensible heat by raising its temperature or as latent heat during the phase change process. Sensible heat storage systems have low specific heat capacity. On the other hand, thermal energy storage systems based on phase change materials (PCMs) are particularly attractive because of their high energy storage capacity and isothermal behavior during charging (melting) and discharging (solidification) processes. There is a wide range of applications for PCMs such as solar thermal systems [1,2], desalination [3], heat recovery [4], buildings [5,6], refrigeration [7], electronics cooling [8,9] and spacecrafts [10,11]. PCMs can be generally classified into metallic and nonmetallic groups. Metallic PCMs such as tin and gallium have high thermal conductivity but they are rarely used for commercial purposes due to their high cost, high density and very high or low phase change temperature. In contrast, nonmetallic PCMs including

⇑ Corresponding author. Tel.: +98 9124034778; fax: +98 2188013029. E-mail address: [email protected] (B. Kamkari). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.07.056 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

paraffins, fatty acids and hydrated salts have lower cost and a wider range of melting temperature which make them as promising candidates for different thermal applications. However, they suffer from low thermal conductivity leading to slow charging and discharging rates, hence requiring heat transfer enhancement techniques. Various methods for heat transfer enhancement of PCMs have been proposed and studied by many researchers. Some of the most common methods include using extended surfaces [12– 17], impregnation of porous materials [18–21], placement of high thermal conductivity metal structures [22,23], embedding heat pipes [24,25], dispersing high conductivity particles [26–28], adding carbon fibers [29,30] and carbon nanotubes [31,32]. Dispersing high thermal conductivity materials into PCMs seems to be less practical compared with incorporating metal structures into PCMs since the dispersed material usually agglomerates and sediments to the bottom of the enclosure in long-term operation [33]. It has been reported that low concentration of nanoparticle in PCM can improve the melting rate. However, melting rate is decelerated in the presence of high concentration of nano-additives as a result of the increased viscosity which leads to a significant degradation of natural convection during the melting process [34,35].

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Nomenclature Aw D Fo ¼ Hat2 H HAR  h hSL k L N NuðtÞ   Nu

total heat transfer area including base and fins (m2) depth of the enclosure (m) Fourier number height of the enclosure (m) heat transfer area ratio surface averaged heat transfer coefficient (W/m2 K) latent heat (kJ/kg) thermal conductivity (W/m K) fin length (m) number of fins surface averaged Nusselt number

Q ðtÞ

surface averaged heat transfer rate

time averaged Nusselt number

Using high thermal conductive fins in latent heat thermal storage systems is one of the simple, reliable and effective approaches to enhance the melting rate. Hence, this study is focused on the use of fins to improve the melting rate of the PCM. There are many studies related to heat transfer enhancement in PCM enclosures equipped with metallic internal fins. These researches can be divided into two groups based on the fin type: partitioning fin or partial fin. Partitioning fins extend into the PCM from the hot wall and divide the PCM enclosure into smaller individual enclosures so that the PCM is confined between the fins [36–38]. Reddy [36] carried out a numerical study on the melting process of paraffin wax in a solar integrated collector water heating system. The PCM was stored in a tilted rectangular enclosure heated from top and cooled from below. The simulation was performed with 4, 9 and 19 partitioning fins and without fins. Finned enclosures showed higher melting rates in comparison with enclosures without fins, while the best performance was attained with 9 fins. Gharebaghi and Sezai [37] investigated the enhancement of energy storage rate in a rectangular enclosure with partitioning fins which was filled with paraffin (RT27). Both horizontal and vertical modules were investigated with different fin spacings and wall temperatures. The heat transfer increased with decrease in the fin spacing for both the vertical and horizontal modules. It was also found that there is no distinct difference between the melting time of horizontal and vertical modules. Huang et al. [38] evaluated the effect of applying PCM on limiting the temperature rise of a silicon photovoltaic device and consequently maintaining the electrical conversion efficiency of the photovoltaic module. The average temperature on the front surface of the system was measured for finned and unfinned cases. The temperature rise on the front surface decreased and thermal stratification within the PCM reduced as the number of fins increased. Despite the beneficial effect of adding partitioning fins, the reduced time of the temperature control and increased weight of the system due to the metal fins were mentioned as potential problems of this system. Shatikian et al. [12] numerically simulated melting of PCM (paraffin wax) between partitioning vertical fins in a horizontal heat sink with constant base temperature. They performed a parametric study to consider the effect of fin length, fin thickness and fin spacing on melting rate. The melting rate accelerated as the fin spacing decreased. They generalized the results through dimensional analysis and showed that for wide vertical PCM layers, convection motion in the melted PCM should be taken into account. In another study, the same authors [39] considered the melting process in the same physical model by applying a constant heat flux to the horizontal base plate.

