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Thermal performance of water-based suspensions of phase change nanocapsules in a natural circulation loop with a mini-channel heat sink and heat source
Applied Thermal Engineering 64 (2014) 376e384
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Thermal performance of water-based suspensions of phase change nanocapsules in a natural circulation loop with a mini-channel heat sink and heat source C.J. Ho a, b, Y.Z. Chen a, Fong-Jou Tu c, Chi-Ming Lai b, d, * a
Department of Mechanical Engineering, National Cheng-Kung University, Taiwan Research Center for Energy Technology and Strategy, National Cheng Kung University, Taiwan Department of Electrical Engineering, Nan-Jeon University of Science and Technology, Taiwan d Department of Civil Engineering, National Cheng-Kung University, Taiwan b c
h i g h l i g h t s Phase-change nanocapsule suspensions can enhance the heat-transfer performance of the loop. The 0.5% suspension was most prominent in the hot wall temperature reduction. High viscosity of the suspension at low temperature affects the heat transfer. Nusselt numbers at the inlets increased with increases in the Rayleigh number.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 August 2013 Accepted 21 December 2013 Available online 28 December 2013
In this study, the heat transfer characteristics of water-based suspensions of phase-change nanocapsules were investigated in a natural circulation loop with a mini-channel heat sink and heat source. A total of 23 and 34 rectangular mini-channels, each with a width of 0.8 mm, a depth of 1.2 mm, a length of 50 mm, and a hydraulic diameter of 0.96 mm, were evenly placed on the copper blocks as the heat source and heat sink, respectively. Adiabatic sections of the circulation loop were constructed using polymethylmethacrylate tubes with an outer diameter of 6 mm and an inner diameter of 4 mm, which were fabricated and assembled to construct a rectangular loop with a height of 630 mm and a width of 220 mm. Using a core material of eicosane and a shell of urea-formaldehyde resin, phase-change nanocapsules with a mean particle size of 150 nm were successfully fabricated and then dispersed in pure water as the working fluid to form water-based suspensions with nanocapsule mass fractions in the range of 0.1e1 wt.%. The results clearly indicate that water-based suspensions of phase-change nanocapsules can markedly enhance the heat-transfer performance of the natural circulation loop considered. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Phase-change nanocapsules Suspension Mini-channel heat sink/source Natural circulation loop
1. Introduction Natural circulation (thermosyphon) loops of various configurations and under various operating conditions have been the subject of numerous investigations due to their wide range of technological applications. These applications include nuclear reactor emergency cooling systems, solar heating and cooling systems, geothermal energy generation, waste heat recovery systems, turbine blade cooling, and electronic cooling. In a natural circulation loop, fluid flow driven by thermally induced density gradients removes heat from a heated section and transports the heat to a cooled section at * Corresponding author. 1, University Road, Tainan City 701, Taiwan. Tel.: þ886 6 2757575x63136; fax: þ886 6 2090569. E-mail addresses: [email protected], [email protected] (C.-M. Lai). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.12.051
a higher elevation. Such a loop can serve as a low-cost and highly reliable passive heat-transfer device. Extensive analytical and experimental investigations have been conducted to study the dynamic response of natural circulation loops to variations in the loop configuration, loop materials, geometric parameters, and instabilities, as exemplified in Refs. [1e8]. In most cases, the heating conditions considered were restricted to those of a time-independent heat input at the heated section of the loop. In practice, however, the circulation loop could be subjected to a time-dependent heat load, which, for example, could be provided by temporal variations in solar irradiation or nuclear reactions. Moreover, the influence of the time-dependent boundary condition is of interest with respect to the feasibility and means of controlling the thermal behavior of circulation loops through boundary perturbations. Tan and Ho [9] experimentally investigated the thermal
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characteristics of a rectangular, annular, single-phase natural circulation loop in which the inner tube was filled with a solideliquid phase-change material (PCM) under a cyclic pulsating heat load. The thermal performance of natural circulation loop systems can be improved not only by modifying the loop itself but also by either enhancing the heat-exchange performance of the heated end or the cooled end or by changing the working fluid. Many studies have focused on micro-level heat dissipation because of the increasing demand for a high heat-dissipation density in the heat-exchange region [10e12]. The heat transfer enhancement obtained by using PCM suspensions as the working fluid has been demonstrated extensively for forced convection [13e17]. In contrast, limited studies have been reported on heat transfer enhancements obtained by using PCM suspensions in a natural circulation loop. Ho et al. [18]
377
used a 2D analysis to explore the feasibility of incorporating PCM suspensions as the heat transfer enhancement medium in such a loop. This study experimentally investigates the thermal performance of a rectangular circulation loop with a mini-channel heat sink and source, as illustrated in Fig. 1, filled with a water-based suspension of phase-change nanocapsules. 2. Experiments 2.1. The natural circulation loop The rectangular natural circulation loop constructed is schematically illustrated in Fig. 1 and has a height of 630 mm and a width of 220 mm. The 120-mm-long heater section and 155-mm-
Fig. 1. Schematic of the experimental setup.
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long cooler section in the loop were constructed with mini-channel heat exchangers. Adiabatic sections of the circulation loop were fabricated using polymethylmethacrylate tubes with an outer diameter of 6 mm and a wall thickness of 1 mm. The heating section, cooling section, and piping periphery were covered with foam insulation to reduce heat loss. Resistance temperature detectors (RTDs) were placed in the heating section, the cooling section, and the inlet and outlet of the cooling water jacket to obtain temperature measurements. T-type thermocouples were installed along the loop to measure the wall temperature. A thermo-regulated water bath was used to achieve an isothermal wall temperature in the cooling section, and a film heater connected to a DC power supply provided a constant heating rate to the outer surface of the heating section. 2.2. Mini-channel heat source and heat sink Fig. 1 also presents a schematic of the fabricated mini-channel heat source (heater) and heat sink (cooler). In total, 23 and 34 parallel rectangular mini-channels were machined into a copper block to form the mini-channel heater and cooler, respectively. The mini-channels were equidistantly spaced with a fin width of 0.8 mm; each mini-channel has a length (Lch) of 50 mm with a cross-sectional area of 0.8 mm in width (Wch) and 1.2 mm in height (Hch). The mini-channel heater is 50 mm long and 48 mm wide and featured a total of 23 mini-channels with a hydraulic diameter of 0.96 mm for each channel. The base of the mini-channel heater was 6 mm thick and was cut into two 3-mm-thick blocks. Six grooves were cut into the back regions of these two segments along the vertical flow direction for thermocouple placement. Thermal paste was applied to the groove at the thermocouple locations to reduce thermal contact resistance. A primary film heater was attached to the bottom of the mini-channel heater to provide the mini-channel heater with a uniform heat flux. An auxiliary film heater was placed 2 cm from the rear surface of the primary film heater as an auxiliary heater to minimize heat loss to the environment. The mini-channel cooler measured 105 mm long and 58 mm wide and featured a total of 34 mini-channels with a hydraulic diameter identical to that of the mini-channel heater. The base of the 9-mm-thick cooler was fabricated with a 5-mm labyrinth channel path in its rear side to allow cooling water to flow from a constant temperature bath for isothermal control. Teflon was used as the fixture material. A 1-mm-thick transparent acrylic board was used as the top cover for the mini-channel cooler to facilitate observation. 2.3. Preparation and properties of water-based suspensions of phase-change nanocapsules In this study, the interface condensation polymerization method was used to prepare phase-change nanocapsules. The core PCM was eicosane, and urea-formaldehyde was used as the shell material. An ultrasound was used to produce an emulsion to further coat the phase-change nanocapsules, thereby reducing the possibility of blocking the mini-channels and increasing the capsule surface area. The capsules contained the following proportions of component materials: the ratio of eicosane to urea-formaldehyde was 1:1, the ratio of urea to formaldehyde was 1:2, and the ratio of surfactant to eicosane was 1:5. Detailed capsule preparation procedures have been described in the literature [19]. The phase-change nanocapsules fabricated in the laboratory were then dispersed in ultrapure Milli-Q water (the base fluid) to form water-based suspensions containing various nanocapsule mass fractions up of 0.1%, 0.5%, and 1%. Nanocapsules in the finished samples could remain in suspension for longer than two weeks. The volume-mean diameters of
the phase-change nanocapsules dispersed in the suspensions were measured using a laser diffraction technique and were found to be 50e375 nm, depending on the mass fraction. This study employed the correction method proposed by Mohamed [19] to correct the measured differential scanning calorimetry (DSC; DSC 7 Perkin Elmer, DSC1 Mettler-Toledo) data. The corrected melting point, freezing point, heating peak, cooling peak, supercooling point, heating enthalpy, and cooling enthalpy were 29.00 C, 24.21 C, 36.93 C, 21.91 C,1.48 C,109.37 J/g, and 105.89 J/g, respectively. The effective thermal properties of the water-based suspensions, including the density r, specific heat Cp, thermal conductivity k, and dynamic viscosity m, were measured using various techniques, as described in Ref. [20]. Fig. 2(a) and (b) illustrates that the density and thermal conductivity of the working fluid at different temperatures do not differ greatly from those of water. Fig. 2(c) indicates that solutions with higher nanocapsule concentrations or at lower temperature environment exhibited a greater viscosity.
2.4. Data deduction Before the experiments were initiated, the working fluid was first heated to 90 C to reduce excess air dissolved in the solution. This working fluid was then used to fill the entire loop. Residual air was discharged through the upper and lower valves. Subsequently, the data acquisition was carried out. (1) The modified Rayleigh number, Ra*, is
Ra* ¼
g bq_ h l4c nak
(1)
The modified Rayleigh number uses the heating power q_ h of the hot wall to assess the impact of natural convection of the loop and is used to replace the general Rayleigh number, which is estimated using the temperature difference between the hot and cold ends of the loop. The physical properties in Equation (1) such as the kinematic viscosity n (m2/s), the thermal conductivity k (W/m), and the thermal diffusivity a (m2/s) depend on whether the thermal analysis is applied to the heated section ðRa*h Þ or the cooled section ðRa*c Þ and are referenced to the average water temperatures in the heated and cooled sections as appropriate. For a given power, the modified Rayleigh number decreased with decreases in the coldwall temperature. (2) The average Nusselt number at the heating section inlet, Nuh;itd , is
Nuh;itd ¼
hh;itd Dch k
q_ h hh;itd ¼ T h;w Th;in
(2)
(3)
The average Nusselt number at the inlet is used because the latent heat of the PCM affects the temperature difference between the inlet and outlet of the heating zone, thereby causing temperatures to change in a nonlinear fashion. Thus, when the working fluid is a capsule suspension, both the quantity of heat transferred and the temperature difference between the inlet temperature and average wall temperature of the heating section are used to calculate the heat transfer coefficient. (3) The average Nusselt number at the cooling section inlet, Nuc;itd , is
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Fig. 2. Thermal conductivity, density, and viscosity of the suspensions of phase-change nanocapsules at different temperatures.
Nuc;itd ¼
hc;itd Dch k
q_ c hc;itd ¼ Tc;in T c;w
(4)
In these equations, Rfin is the fin thermal resistance, and Rflow is the flow thermal resistance. As Incropera and Dewitt [21] demonstrated, the heat transfer of a fin can be calculated for analysis as:
(5)
hh;lm ¼
The same calculation approach was used for the cooling and heating sections, and the experimental parameters of the calculation were adjusted to reflect the cooling section conditions. (4) The average heat transfer effectiveness at the channel inlet, εh , is
q_ h =Nh Afin DTlm
Afin ¼ Lch Wch þ 2hfin Hch
DTlm ¼
T h;w Th;in T h;w Th;out T h;w Th;out ln T h;w Th;in
(10)
(11)
(12)
itd
εh
itd
¼
hitd;nf hitd;bf
(6)
(5) The total thermal resistance of the loop flow, Rtot, is
Rtot ¼ Rfin þ Rflow Rfin ¼
Rflow
1
hfin hh;lm Afin
1 ¼ _ Cp m
(7) (8)
(9)
where Nh is the total number of flow channels in the heating section, Afin is the heat transfer area of a single flow channel, and DTlm is the logarithmic mean temperature difference. Thus, using qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hfin ¼ tanh(mHch)/mHch and m ¼ 2hh;lm =ks Wrib , hh;lm can be obtained through an iterative calculation. The same calculation approach was used for the cooling section and the experimental parameters of the calculation were adjusted to reflect the cooling section conditions. (6) The loop system thermal resistance, Rsys, is
Rsys
T h;w T c;w ¼ q_ h
(13)
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Uncertainties in the measured quantities for the present study were estimated to be 0.3 C in the temperature, 2% in the flow rate. Following the uncertainty propagation analysis, the uncertainties for the deducted experimental results were estimated as follows: 2.02e2.26% and 21.99e30.81% for the Average heat convection coefficient at the heating and cooling section inlets respectively; 7.72e8.79% and 23.15e31.53% for the average Nusselt number at the heating and cooling section inlets respectively. Specifically, the uncertainty in determining the average heat transfer coefficient, hitd and thus the corresponding average Nusselt number, Nuitd , stem from errors in the measurements of the following quantities: the hydraulic diameter of the channels, Dch; the geometric dimensions of the channels, Lch, Wch, and Hch; the volumetric flow rate, the temperature difference between the heating section surface and fluid at the heating section inlet, ðT h;w Th;in Þ; the temperature difference between the fluid at the cooling section inlet and cooling section surface, ðTc;in T c;w Þ; in addition to the errors in evaluating the relevant thermophysical properties of the fluid, including the density r, the specific heat Cp, and the thermal conductivity, k. The largest uncertainty for the average heat transfer coefficient was estimated, in particular, under the condition of the highest flow rate due to the largest relative errors, coming from the smallest values of temperature difference, ðTc;in T c;w Þ.
Fig. 3. Axial distribution of the wall temperature for various heating powers under a cold-wall temperature of 10 C and nanocapsule suspension (up) of 0%.