D E Q Ra ¼ Ste⁄ t T Tm Tw

time averaged heat transfer rate gbðT w T m ÞH3

Rayleigh number based on the height of the enclosure modified Stefan number time (s) temperature (°C) melting temperature (°C) wall temperature (°C)

ma

Greek symbols efin overall overall fin effectiveness a thermal diffusivity (m2/s)

Akhilesh et al. [17] performed a numerical study to find the appropriate size of composite heat sink constructed from a vertical array of partitioning fins extended downward from a horizontal base plate. The study excluded the role of natural convection inside the melted PCM and found that increasing the number of fins beyond a critical value does not show any significant enhancement in thermal performance of the composite heat sink. Levin et al. [40] presented an optimization procedure for the design of a PCM based heat sink used for transient cooling of electronic devices. Neglecting the internal convection in the liquid PCM, it was found that optimal PCM percentage depends on the number and length of the fins, heat flux, and the difference between the critical and melting temperature of the PCM. Wang et al. [41] numerically investigated the effect of orientation of a PCM (paraffin wax) based heat sink with vertical partitioning fins. It was concluded that the orientation of the heat sink has a limited effect on the thermal performance of the system. Unlike the partitioning finned enclosure in which the PCM is confined between the fins, in an enclosure with partial fins, the melted PCM can flow between the fins. Plate fins with a length less than the PCM thickness [42,43] and pin fins [13] can be classified as partial fins. Lacroix and Benmadda [42] studied convection-dominated melting of PCM (n-octadecane) in a vertical rectangular enclosure with partial plate fins which extended horizontally from the heated wall. The study included the effect of number and length of the fins on the melting rate. It was concluded that a few longer fins significantly accelerate the melting process while the effect of shorter fins is much less significant. Applying a few longer fins was found to be more efficient for reducing the melting time than increasing the temperature of the vertical wall. Huang et al. [43] numerically and experimentally investigated thermal regulation of building integrated photovoltaic system by applying PCM in a rectangular enclosure attached to the rear side of the photovoltaic module. The effect of using partial plate fins on operational efficiency of the photovoltaic facade was studied. Thermal performance of the photovoltaic system was increased by using metal fins in the PCM enclosure. However, increased number of fins hampered the convection driven flow of the melted PCM and decreased the beneficial effect of natural convection on regulating the temperature of the photovoltaic module. Baby and Balaji [13] investigated the thermal performance of finned heat sinks filled with PCM (n-eicosane) for thermal management of electronic devices. Experiments were performed for heat sinks with vertical fins (partitioning or pin fins) and without fins while a uniform heat load was applied to the base plate. Among the fin geometries, the heat sink with pin fins showed the maximum performance.

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From the above literature review, one can see that there are very few studies on melting heat transfer in rectangular enclosures with horizontal partial fins. Moreover, there are not much experimental data about the shape of the solid–liquid interface and temperature history of the PCM in this regard. Therefore, in the present study a detailed experimental investigation is carried out by visualizing the solid–liquid interface evolution and temperature distribution in rectangular enclosures with and without partial fins during the melting process. Visualization of the melting process clearly demonstrates the contribution of natural convection to the melting process, and the extent that the melting rate can be enhanced in the presence of partial fins. The results of the present study improve the fundamental understanding of the phenomena of convection driven melting process in enclosures with partial fins and quantify the effectiveness of fins to increase the melting rate. Furthermore, two correlation equations for melt fraction and Nusselt number are developed based on the combination of dimensionless parameters. 2. Experimental apparatus Detailed explanation of the experimental setup and test procedure have been described in the previous study [44]. Lauric acid with 99% purity was used as PCM in this research. It is an environment friendly material obtained from vegetable and animal oils [45]. Table 1 shows the thermophysical properties of the lauric acid. The PCM was contained in a rectangular enclosure with interior dimensions of 50 mm in width, 120 mm in height and 120 mm in depth. Three types of heat exchangers with plain wall, 1-fin wall Table 1 Thermophysical properties of lauric acid [44]. Specific heat capacity solid/liquid (kJ/kg K) Melting temperature range (°C) Latent heat of fusion (kJ/kg) Thermal conductivity solid/liquid (W/m K) Density solid/liquid (kg/m3) Kinematic viscosity (m2/s) Prandtl