3. Results and discussion The control parameters included not only the heating power of the heat source and the cold-wall temperature of the heat sink but also the weight concentration of the phase-change capsules. The heating powers were 4, 8, 12, and 16 W, and the cold-wall temperatures were 4, 10, and 15 C. Pure water and phase-change nanocapsule suspensions were selected as the working fluids. The mass fractions of the formulated nanocapsule suspensions (up) were 0, 0.1, 0.5, and 1%; these suspensions featured PCM mass fractions (upcm) of 0, 0.039, 0.202, and 0.410%, respectively. First, the axial distributions of the wall temperature were examined to gain a basic understanding of the steady-state thermal behavior of the circulation loop using a working fluid of pure water at different heating powers and a cold-wall temperature of 10 C, as presented in Fig. 3. The dashed lines in the figure divide the loop into five sections, with a starting point (dimensionless distance xloop ¼ 0) at the lower-right corner of the loop (Fig. 1). xloop values of 0e0.15 represent the adiabatic section just prior to the heating section. xloop values of 0.15e0.22 represent the heating section. xloop values of 0.22e0.66 represent the adiabatic section between the heating section outlet and cooling section inlet. xloop values of 0.66e0.74 represent the cooling section. xloop values of 0.74e1 represent the adiabatic section after the cooling section. Finally, an xloop value of 1 represents a return to the starting point of the loop. The loop wall temperature in the adiabatic section prior to the heating section was higher than the temperature of the cold wall, possibly due to axial heat transfer through the loop wall. The wall temperature linearly increased after the heating section and reached a maximum at the end of the mini-channel heat source. The temperature then decreased slightly in the subsequent adiabatic sections. In the cooling section, the wall temperature quickly decreased to the set temperature of the cold wall, thereby confirming the established isothermal state. The wall temperature rose after the cooling section due to axial heat conduction. Over the heated isoflux section, the wall temperatures displayed a linear increase with an increasing slope with increasing heating powers, leading to an increasingly larger temperature rise. The thermal performance obtained using the phase-change nanocapsule suspensions in the mini-channel heat source was
examined by plotting the average Nusselt number at the heating section inlet for various modified Reynolds numbers, as shown in Fig. 4. The average Nusselt number Nuh;itd increased with increases in the modified Rayleigh number. A comparison with the data for pure water clearly reveals a significant enhancement in the Nusselt number as more phase-change nanocapsules are dispersed in water. This finding demonstrates that phase-change nanocapsules can indeed produce heat convection enhancement in the mini-channel heat source of a natural convection loop. Quantitatively, the enhancement achieved through phase-change nanocapsule suspensions in the average Nusselt numbers can be further quantified by the average convective heat transfer effectiveness. Fig. 5 illustrates that the effectiveness at the heating section inlet decreased with increases in the modified Rayleigh number. For a given power, the average convective heat transfer effectiveness at the heating channel inlet εh increased with decreases in the cold-wall temh;itd
perature, due to the low cold-wall temperature ensured effective solidification of the phase-change nanocapsules. For example, at a heating power of 4 W, the effectiveness of the 4 C cases (hitd;nf w 5.9 107) was higher than those of the 15 C cases (q_ c w 6.7 107). A comparison of different powers revealed that the effectiveness decreased with increasing wattage because the concentration of the PCM gradually became inadequate. The 0.1% suspension at 8 W/15 C (Ra*h;bf ¼ 1.58 108), 12 W/15 C (Ra*h;bf ¼2.5 108), 16 W/10 C (Ra*h;bf ¼ 3.41 108) and 16 W/15 C (Ra*h;bf ¼3.67 108) did not exhibit large differences from pure water, whereas the effectiveness values for the 0.5% and 1% suspensions were greater than one. Fig. 6 indicates that higher modified Rayleigh numbers were associated with a smaller total thermal resistance (Rh,tot), flow thermal resistance (Rh,flow), and fin thermal resistance (Rh,fin) of the heating section. Greater heating power produced larger thermal buoyancy effects, thereby increasing the flow rate and reducing the flow thermal resistance. An increase in the convective heat transfer coefficient reduced the fin thermal resistance and thereby caused the overall thermal resistance to decline. A comparison of the impact of different cold-wall temperatures at the same heating
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Fig. 4. Variations of the average Nusselt number at the heating section inlet Nuh;itd with the modified Rayleigh number Ra*h;bf for various nanocapsule suspension (up).
power revealed that lower cold-wall temperatures were associated with lower modified Rayleigh numbers and greater viscous forces, thus reducing the flow rate and increasing the flow thermal resistance. These low cold-wall temperatures reduced convective motion, thereby increasing the fin thermal resistance. For example, at a heating power of 12 W, the resistances for the 4 C cases (Ra*h;bf ¼ 2.3 108) were higher than those of 15 C cases (Ra*h;bf ¼ 2.5 108). The flow thermal resistance was high due to the weak natural convection flow within the mini-channels and constituted approximately two-thirds of the total thermal resistance. A comparison of the impact of different suspension concentrations indicates that lower thermal resistances were produced by the 1% suspension compared to the other three concentrations tested. The 0.5% suspension exhibited the second lowest thermal resistance, and the pure water case generated a lower resistance than the 0.1% suspension. Fig. 7 presents the heat transfer characteristics at the isothermally cooled wall, where the average Nusselt number at the cooling
381
Fig. 6. Variations of the thermal resistances of the heating section Rh with the modified Rayleigh number Ra*h;bf for various nanocapsule suspension (up).
section inlet is plotted against the modified Rayleigh number. Because the heat transfer of the cold wall was significantly impacted by the working fluid viscosity, the variations were examined separately for TC ¼ 4, 10, and 15 C. The average Nusselt number Nuc;itd increased with increases in the modified Rayleigh number. A comparison of different cold-wall temperatures revealed that for a given modified Rayleigh number, higher cold-wall temperatures were associated with greater Nusselt numbers. Subsequently, the results obtained for different concentrations revealed that the Nusselt number was greater for the 0.5% capsule suspension than for pure water. However, the 1% and 0.1% suspensions did not exhibit the same trend, particularly at low modified Rayleigh numbers. At a heating power of 4 W (Ra*c;bf ¼ 1.15 107e 1.75 107), the average Nusselt numbers at the inlet for the 0.1% and 1% cases were lower than that of pure water. This result demonstrates that the high viscosity of the nanocapsule suspension in the cooling section indeed affects the heat transfer. For a heating power of 8 W (Ra*c;bf ¼ 2.87 107e4.6 107), the Nusselt number for the 1% suspension was only slightly lower than that of the 0.5%
Fig. 5. Relation of the average heat-transfer effectiveness at the heating section inlet εh with the modified Rayleigh number Ra*h;bf for various heating powers qh and nanocapsule h;itd suspension (up).
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Fig. 7. Variations of the average Nusselt number at the cooling section inlet Nuc;itd with the modified Rayleigh number Ra*c;bf for various cold-wall temperature (4, 10, 15 C) and nanocapsule suspension (up).
suspension; both of these suspensions exhibited higher Nusselt numbers than the 0.1% suspension. All of the phase-change capsule suspensions exhibited higher Nusselt numbers than water at a heating power of 8 W or greater (Ra*c;bf > 2.87 107), indicating that the phase-change nanocapsules performed their functions well and were recycled successfully in the natural convection loop. However, as the power increased, the difference between the Nusselt numbers of the suspensions and that of pure water slowly decreased. Thus, higher PCM concentrations were required to achieve adequate heat transfer enhancement in increased wattages. The heat-transfer effectiveness at the cooling section inlet displayed a convex trend with increasing modified Rayleigh numbers, as shown in Fig. 8. Improved effectiveness was observed as the heating power increased to 8 and 12 W (Ra*c;bf ¼ 2.87 107e 6.7 107), and a slow decrease in the effectiveness was observed at a heating power of 16 W (Ra*c;bf ¼ 7.2 107e1.17 108). For a fixed heating power, different cold-wall temperatures affected the average heat transfer effectiveness at the cooling section inlet. In particular, different trends occurred at 4 W compared to other power inputs. At 4 W (Ra*c;bf ¼ 1.15 107e1.75 107), lower coldwall temperatures were associated with lower heat transfer effectiveness. Some of the nanocapsule suspensions exhibited lower heat transfer effectiveness than water at cold-wall temperatures of 4 C (Ra*c;bf ¼ 1.15 107) and 10 C (Ra*c;bf ¼ 1.32 107) and only
achieved heat transfer coefficients similar to that of water at a coldwall temperature of 15 C (Ra*c;bf ¼1.75 107). Due to these viscosity effects, at 4 C, the 1% suspension exhibited a lower heat transfer coefficient than the 0.1% suspension. At 16 W, the 0.5% capsule suspension could not provide sufficient cooling to achieve a steady state, and the effectiveness of the 1% and 0.1% suspensions decreased to less than 1.1. This result indicates that an increased concentration of PCM may improve thermal performance at high heating powers. Similar to the results for the thermal resistances of the hot wall, larger modified Rayleigh numbers were associated with lower thermal resistances of the cold wall, as shown in Fig. 9. However, the thermal resistances of the hot and cold walls differed with respect to change trends and the proportion of flow and fin thermal resistances. The flow thermal resistance (Rc,flow) (Fig. 9, right) decreased as the modified Rayleigh number increased, and the suspension concentrations had little effect on the results, accounting for approximately half of the total thermal resistance. This proportion is lower than the corresponding proportion for the hot wall (the flow thermal resistance accounted for two thirds of the overall thermal resistance in the heating section). Consequently, the contribution of the fin thermal resistance (Rc,fin) (Fig. 9, left) to the overall thermal resistance was greater in the cooling section than in the heating section. Appearance of jagged local extremes in the fin thermal resistance was observed. These local extremes were more obvious at high power compared to
Fig. 8. Relation of the average heat-transfer effectiveness at the cooling section inlet εh with the modified Rayleigh number Ra*c;bf for various heating powers qh and nanocapsule c;itd suspension (up).
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revealed that for a given heating power, compared to water, the phase-change suspensions could reduce the hot-wall temperature, decrease the hot-/cold-wall temperature difference, and reduce the system thermal resistance. However, the phase-change suspensions gradually became less effective as the power increased due to insufficient PCM concentrations. 4. Conclusions This study experimentally investigated the thermal performance of a natural circulation loop with a mini-channel heat sink and heat source using water-based suspensions of phase-change nanocapsules as the working fluid. The major findings can be summarized as follows:
Fig. 10. Variations of the thermal resistances of the system Rsys with the modified Rayleigh number Ra*bf for various nanocapsule suspension (up).
low power. A detailed examination of the data revealed that relative maxima for these jagged fin thermal resistances were obtained at a cold-wall temperature of 4 C (8 W (Ra*c;bf ¼ 2.87 107); 12 W (Ra*c;bf ¼ 4.7 107); 16 W (Ra*c;bf ¼ 7.2 107)). Because the temperature difference between the inlet and outlet of the cooling section is quite large at low cold-wall temperatures, the viscosity has a significant influence, thereby reducing the effects of natural convection. In contrast, relative minima in the fin thermal resistance were obtained at a cold-wall temperature of 15 C (4 W (Ra*c;bf ¼ 1.75 107); 8 W (Ra*c;bf ¼ 4.6 107); 12 W (Ra*c;bf ¼6.7 107); 16 W (Ra*c;bf ¼1.17 108)). A comparison of working fluids with different nanocapsule concentrations revealed that pure water typically exhibited a higher thermal resistance than the various capsule suspensions. Only some of the flow thermal resistances for the water were lower than those of the suspension cases. Fig. 10 presents the thermal resistance of the system. For pure water, the system thermal resistance decreases with increases in the modified Rayleigh number, i.e., increasing flow rates for a greater temperature difference. Subsequently, the results for different suspension concentrations were analyzed. These analyses
(1) The dispersion of phase-change nanocapsules in water in a natural circulation loop with a mini-channel heat sink and heat source can reduce the hot wall temperature and achieve heat convection enhancement, except some cases at the cooling section at 4 W heating. The 0.5% capsule suspension was most prominent in the hot wall temperature reduction. (2) At the mini-channel heat source: (a) Higher modified Rayleigh numbers were associated with smaller thermal resistances. The flow thermal resistance constituted approximately two-thirds of the total thermal resistance. (b) The average Nusselt number increased with increases in the modified Rayleigh number and more phase-change nanocapsules. (c) The heat-transfer effectiveness increased with decreases in the modified Rayleigh number and more phasechange nanocapsules. For a given power, the effectiveness increased with decreases in the cold-wall temperature. (3) At the mini-channel heat sink: (a) Larger modified Rayleigh numbers were associated with lower thermal resistances. The flow thermal resistance and fin thermal resistance accounted for approximately half of the total thermal resistance. Jagged local extremes in the fin thermal resistance were observed. (b) The average Nusselt number increased with increases in the modified Rayleigh number; for a given modified Rayleigh number, higher cold-wall temperatures were associated with greater Nusselt numbers. At a heating power of 4 W, the average Nusselt numbers for the 0.1%
Fig. 9. Variations of the thermal resistances of the cooling section Rc with the modified Rayleigh number Ra*c;bf for various nanocapsule suspension (up).