2.18/2.39 43.5/48.2 187.21 0.16/0.14 940/885 6.7  106 100.7

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and 3-fin wall were made from aluminum slabs using milling process. Fabrication of the finned heat exchangers using milling process ensured no thermal contact resistance between the fin base and heated wall. Fins had a thickness of 4 mm and a length of 25 mm. Thermocouples with a small wire diameter of 0.21 mm were placed at the vertical mid-plane of the enclosure to measure the transient temperature distribution within the enclosure. Numbers of the thermocouples in the unfinned, 1-fin and 3-fin enclosures were 32, 30 and 26, respectively. Fig. 1 shows the arrangements of thermocouples in the finned and unfinned enclosures. The thermocouples were arranged in a staggered way in 7 rows and 9 columns. Although the number of thermocouples in the finned enclosures was reduced in comparison with the unfinned one, the numbering procedure remained the same. This was done for the ease of comparison of the temperatures at the same locations in the different enclosures. Three sets of experiments were conducted for each enclosure at different wall temperatures of 55, 60, and 70 °C. All experiments were initiated by the solid PCM at a uniform temperature of 25 °C and continued until the PCM melted completely.

3. Results and discussions 3.1. Solid–liquid interface evolution Visualization of the instantaneous shape of the solid–liquid interface can reveal the dominant role of convection currents on the melting phenomena. Fig. 2 presents the photographs of the melting process in the finned and unfinned enclosures at different times while the right wall is maintained at 70 °C. Special lighting photography enabled clear identification of the solid and liquid phases of the PCM. In these photographs, the white and black colors represent the solid and liquid phases of the PCM, respectively. Fig. 2(a)–(e) visualizes the melting process of the PCM in the unfinned enclosure. Initially, the thickness of the liquid PCM is nearly uniform along the height of the enclosure indicating the dominant role of conduction heat transfer within the thin liquid layer. As the time progresses, the thickness of the liquid PCM at the top of the

Fig. 1. Arrangements of thermocouples in the finned and unfinned enclosures: (a) unfinned enclosure (b) 1-fin enclosure (c) 3-fin enclosure.

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Fig. 2. Photographs of the melting process in the rectangle enclosure with partial fins and without fins at every 10 min while the right wall is maintained at 70 °C.

enclosure grows faster than that of the lower part of the enclosure. This interface behavior implies the prevalence of the buoyant force to the viscous force and consequently, the initiation of natural convection current in the liquid region. Liquid PCM rises along the hot wall and descends along the solid–liquid interface making

a counter-clockwise circulating current. The strength and size of the circulating flow decrease as the melting continues and the solid PCM shrinks. Fig. 2(f)–(j) shows the melting process in the enclosure with one horizontal partial fin added at the middle of the enclosure. Higher

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melting rate of the PCM at the base of the fin relative to the tip of the fin is due to the temperature decrease along the fin length as a result of the heat conduction and limited thermal conductivity of the aluminum fin (Kal = 130 W/m K). During the early time of convection dominated melting (Fig. 2(g)), the vertical shapes of the interface below and above the fin are similar, indicating analogous buoyant circulating flows in both halves of the enclosure. As time elapses (Fig. 2(h)–(j)), the melting rate above the fin increases significantly in comparison with lower part of the enclosure. The heat transfer at lower half of the enclosure, under the fin, is governed by a continuous thermal boundary layer initiating from the bottom of the hot wall and ends at the tip of the fin. In lower half of the enclosure, the uprising liquid PCM along the hot wall is diverted to the left as it reaches to the fin and continues its way along the bottom surface of the fin. The flow is divided into two streams when it reaches to the tip of the fin. A portion of the liquid PCM impinges to the solid–liquid interface and cools down along the interface and the other part flows to the upper half of the enclosure through the gap between the fin tip and the interface. The heat transfer at

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the upper half of the enclosure is controlled by the thermal plumes arising from the top surface of the fin and natural convection boundary layer on the vertical hot wall. The enhanced melting rate over the horizontal fin is attributed to the vortex motion of thermally driven flows above the fin surface. It is interesting to draw attention to the similarity of interface curvature at the top of 1-fin (Fig. 2(f)–(j)) and unfinned (Fig. 2(a)–(e)) enclosures. This reveals that circulating convection current at the top of the 1-fin enclosure is not influenced by the thermal plumes originating from the fin surface. Fig. 2(k)–(o) illustrates the melting process in the enclosure with three partial fins. The concave and convex curvatures of the interface show that the natural convection is totally altered by the fins. Afterwards the solid PCM between the fins melts completely, the interface at upper part of the enclosure advances more uniformly in comparison with the other two enclosures. Fig. 3 shows the evolution of the solid–liquid interface in the finned and unfinned enclosures at different wall temperatures of 55, 60 and 70 °C. It can be seen that any increase in the wall

Fig. 3. Solid–liquid interface progress during the melting of PCM in the finned and unfinned enclosures at different wall temperatures.