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and 1% cases were lower than that of pure water, due to the high viscosity of the nanocapsule suspension. (c) The heat-transfer effectiveness displayed a convex trend with increasing modified Rayleigh numbers and improved effectiveness was observed as the heating power increased to 8 and 12 W, and a slow decrease was observed at a heating power of 16 W. At 4 W, some of the nanocapsule suspensions exhibited lower heat transfer effectiveness than water at cold-wall temperatures of 4 C and 10 C and only achieved heat transfer coefficients similar to that of water at a cold-wall temperature of 15 C. (d) Higher PCM concentrations were required to achieve adequate heat transfer enhancement in increased wattages. Acknowledgements Support from the National Science Council of ROC through Grant No. NSC100-2221-E006-190 is gratefully acknowledged. References [1] C.J. Ho, S.P. Chiou, C.S. Hu, Heat transfer characteristics of a rectangular natural circulation loop containing water near its density extreme, Int. J. Heat Mass Tranfer 40 (1997) 3553e3558. [2] P.K. Vijayan, M. Sharma, D. Saha, Steady state and stability characteristics of single-phase natural circulation in a rectangular loop with different heater and cooler orientations, Exp. Therm. Fluid Sci. 31 (2007) 925e945. [3] M. Misale, P. Garibaldi, J. Passos, G.G. de Bitencourt, Experiments in a singlephase natural circulation mini-loop, Exp. Therm. Fluid Sci. 31 (2007) 1111e 1120. [4] J.F. Lin, A.S.Y. Chiu, C.J. Ho, Conjugate heat transfer simulation of a rectangular natural circulation loop, Heat Mass Transfer 45 (2008) 167e175. [5] S. Küçüka, T. Bas¸aran, Laminar flow modelling of a thermosyphon loop at specified wall temperatures, Heat Mass Transfer 43 (2007) 1293e1302. [6] M. Misale, P. Garibaldi, L. Tarozzi, G.S. Barozzi, Influence of thermal boundary conditions on the dynamic behaviour of a rectangular single-phase natural circulation loop, Int. J. Heat Fluid Flow 32 (2011) 413e423. [7] B. Swapnalee, P. Vijayan, A generalized flow equation for single phase natural circulation loops obeying multiple friction laws, Int. J. Heat Mass Tranfer 51 (2011) 2618e2629. [8] C.M. Lai, R.H. Chen, C.S. Huang, Development and thermal performance of a wall heat collection prototype, Build. Environ. 57 (2012) 156e164. [9] G.H. Tan, C.J. Ho, Experiments on thermal characteristics of a natural circulation loop with latent heat energy storage under cyclic pulsed heat load, Heat Mass Transfer 39 (2002) 11e17. [10] D.B. Tuckerman, R. Pease, High-performance heat sinking for VLSI, Electron Dev. Lett. 2 (1981) 126e129. [11] P.S. Lee, S.V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, Int. J. Heat Mass Tranfer 48 (2005) 1688e1704. [12] X. Zhang, J. Huo, S. Wang, Experimental investigation on temperature oscillation in a miniature loop heat pipe with flat evaporator, Exp. Therm. Fluid Sci. 37 (2011) 29e36. [13] M. Choi, K. Cho, Liquid cooling for a multichip module using Fluorinert liquid and paraffin slurry, Int. J. Heat Mass Tranfer 43 (2000) 209e218. [14] C.J. Ho, J.F. Lin, S.Y. Chiu, Heat transfer of solideliquid phase-change material suspensions in circular pipes: effects of wall conduction, Numer. Heat Transfer A Appl. 45 (2004) 171e190. [15] C.J. Ho, J.B. Huang, P.S. Tsai, Y.M. Yang, Water-based suspensions of Al2O3 nanoparticles and MEPCM particles on convection effectiveness in a circular tube, Int. J. Therm. Sci. 50 (2011) 736e748. [16] F. Dammel, P. Stephan, Heat transfer to suspensions of microencapsulated phase change material flowing through minichannels, J. Heat Transfer 134 (2012) 020907. [17] C.J. Ho, J.B. Huang, C.P. Chen, P.S. Tsai, Y.M. Yang, Forced convection performance of a MEPCM suspension through an iso-flux heated circular tube: an experimental study, Heat Mass Transfer 48 (2012) 487e496. [18] C.J. Ho, S.Y. Chiu, J.F. Lin, Heat transfer characteristics of a rectangular natural circulation loop containing solideliquid phase-change material suspensions, Int. J. Numer. Method Heat Fluid Flow 15 (2005) 441e461.
[19] R. Mohamed, Study of phase changing characteristics of granular composites using differential scanning calorimetry, Energy Convers. Manag. 50 (2009) 1210e1217. [20] C.J. Ho, J.B. Huang, P.S. Tsai, Y.M. Yang, Preparation and properties of hybrid water-based suspension of Al2O3 nanoparticles and MEPCM particles as functional forced convection fluid, Int. Commun. Heat Mass Transfer 37 (2010) 490e494. [21] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavines, Principles of Heat and Mass Transfer, seventh ed., John Wiley & Sons, 2013.
Nomenclature Afin: heat transfer area of a single mini-channel (m2) Cp: specific heat capacity (kJ/kg K) Dch: hydraulic diameter of the mini-channel (m) g: acceleration due to gravity (m/s) hc;itd : average heat convection coefficient at the cooling section inlet (W/m2 K) hh;lm : average heat convection coefficient at the mini-channel heat source (W/m2 K) hh;itd : average heat convection coefficient at the heating section inlet (W/m2 K) hitd;bf : average heat convection coefficient with the base fluid (water) (W/m2 K) hitd;nf : average heat convection coefficient with the phase-change nanocapsule suspension (W/m2 K) Hch: height of a single mini-channel (m) k: thermal conductivity of the working fluid (W/m K) ks: thermal conductivity of the copper base (W/m K) lc: length of the cooling section (m) Lht: length of the heating sheets (mm) _ working fluid mass flow rate within the loop (kg/s) m: Nh: total number of flow channels in the heating section Nuc;itd : average Nusselt number at the cooling section inlet ðNuc;itd ¼ hc;itd Dch =kÞ Nuh;itd : average Nusselt number at the heating section inlet ðNuh;itd ¼ hh;itd Dch =kÞ q_ c : cooling power (W) q_ h : heating power (W) Ra*: modified Rayleigh number ðRa* ¼ gbq_ h l4c =nakÞ Rfin: fin thermal resistance of the mini-channel ð ¼ 1=hfin hh;lm Afin Þ (K/W) _ (K/W) Rflow: thermal resistance of the working fluid flow ð ¼ 1=Cp mÞ Rsys: loop system thermal resistance ð ¼ ðT h;w T c;w Þ=q_ h Þ (K/W) Rtot: total thermal resistance of the loop flow (K/W) T: temperature ( C) Tc,in: fluid temperature at the cooling section inlet ( C) Th,in: fluid temperature at the heating section inlet ( C) Th,out: fluid temperature at the heating section exit ( C) T c;w : average surface temperature of the cooling section ( C) T h;w : average surface temperature of the heating section ( C) DTlm: logarithmic mean temperature difference (Eq. (12)) ( C) Wch: width of a single mini-channel (m) Wht: width of the heating sheets (m) Wrib: width of the fin in the mini-channel (m) xloop: dimensionless distance Greek symbols
a: thermal diffusion coefficient (m2/s) b: mal expansion coefficient (1/K) r: density (kg/m3) m: viscosity (N s/m2) n: kinematic viscosity (m2/s) hfin: fin efficiency (hfin ¼ tanh(mHch)/mHch)
εh : heat transfer effectiveness at the channel inlet ðεh
u: weight percentage concentration itd
Subscripts bf: base fluid (water) c: cooling ch: channel fin: fins of the mini-channel h: heating in: mini-channel inlet itd: inlet temperature difference lm: logarithmic mean m: phase-change nanocapsule suspension nf: nanocapsulate fluid p: phase-change nanocapsule pcm: phase change material w: wall
itd
¼ hitd;nf =hitd;bf Þ
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Thermal performance of water-based suspensions of phase change nanocapsules in a natural circulation loop with a mini-channel heat sink and heat source C.J. Ho a, b, Y.Z. Chen a, Fong-Jou Tu c, Chi-Ming Lai b, d, * a
Department of Mechanical Engineering, National Cheng-Kung University, Taiwan Research Center for Energy Technology and Strategy, National Cheng Kung University, Taiwan Department of Electrical Engineering, Nan-Jeon University of Science and Technology, Taiwan d Department of Civil Engineering, National Cheng-Kung University, Taiwan b c
h i g h l i g h t s Phase-change nanocapsule suspensions can enhance the heat-transfer performance of the loop. The 0.5% suspension was most prominent in the hot wall temperature reduction. High viscosity of the suspension at low temperature affects the heat transfer. Nusselt numbers at the inlets increased with increases in the Rayleigh number.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 August 2013 Accepted 21 December 2013 Available online 28 December 2013