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temperature in the range of 55–70 °C expedites the melting process and advances the initiation of convection current. However, increasing the wall temperature has no distinct influence on the shape of the solid–liquid interface. 3.2. Temperature distribution Qualitative presentations of the temperature distribution at the vertical mid-plane of the enclosures are obtained using the instantaneous temperature data of thermocouples and the solid–liquid interface as an isothermal curve with constant temperature of 43.5 °C. Fig. 4 illustrates the evolution of temperature contours at the vertical mid-planes of the enclosures with and without fins while the right wall temperature is maintained at 70 °C. Fig. 4(a)–(e) shows the transient temperature field during melting of the PCM in the unfinned enclosure. At early stages (Fig. 4(a)), the isotherms appear to be uniformly parallel to the hot wall indicating that the dominant mode of heat transfer is conduction. As time elapses, the liquid PCM rises up along the hot wall. It gains heat and attains the maximum temperature at the top of the enclosure. Hot liquid PCM is deflected towards the solid–liquid interface and impinges perpendicularly on the cold interface resulting in high melting rate at the top of the enclosure. Then the liquid PCM cools down as it descends along the interface leading to lesser melting rate at the lower part of the enclosure than the upper part. Fig. 4(f)–(j) illustrates the temperature distribution in the 1-fin enclosure. It clearly depicts the temperature rise of the PCM at the middle of the enclosure where the fin is added. The high-temperature region extends with time especially to the region above the fin indicating the existence of buoyancy driven vortex flows above the fin surface. Increasing the number of partial fins from 1 to 3 (Fig. 4(k)–(o)), shows that the temperature distribution in the melt region becomes more uniform due to the formation of vortex motions above the fins. The average temperature at the upper part of the enclosure increases and the melting rate accelerates. 3.3. Temperature history Temperature history of the thermocouples reveals more detailed information on thermal and flow characteristics of the PCM during melting in enclosures. Fig. 5 shows the temperature histories of some selected thermocouples placed at the first and fifth columns of thermocouples (T5, T14, T23, T32 and T3, T12, T21, T30) in finned and unfinned enclosures while the wall temperature is maintained at 70 °C. For all cases, when the temperature of thermocouples is below the melting limit (43.5 °C), heat is transferred to the thermocouples by conduction through the solid PCM. For the unfinned enclosure (Fig. 5(a)), initially the rates of the temperature increases for the first column of thermocouples (T5, T14, T23 and T32) are higher than those of the fifth column (T3, T12, T21 and T30), indicating the greater rate of heat conduction and more melting rate during the early time of the experiment. For the finned enclosures (Fig. 5(b) and (c)), the rates of temperature increases for those of the thermocouples at the fifth column placed above the fins (T21 in 1-fin enclosure and T12, T21, T30 in 3-fin enclosure) are higher in comparison to the same thermocouples in the unfinned enclosure. This is due to a higher rate of heat transfer to the solid–liquid interface above the horizontal fins. For all cases, when the temperatures of thermocouples rise to the melting limit of the PCM, sharp increase in temperature is observed as the liquid PCM passes the tips of the thermocouples, showing the transition time of the thermocouple tip from the solid–liquid interface to the edge of thermal boundary layer. Fig. 5(a) shows that the values corresponding to sharp temperature