In this study, the heat transfer characteristics of water-based suspensions of phase-change nanocapsules were investigated in a natural circulation loop with a mini-channel heat sink and heat source. A total of 23 and 34 rectangular mini-channels, each with a width of 0.8 mm, a depth of 1.2 mm, a length of 50 mm, and a hydraulic diameter of 0.96 mm, were evenly placed on the copper blocks as the heat source and heat sink, respectively. Adiabatic sections of the circulation loop were constructed using polymethylmethacrylate tubes with an outer diameter of 6 mm and an inner diameter of 4 mm, which were fabricated and assembled to construct a rectangular loop with a height of 630 mm and a width of 220 mm. Using a core material of eicosane and a shell of urea-formaldehyde resin, phase-change nanocapsules with a mean particle size of 150 nm were successfully fabricated and then dispersed in pure water as the working fluid to form water-based suspensions with nanocapsule mass fractions in the range of 0.1e1 wt.%. The results clearly indicate that water-based suspensions of phase-change nanocapsules can markedly enhance the heat-transfer performance of the natural circulation loop considered. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Phase-change nanocapsules Suspension Mini-channel heat sink/source Natural circulation loop
1. Introduction Natural circulation (thermosyphon) loops of various configurations and under various operating conditions have been the subject of numerous investigations due to their wide range of technological applications. These applications include nuclear reactor emergency cooling systems, solar heating and cooling systems, geothermal energy generation, waste heat recovery systems, turbine blade cooling, and electronic cooling. In a natural circulation loop, fluid flow driven by thermally induced density gradients removes heat from a heated section and transports the heat to a cooled section at * Corresponding author. 1, University Road, Tainan City 701, Taiwan. Tel.: þ886 6 2757575x63136; fax: þ886 6 2090569. E-mail addresses: [email protected], [email protected] (C.-M. Lai). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.12.051
a higher elevation. Such a loop can serve as a low-cost and highly reliable passive heat-transfer device. Extensive analytical and experimental investigations have been conducted to study the dynamic response of natural circulation loops to variations in the loop configuration, loop materials, geometric parameters, and instabilities, as exemplified in Refs. [1e8]. In most cases, the heating conditions considered were restricted to those of a time-independent heat input at the heated section of the loop. In practice, however, the circulation loop could be subjected to a time-dependent heat load, which, for example, could be provided by temporal variations in solar irradiation or nuclear reactions. Moreover, the influence of the time-dependent boundary condition is of interest with respect to the feasibility and means of controlling the thermal behavior of circulation loops through boundary perturbations. Tan and Ho [9] experimentally investigated the thermal
C.J. Ho et al. / Applied Thermal Engineering 64 (2014) 376e384
characteristics of a rectangular, annular, single-phase natural circulation loop in which the inner tube was filled with a solideliquid phase-change material (PCM) under a cyclic pulsating heat load. The thermal performance of natural circulation loop systems can be improved not only by modifying the loop itself but also by either enhancing the heat-exchange performance of the heated end or the cooled end or by changing the working fluid. Many studies have focused on micro-level heat dissipation because of the increasing demand for a high heat-dissipation density in the heat-exchange region [10e12]. The heat transfer enhancement obtained by using PCM suspensions as the working fluid has been demonstrated extensively for forced convection [13e17]. In contrast, limited studies have been reported on heat transfer enhancements obtained by using PCM suspensions in a natural circulation loop. Ho et al. [18]
377
used a 2D analysis to explore the feasibility of incorporating PCM suspensions as the heat transfer enhancement medium in such a loop. This study experimentally investigates the thermal performance of a rectangular circulation loop with a mini-channel heat sink and source, as illustrated in Fig. 1, filled with a water-based suspension of phase-change nanocapsules. 2. Experiments 2.1. The natural circulation loop The rectangular natural circulation loop constructed is schematically illustrated in Fig. 1 and has a height of 630 mm and a width of 220 mm. The 120-mm-long heater section and 155-mm-
Fig. 1. Schematic of the experimental setup.
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long cooler section in the loop were constructed with mini-channel heat exchangers. Adiabatic sections of the circulation loop were fabricated using polymethylmethacrylate tubes with an outer diameter of 6 mm and a wall thickness of 1 mm. The heating section, cooling section, and piping periphery were covered with foam insulation to reduce heat loss. Resistance temperature detectors (RTDs) were placed in the heating section, the cooling section, and the inlet and outlet of the cooling water jacket to obtain temperature measurements. T-type thermocouples were installed along the loop to measure the wall temperature. A thermo-regulated water bath was used to achieve an isothermal wall temperature in the cooling section, and a film heater connected to a DC power supply provided a constant heating rate to the outer surface of the heating section. 2.2. Mini-channel heat source and heat sink Fig. 1 also presents a schematic of the fabricated mini-channel heat source (heater) and heat sink (cooler). In total, 23 and 34 parallel rectangular mini-channels were machined into a copper block to form the mini-channel heater and cooler, respectively. The mini-channels were equidistantly spaced with a fin width of 0.8 mm; each mini-channel has a length (Lch) of 50 mm with a cross-sectional area of 0.8 mm in width (Wch) and 1.2 mm in height (Hch). The mini-channel heater is 50 mm long and 48 mm wide and featured a total of 23 mini-channels with a hydraulic diameter of 0.96 mm for each channel. The base of the mini-channel heater was 6 mm thick and was cut into two 3-mm-thick blocks. Six grooves were cut into the back regions of these two segments along the vertical flow direction for thermocouple placement. Thermal paste was applied to the groove at the thermocouple locations to reduce thermal contact resistance. A primary film heater was attached to the bottom of the mini-channel heater to provide the mini-channel heater with a uniform heat flux. An auxiliary film heater was placed 2 cm from the rear surface of the primary film heater as an auxiliary heater to minimize heat loss to the environment. The mini-channel cooler measured 105 mm long and 58 mm wide and featured a total of 34 mini-channels with a hydraulic diameter identical to that of the mini-channel heater. The base of the 9-mm-thick cooler was fabricated with a 5-mm labyrinth channel path in its rear side to allow cooling water to flow from a constant temperature bath for isothermal control. Teflon was used as the fixture material. A 1-mm-thick transparent acrylic board was used as the top cover for the mini-channel cooler to facilitate observation. 2.3. Preparation and properties of water-based suspensions of phase-change nanocapsules In this study, the interface condensation polymerization method was used to prepare phase-change nanocapsules. The core PCM was eicosane, and urea-formaldehyde was used as the shell material. An ultrasound was used to produce an emulsion to further coat the phase-change nanocapsules, thereby reducing the possibility of blocking the mini-channels and increasing the capsule surface area. The capsules contained the following proportions of component materials: the ratio of eicosane to urea-formaldehyde was 1:1, the ratio of urea to formaldehyde was 1:2, and the ratio of surfactant to eicosane was 1:5. Detailed capsule preparation procedures have been described in the literature [19]. The phase-change nanocapsules fabricated in the laboratory were then dispersed in ultrapure Milli-Q water (the base fluid) to form water-based suspensions containing various nanocapsule mass fractions up of 0.1%, 0.5%, and 1%. Nanocapsules in the finished samples could remain in suspension for longer than two weeks. The volume-mean diameters of
the phase-change nanocapsules dispersed in the suspensions were measured using a laser diffraction technique and were found to be 50e375 nm, depending on the mass fraction. This study employed the correction method proposed by Mohamed [19] to correct the measured differential scanning calorimetry (DSC; DSC 7 Perkin Elmer, DSC1 Mettler-Toledo) data. The corrected melting point, freezing point, heating peak, cooling peak, supercooling point, heating enthalpy, and cooling enthalpy were 29.00 C, 24.21 C, 36.93 C, 21.91 C,1.48 C,109.37 J/g, and 105.89 J/g, respectively. The effective thermal properties of the water-based suspensions, including the density r, specific heat Cp, thermal conductivity k, and dynamic viscosity m, were measured using various techniques, as described in Ref. [20]. Fig. 2(a) and (b) illustrates that the density and thermal conductivity of the working fluid at different temperatures do not differ greatly from those of water. Fig. 2(c) indicates that solutions with higher nanocapsule concentrations or at lower temperature environment exhibited a greater viscosity.
2.4. Data deduction Before the experiments were initiated, the working fluid was first heated to 90 C to reduce excess air dissolved in the solution. This working fluid was then used to fill the entire loop. Residual air was discharged through the upper and lower valves. Subsequently, the data acquisition was carried out. (1) The modified Rayleigh number, Ra*, is
Ra* ¼
g bq_ h l4c nak
(1)
The modified Rayleigh number uses the heating power q_ h of the hot wall to assess the impact of natural convection of the loop and is used to replace the general Rayleigh number, which is estimated using the temperature difference between the hot and cold ends of the loop. The physical properties in Equation (1) such as the kinematic viscosity n (m2/s), the thermal conductivity k (W/m), and the thermal diffusivity a (m2/s) depend on whether the thermal analysis is applied to the heated section ðRa*h Þ or the cooled section ðRa*c Þ and are referenced to the average water temperatures in the heated and cooled sections as appropriate. For a given power, the modified Rayleigh number decreased with decreases in the coldwall temperature. (2) The average Nusselt number at the heating section inlet, Nuh;itd , is
Nuh;itd ¼
hh;itd Dch k
q_ h hh;itd ¼ T h;w Th;in
(2)
(3)
The average Nusselt number at the inlet is used because the latent heat of the PCM affects the temperature difference between the inlet and outlet of the heating zone, thereby causing temperatures to change in a nonlinear fashion. Thus, when the working fluid is a capsule suspension, both the quantity of heat transferred and the temperature difference between the inlet temperature and average wall temperature of the heating section are used to calculate the heat transfer coefficient. (3) The average Nusselt number at the cooling section inlet, Nuc;itd , is
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379
Fig. 2. Thermal conductivity, density, and viscosity of the suspensions of phase-change nanocapsules at different temperatures.
Nuc;itd ¼
hc;itd Dch k
q_ c hc;itd ¼ Tc;in T c;w
(4)
In these equations, Rfin is the fin thermal resistance, and Rflow is the flow thermal resistance. As Incropera and Dewitt [21] demonstrated, the heat transfer of a fin can be calculated for analysis as:
(5)
hh;lm ¼
The same calculation approach was used for the cooling and heating sections, and the experimental parameters of the calculation were adjusted to reflect the cooling section conditions. (4) The average heat transfer effectiveness at the channel inlet, εh , is
q_ h =Nh Afin DTlm
Afin ¼ Lch Wch þ 2hfin Hch
DTlm ¼
T h;w Th;in T h;w Th;out T h;w Th;out ln T h;w Th;in
(10)
(11)
(12)
itd
εh
itd
¼
hitd;nf hitd;bf
(6)
(5) The total thermal resistance of the loop flow, Rtot, is
Rtot ¼ Rfin þ Rflow Rfin ¼
Rflow
1
hfin hh;lm Afin
1 ¼ _ Cp m
(7) (8)
(9)
where Nh is the total number of flow channels in the heating section, Afin is the heat transfer area of a single flow channel, and DTlm is the logarithmic mean temperature difference. Thus, using qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hfin ¼ tanh(mHch)/mHch and m ¼ 2hh;lm =ks Wrib , hh;lm can be obtained through an iterative calculation. The same calculation approach was used for the cooling section and the experimental parameters of the calculation were adjusted to reflect the cooling section conditions. (6) The loop system thermal resistance, Rsys, is
Rsys
T h;w T c;w ¼ q_ h
(13)
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Uncertainties in the measured quantities for the present study were estimated to be 0.3 C in the temperature, 2% in the flow rate. Following the uncertainty propagation analysis, the uncertainties for the deducted experimental results were estimated as follows: 2.02e2.26% and 21.99e30.81% for the Average heat convection coefficient at the heating and cooling section inlets respectively; 7.72e8.79% and 23.15e31.53% for the average Nusselt number at the heating and cooling section inlets respectively. Specifically, the uncertainty in determining the average heat transfer coefficient, hitd and thus the corresponding average Nusselt number, Nuitd , stem from errors in the measurements of the following quantities: the hydraulic diameter of the channels, Dch; the geometric dimensions of the channels, Lch, Wch, and Hch; the volumetric flow rate, the temperature difference between the heating section surface and fluid at the heating section inlet, ðT h;w Th;in Þ; the temperature difference between the fluid at the cooling section inlet and cooling section surface, ðTc;in T c;w Þ; in addition to the errors in evaluating the relevant thermophysical properties of the fluid, including the density r, the specific heat Cp, and the thermal conductivity, k. The largest uncertainty for the average heat transfer coefficient was estimated, in particular, under the condition of the highest flow rate due to the largest relative errors, coming from the smallest values of temperature difference, ðTc;in T c;w Þ.
Fig. 3. Axial distribution of the wall temperature for various heating powers under a cold-wall temperature of 10 C and nanocapsule suspension (up) of 0%.