increases, reduce from upper to lower thermocouples in each column. The dashed curves show the temperatures of the liquid PCM at the edges of the thermal boundary layers at two different vertical positions, first and fifth columns of the thermocouples. The decreasing trend of the temperature at the edge of the thermal boundary layer and increasing the transition time from upper to lower thermocouples are attributed to thickening of the thermal boundary layer as it flows down along the interface and also reveal the decreasing temperature of the bulk of the liquid PCM at lower level of the enclosure. During the melting process in finned enclosures (Fig. 5(b) and (c)), some temperature fluctuations are observed in temperature histories of the thermocouples placed above the fins. Similar temperature fluctuations were detected by Kamkari et al. [46] during melting of the PCM from below. Temperature fluctuations imply the presence of chaotic and vortical flow structures in the liquid PCM above the fin. It is interesting to note that the amplitude of temperature fluctuations decreases as the distance of the thermocouple from the hot wall decreases relating to wall effect. For instance, in Fig. 5(b), the amplitude of temperature fluctuations corresponding to T21 is more than T23 and the same is true for T21 and T23 in Fig. 5(c). The temperature fluctuations diminish as the interface above the fin recedes and the thickness of the liquid PCM increases. This temperature behavior implies the joining of transient vortical flow structures to form larger stable vortices. Also, it is found from Fig. 5 that thermal stratification occurs at some parts of the enclosures depending on the number of fins. During this process, hot lighter liquid overlays the cold denser liquid to form thermally stable layers. Fig. 5(a) depicts that the thermal stratification occurs in the unfinned enclosure and develops from upper part of the enclosure to its lower part, as time elapses. Table 2 lists the temperatures of the liquid PCM at the end of the melting process at some specific locations in four different rows of the thermocouples for finned and unfinned enclosures. It can help to find the thermally stratified regions for different cases. It clearly shows the closeness of the temperatures at each row and the decreasing trend of the temperatures from upper to lower rows in the unfinned enclosure. The average values of the temperatures of the 1st, 3rd, 5th and 7th rows are 62.3, 65.7, 67.4 and 68.4 °C, respectively. This thermal layering implies diminishing of convection currents at the upper part of the unfinned enclosure, as the melting completes. It can be seen from Fig. 5(b) that the thermally stratified region in the 1-fin enclosure is confined to the lower half of the enclosure while the temperatures of the thermocouples at the upper half of the enclosure converge to a limiting value indicating good mixing of the liquid PCM due to circulating current above the fin surface. Table 2 shows that the temperatures of the 5th and 7th rows of thermocouples in the 1-fin enclosure are close together with an average value of 68.5 °C due to liquid mixing while the average temperature of the 1st and 3rd rows of the thermocouples are 61.8 and 66.8 °C, respectively, which shows thermal stratification occurring at lower half of the enclosure. Similar explanations exist for the 3-fin enclosure. For 3-fin case, stratified region appears in a small region below the first fin and liquid mixing takes place in the regions between the fins and at the top of the enclosure. 3.4. PCM melting rate The influence of adding fins on the melting rate can be evaluated by temporal melt fraction which is defined as the ratio of the volume of the liquid PCM at each time to the initial volume of the solid PCM. Fig. 6 compares the melt fractions in the finned and unfinned enclosures with a wall temperature of 70 °C. For all considered cases, the ultimate values of liquid fractions are equal to unity which are corresponding to complete melting of the

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Fig. 4. Instantaneous temperature distribution at the vertical mid-plane of the enclosures with fins and without fins while the right wall temperature is maintained at 70 °C.

PCM in the enclosures. As evident, adding fins can accelerate the melting rate significantly. However, the mass of PCM in the enclosure decreases when the fins are incorporated. As mentioned by Sharifi et al. [14] a tradeoff exists between enhancement in the melting rate and the amount of energy that can be stored in the

enclosure. So, a modified melt fraction can be defined as the volume of the liquid PCM relative to the volume of the initial solid PCM in the enclosure without fins [14]. Fig. 7 illustrates the modified melt fractions in the finned and unfinned enclosures with hot wall temperature of 70 °C. It is apparent that the modified melt

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absorbed in the 3-fin enclosure is about 5% less than that of the unfinned enclosure. Dimensional analysis applied herein follows the approach suggested by Ho and Viskanta [47] and Shatikian et al. [12]. The product of the Fourier and Stefan numbers, SteFo, serves as an independent dimensionless parameter that takes into account the transient heat conduction and phase change. In the present study, the solid PCM is initially subcooled at 25 °C. Hence, a modified Stefan number, Ste⁄, is defined which accounts sensible heating of both solid and liquid phases of the PCM [24].

Ste ¼

C p;s ðT m  T o Þ þ C p;l ðT w  T m Þ hSL

ð1Þ

The evolution of the solid–liquid interface (Fig. 2) indicates that the natural convection in the liquid PCM plays an important role in the melting process. Thus, convection in the liquid phase is an additional physical phenomenon that should be accounted in this analysis. Rayleigh number is the appropriate parameter for this purpose defined based on the height of the enclosure. Fig. 8 shows the melt fraction versus an appropriate combination of the Fourier, Stefan, and Rayleigh numbers, namely Ste2FoRa0.25, for all cases considered in the present study. In this figure, Stefan numbers of 0.36, 0.43 and 0.55 are corresponding to wall temperatures of 55, 60 and 70 °C. It can be seen from Fig. 8(a) that the melt fractions for different cases, finned and unfinned enclosures, merge into single curves for various Stefan numbers, while the results remain clearly separated for the enclosures with different number of fins. In order to generalize the results for different cases, the effect of fins should be included in this analysis. It was found that the data can be well correlated by adding the parameter of (1 + N)0.5 to the group of dimensionless numbers. Fig. 8(b) shows that the melt fractions coincide on a single curve when they are plotted versus Ste⁄2FoRa0.25(1 + N)0.5. It can be seen that a remarkable agreement between the different cases has been achieved. An analysis of the results in Fig. 8(b) yields the following expression for the melt fraction:

MF ¼ a X b þ c X d

Fig. 5. Temperature history of thermocouples (T3, T5, T12, T14, T21, T23, T30 and T32) during melting of the PCM in the finned and unfinned enclosures at wall temperature of 70 °C: (a) unfinned enclosure (b) 1-fin enclosure (c) 3-fin enclosure.

fraction obtains a final value less than unity when melting occurs in the finned enclosure. The ultimate value of modified melt fraction reduces from 1 to 0.95 as the number of fins increases from 0 to 3. This implies that the maximum value of latent heat

ð2Þ

where X = Ste⁄2FoRa0.25(1 + N)0.5 and a, b, c and d are constants which are equal to 0.208, 1.900, 0.690 and 1.230, respectively. The root mean square deviation between the experimental data and correlation equation is 0.014. It should be noted that the effects of aspect ratio of the enclosure and fin length are not included in this correlation. The effect of increasing the number of fins on acceleration of the melting rate can be evaluated by introducing a new parameter, named ‘‘melting enhancement ratio’’ which is defined as the melt fraction in the finned enclosure relative to the unfinned enclosure at the same time. Fig. 9 presents the transient variation of the melting enhancement ratios for the finned enclosures with different wall temperatures. It shows that initially the enhancement ratios increase sharply and then decrease gradually after reaching a maximum value. The initial sharp increases are attributed to transition from conduction to convection heat transfer over the fin surfaces and formation of convective currents which accelerate the melting rate in the finned enclosure higher than that of the unfinned one. As the time passes, the effect of fins on melting rates decreases and the values of the enhancement ratios drop down to limiting values greater than unity. This decreasing trend is attributed to increasing thickness of the liquid PCM and hindering of the vertical convection current due to adding the horizontal fins. It can also be observed that for both 1 and 3-fin enclosures, the enhancement ratios increase with decreasing the hot wall temperature. In other words, fins are more efficient at lower wall temperatures.

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B. Kamkari, H. Shokouhmand / International Journal of Heat and Mass Transfer 78 (2014) 839–851 Table 2 Temperature of the liquid PCM at specific locations at the end of the melting process. Number of fins

Temperature (°C) 1st row

0 1 3

3rd row

5th row

7th row

T1

T3

T5

T10

T12

T14

T19

T21

T23

T28

T30

T32

61.5 61.0 64.0

62.5 62.0 64.1

63.0 62.3 64.5

65.0 66.6 68.2

65.7 66.8 68.3

66.4 67.0 68.5

67.2 68.1 68.4

67.4 68.4 68.9

67.5 68.5 69.2

68.3 68.4 68.7

68.4 68.8 69.1

68.6 68.9 69.2

Fig. 6. Comparison of the melt fraction variation versus time for finned and unfinned enclosures at wall temperature of 70 °C.

Fig. 7. Time history of the modified melt fractions in the finned and unfinned enclosures at wall temperature of 70 °C.

Fig. 8. Generalized results for the melt fraction at various wall temperatures and different number of fins: (a) Melt fraction versus Ste⁄2FoRa0.25 (b) Melt fraction versus Ste⁄2FoRa0.25(1 + N)0.5.

Fig. 10 shows the total melting time versus the number of fins at different wall temperatures. It clearly illustrates that the melting time decreases with increase in the number of fins. However, decreasing rate of the melting time reduces gradually as the number of fins increases due to the obstruction to the flow of natural convection currents owing to the presence of more fins, as explained before. As expected, increasing of wall temperature results in less melting time which is attributed to intensification of the convection currents in the enclosures.

Table 3 summarizes the melting time ratios for finned and unfinned enclosures with different wall temperatures. The melting time ratio is defined as the ratio of the total melting time of the PCM in the finned enclosure to the melting time in the unfinned enclosure. It can be seen that in 1 or 3-fin enclosures there is no significant changes in the values of melting time ratios with increasing the wall temperature. Hence, it can be concluded that irrespective of the wall temperature, adding 1 and 3 fins to the enclosure decreases the melting time about 18% and 37%, respectively.

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 ¼ hðtÞ

Q total ðtÞ Aw ðT w  T m ÞDt

ð4Þ

where Qtotal is the total heat absorbed by the PCM during the time interval (Dt) [44]. Aw is the total heat transfer area including base and fins calculated by:

Aw ¼ ðH  DÞ þ 2NðL  DÞ

Fig. 9. Variation of the melting enhancement ratio for finned enclosures at different wall temperatures.

Fig. 10. Total melting time versus number of fins at different wall temperatures.

ð5Þ

Fig. 11 compares the transient variation of surface-averaged Nusselt numbers for finned and unfinned enclosures with a wall temperature of 70 °C. For all cases, initially Nusselt numbers decrease sharply indicating the growing of the liquid layer thickness in the absence of the convection current. Then, Nusselt numbers reach quasi-steady values representing the convection dominated melting. Quasi-steady heat transfer is followed by reduction in Nusselt numbers due to weakening of the convection currents and increasing the temperature of the liquid PCM. It is also observed that the surface-averaged Nusselt numbers decrease when the number of fins increases. This is attributed to hampering of vertical convection currents along the vertical direction of the hot wall and decrease of the flow intensity, which result in decreasing of surface averaged Nusselt number when the fins are added. However, as shown in Fig. 12, total heat transfer rate augments when the number of fins increases due to the increase of the heat transfer area. So, it can be inferred that, in the tradeoff between the decrease in Nusselt number and increase in heat transfer area, the latter exceeds the former. It should also be mentioned that increasing the number of fins beyond an optimum value may lead to a significant increase in flow resistance and therefore the decreased Nusselt number overcomes the increased heat transfer area. This phenomenon has been reported by several researchers who investigated the singlephase convection heat transfer on finned surfaces [48–50]. The same approach used for correlating the melt fractions is applied to generalize the Nusselt numbers. Fig. 13 shows the Nusselt numbers normalized by Ra0.25 versus the combination of dimensionless parameters. Fig. 13(a) illustrates that for each enclosure, the normalized Nusselt numbers regarding to different Stefan numbers come together. However, the Nusselt numbers stay separate when the number of fins differs. Fig. 13(b) depicts that all normalized Nusselt numbers merge into single curve when the fin effect, (1 + N)0.5, is added to the combination of dimensionless parameters. The melt fractions for all cases are correlated by the following equation:

Table 3 Melting time ratios for different number of fins and temperatures. Wall temperature (°C)

Melting time ratio Number of fins 0

1

3

70 60 55

1 1 1

0.82 0.83 0.81

0.64 0.62 0.63

3.5. Heat transfer characteristics Variation of Nusselt numbers with time is used to identify the different heat transfer mechanisms governing the melting process in the enclosure. The transient surface-averaged Nusselt number is expressed as:

NuðtÞ ¼

 H hðtÞ kl

ð3Þ

 is the surface-averaged heat transfer coefficient which is where h calculated as follows:

Fig. 11. Transient variation of surface averaged Nusselt number for finned and unfinned enclosures at wall temperature of 70 °C.

B. Kamkari, H. Shokouhmand / International Journal of Heat and Mass Transfer 78 (2014) 839–851

849

Fig. 14. Variation of the time averaged Nusselt numbers and heat transfer rates with number of fins at different wall temperatures. Fig. 12. Transient variation of total heat transfer rate from the heated wall for finned and unfinned enclosures at wall temperature of 70 °C.

  Nu Ra0:25



¼ a1 e

Xb1 c1

2 

  

þ a2 e

Xb2 c2

2  ð6Þ

where X = Ste⁄2FoRa0.25(1 + N)0.5 and a1, b1, c1, a2, b2 and c2 are constants which are equal to 2.996, 0.731, 0.476, 0.284, 0.418 and 1.795, respectively. The root mean square deviation between the experimental data and correlation equation is 0.032. To further discuss the effect of adding partial fins on heat transfer, the time-averaged Nusselt numbers and heat transfer rates are plotted in Fig. 14, which are calculated by using the following equations:

Z t  1 Nu ¼ NuðtÞdt t total 0 Z D E t 1 Q ¼ Q ðtÞdt t total 0 

ð7Þ ð8Þ

D E   where Nu and Q are time-averaged Nusselt number and heat transfer rate, respectively. Fig. 14 shows that the time-averaged Nusselt number decreases with increasing the number of fins. However, the time-average of the total heat transfer rate increases with increasing the number of fins. It can also be observed that both the time-averaged Nusselt numbers and heat transfer rates increase by raising the wall temperature due to the intensification of the natural convection flows in the enclosure. Fig. 14 depicts that the increasing rate of the time-averaged heat transfer rate declines with increasing the number of fins indicating that for each wall temperature an optimum value exists for the number of fins which any increase beyond it can reduce the heat transfer rate. Also, it is inferred from the slopes of the timeaveraged heat transfer curves at the point corresponding to 3 fins that the optimum number of fins increases with raising the wall temperature. Further investigation is needed to determine the optimum number of fins at different wall temperatures. 3.6. Overall fin effectiveness Another important aspect to be considered to quantify the system performance is overall fin effectiveness which is a relative measure of the improved thermal performance of the system because of adding fins to that of the unfinned system defined as:

D Fig. 13. Generalized results for the Nusselt number at various wall temperatures and different number of fins: (a) Nusselt number versus Ste⁄2FoRa0.25 (b) Nusselt number versus Ste⁄2FoRa0.25(1 + N)0.5.

efin overall ¼ D

Q finned

E

Q unfinned

E

ð9Þ

850

B. Kamkari, H. Shokouhmand / International Journal of Heat and Mass Transfer 78 (2014) 839–851

D E D E where Q finned and Q unfinned denote the time-averaged heat transfer rates from the finned and unfinned surfaces, respectively. Fig. 15 shows the variation of overall fin effectiveness with heat transfer area ratio at different wall temperatures. The heat transfer area ratio is defined as the ratio of the surface heat transfer area of the finned wall to that of the unfinned wall which is calculated as follows:

HAR ¼ 1 þ

2NL H

ð10Þ

Heat transfer area ratios corresponding to 1-fin wall and 3-fin wall are 1.42 and 2.25, respectively. It is observed from Fig. 15 that the overall fin effectiveness increases as the heat transfer area ratio increases and reduces by raising the wall temperature. It is also found again from the slope of the curves in Fig. 15 that the beneficial effect of increasing the number of fins on the system performance is offset by opposing effect of fins on development of the convection currents.

4. Uncertainty analysis The uncertainties of experimental results are always influenced by inevitable errors occurring in the experimental measurements and depend on the uncertainty of the individual measuring instruments. Based on the uncertainty analysis method of Kline and McClintock [51], propagation of uncertainty in the final result is affected by the uncertainties of independent variables. Assuming that final result (M) is derived from independent variables x1, x2, ..., xn, the uncertainty of result U(M) is obtained by appropriately combining the uncertainties of independent variables U(xi) as follows:

M ¼ f ðx1 ; x2 ; . . . ; xn Þ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n  2 uX @f UðMÞ ¼ t Uðxi Þ @x i¼1

ð11Þ ð12Þ

This method is employed to estimate the uncertainties of experimental results. The maximum uncertainties of melt fractions, heat transfer rates and Nusselt numbers were found to be 2.3%, 4.6% and 11.3%, respectively.

5. Conclusion An experimental investigation was conducted to visualize and measure the effect of using partial fins on transient melting phenomena of the PCM in rectangular enclosures. Experiments were performed for finned and unfinned enclosures at different wall temperatures of 55, 60 and 70 °C corresponding to Rayleigh numbers in the range of 3:6  108 6 Ra 6 8:3  108 . Photographic observations showed significant melting enhancement in the presence of fins and revealed the important role of natural convection currents on the melting process. Qualitative timedependent flow structures were deduced indirectly from the instantaneous shapes of the solid–liquid interfaces which were confirmed by quantitative temperature results. Visualization of the melting process showed that higher melting rate occurred above the fin surfaces due to formation of vortex and chaotic motions in the liquid PCM. Temperature fluctuations were detected in the liquid PCM above the fin surfaces during the initial melting of PCM. However, temperature fluctuations diminished as the melting progressed and the thickness of the liquid PCM increased. This temperature behavior revealed the formation of transient chaotic and vortical flow structures in the thin liquid PCM above the fins which combined together to form larger stable vortex flow. Temperature histories revealed the formation of the thermally stratified regions in both finned and unfinned enclosures. For the unfinned enclosure, the thermally stratified region developed from upper to lower part of the enclosure as the melt fraction increased, while for the unfinned enclosure, stratified region shrunk to the lower part of the enclosure. For the range of temperatures considered, the total melting time for the 1-fin and 3-fin enclosures were, on average, 18% and 37% less than that of the unfinned enclosure. Melting enhancement ratios, defined as the ratio of melt fraction in the finned enclosure relative to the unfinned one, decreased with time after reaching some maximum values. It increased with lowering the wall temperature indicating that fins are more efficient at lower wall temperatures. Adding fins resulted in decreasing the surface-averaged Nusselt number and increasing the total heat transfer rate. This revealed that in the range of the parameters considered in this study, the increased heat transfer area due to adding fins overcomes the decreased Nusselt number and leads to an increase in the total heat transfer rate. It was also found that the increasing rate of the total heat transfer rate reduces with increasing the number of fins indicating that the beneficial effect of the increasing surface area is being offset by hindering the convection current. It could be inferred that optimum values for the number of fins exist corresponding to each wall temperature, beyond which the heat transfer rate decreases. Further investigation is needed to determine the optimum number of fins. The overall fin effectiveness increased with increasing the number of fins and decreased with raising the wall temperature, indicating again that fins are more efficient at lower wall temperature. Moreover, two correlation equations were obtained for representing the melt fraction and Nusselt number based on an appropriate combination of dimensionless numbers (Ste⁄2FoRa0.25(1 + N)0.5). The observed phenomena and measured values can be used as a basis for validation of numerical approaches considering the partial fins in PCM enclosures.

Conflict of interest Fig. 15. Variation of overall fin effectiveness versus heat transfer area ratio (HAR) at different wall temperatures.

None declared.

B. Kamkari, H. Shokouhmand / International Journal of Heat and Mass Transfer 78 (2014) 839–851

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