3. Results and discussion The control parameters included not only the heating power of the heat source and the cold-wall temperature of the heat sink but also the weight concentration of the phase-change capsules. The heating powers were 4, 8, 12, and 16 W, and the cold-wall temperatures were 4, 10, and 15 C. Pure water and phase-change nanocapsule suspensions were selected as the working fluids. The mass fractions of the formulated nanocapsule suspensions (up) were 0, 0.1, 0.5, and 1%; these suspensions featured PCM mass fractions (upcm) of 0, 0.039, 0.202, and 0.410%, respectively. First, the axial distributions of the wall temperature were examined to gain a basic understanding of the steady-state thermal behavior of the circulation loop using a working fluid of pure water at different heating powers and a cold-wall temperature of 10 C, as presented in Fig. 3. The dashed lines in the figure divide the loop into five sections, with a starting point (dimensionless distance xloop ¼ 0) at the lower-right corner of the loop (Fig. 1). xloop values of 0e0.15 represent the adiabatic section just prior to the heating section. xloop values of 0.15e0.22 represent the heating section. xloop values of 0.22e0.66 represent the adiabatic section between the heating section outlet and cooling section inlet. xloop values of 0.66e0.74 represent the cooling section. xloop values of 0.74e1 represent the adiabatic section after the cooling section. Finally, an xloop value of 1 represents a return to the starting point of the loop. The loop wall temperature in the adiabatic section prior to the heating section was higher than the temperature of the cold wall, possibly due to axial heat transfer through the loop wall. The wall temperature linearly increased after the heating section and reached a maximum at the end of the mini-channel heat source. The temperature then decreased slightly in the subsequent adiabatic sections. In the cooling section, the wall temperature quickly decreased to the set temperature of the cold wall, thereby confirming the established isothermal state. The wall temperature rose after the cooling section due to axial heat conduction. Over the heated isoflux section, the wall temperatures displayed a linear increase with an increasing slope with increasing heating powers, leading to an increasingly larger temperature rise. The thermal performance obtained using the phase-change nanocapsule suspensions in the mini-channel heat source was
examined by plotting the average Nusselt number at the heating section inlet for various modified Reynolds numbers, as shown in Fig. 4. The average Nusselt number Nuh;itd increased with increases in the modified Rayleigh number. A comparison with the data for pure water clearly reveals a significant enhancement in the Nusselt number as more phase-change nanocapsules are dispersed in water. This finding demonstrates that phase-change nanocapsules can indeed produce heat convection enhancement in the mini-channel heat source of a natural convection loop. Quantitatively, the enhancement achieved through phase-change nanocapsule suspensions in the average Nusselt numbers can be further quantified by the average convective heat transfer effectiveness. Fig. 5 illustrates that the effectiveness at the heating section inlet decreased with increases in the modified Rayleigh number. For a given power, the average convective heat transfer effectiveness at the heating channel inlet εh increased with decreases in the cold-wall temh;itd
perature, due to the low cold-wall temperature ensured effective solidification of the phase-change nanocapsules. For example, at a heating power of 4 W, the effectiveness of the 4 C cases (hitd;nf w 5.9 107) was higher than those of the 15 C cases (q_ c w 6.7 107). A comparison of different powers revealed that the effectiveness decreased with increasing wattage because the concentration of the PCM gradually became inadequate. The 0.1% suspension at 8 W/15 C (Ra*h;bf ¼ 1.58 108), 12 W/15 C (Ra*h;bf ¼2.5 108), 16 W/10 C (Ra*h;bf ¼ 3.41 108) and 16 W/15 C (Ra*h;bf ¼3.67 108) did not exhibit large differences from pure water, whereas the effectiveness values for the 0.5% and 1% suspensions were greater than one. Fig. 6 indicates that higher modified Rayleigh numbers were associated with a smaller total thermal resistance (Rh,tot), flow thermal resistance (Rh,flow), and fin thermal resistance (Rh,fin) of the heating section. Greater heating power produced larger thermal buoyancy effects, thereby increasing the flow rate and reducing the flow thermal resistance. An increase in the convective heat transfer coefficient reduced the fin thermal resistance and thereby caused the overall thermal resistance to decline. A comparison of the impact of different cold-wall temperatures at the same heating
C.J. Ho et al. / Applied Thermal Engineering 64 (2014) 376e384
Fig. 4. Variations of the average Nusselt number at the heating section inlet Nuh;itd with the modified Rayleigh number Ra*h;bf for various nanocapsule suspension (up).
power revealed that lower cold-wall temperatures were associated with lower modified Rayleigh numbers and greater viscous forces, thus reducing the flow rate and increasing the flow thermal resistance. These low cold-wall temperatures reduced convective motion, thereby increasing the fin thermal resistance. For example, at a heating power of 12 W, the resistances for the 4 C cases (Ra*h;bf ¼ 2.3 108) were higher than those of 15 C cases (Ra*h;bf ¼ 2.5 108). The flow thermal resistance was high due to the weak natural convection flow within the mini-channels and constituted approximately two-thirds of the total thermal resistance. A comparison of the impact of different suspension concentrations indicates that lower thermal resistances were produced by the 1% suspension compared to the other three concentrations tested. The 0.5% suspension exhibited the second lowest thermal resistance, and the pure water case generated a lower resistance than the 0.1% suspension. Fig. 7 presents the heat transfer characteristics at the isothermally cooled wall, where the average Nusselt number at the cooling
381
Fig. 6. Variations of the thermal resistances of the heating section Rh with the modified Rayleigh number Ra*h;bf for various nanocapsule suspension (up).
section inlet is plotted against the modified Rayleigh number. Because the heat transfer of the cold wall was significantly impacted by the working fluid viscosity, the variations were examined separately for TC ¼ 4, 10, and 15 C. The average Nusselt number Nuc;itd increased with increases in the modified Rayleigh number. A comparison of different cold-wall temperatures revealed that for a given modified Rayleigh number, higher cold-wall temperatures were associated with greater Nusselt numbers. Subsequently, the results obtained for different concentrations revealed that the Nusselt number was greater for the 0.5% capsule suspension than for pure water. However, the 1% and 0.1% suspensions did not exhibit the same trend, particularly at low modified Rayleigh numbers. At a heating power of 4 W (Ra*c;bf ¼ 1.15 107e 1.75 107), the average Nusselt numbers at the inlet for the 0.1% and 1% cases were lower than that of pure water. This result demonstrates that the high viscosity of the nanocapsule suspension in the cooling section indeed affects the heat transfer. For a heating power of 8 W (Ra*c;bf ¼ 2.87 107e4.6 107), the Nusselt number for the 1% suspension was only slightly lower than that of the 0.5%
Fig. 5. Relation of the average heat-transfer effectiveness at the heating section inlet εh with the modified Rayleigh number Ra*h;bf for various heating powers qh and nanocapsule h;itd suspension (up).
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Fig. 7. Variations of the average Nusselt number at the cooling section inlet Nuc;itd with the modified Rayleigh number Ra*c;bf for various cold-wall temperature (4, 10, 15 C) and nanocapsule suspension (up).
suspension; both of these suspensions exhibited higher Nusselt numbers than the 0.1% suspension. All of the phase-change capsule suspensions exhibited higher Nusselt numbers than water at a heating power of 8 W or greater (Ra*c;bf > 2.87 107), indicating that the phase-change nanocapsules performed their functions well and were recycled successfully in the natural convection loop. However, as the power increased, the difference between the Nusselt numbers of the suspensions and that of pure water slowly decreased. Thus, higher PCM concentrations were required to achieve adequate heat transfer enhancement in increased wattages. The heat-transfer effectiveness at the cooling section inlet displayed a convex trend with increasing modified Rayleigh numbers, as shown in Fig. 8. Improved effectiveness was observed as the heating power increased to 8 and 12 W (Ra*c;bf ¼ 2.87 107e 6.7 107), and a slow decrease in the effectiveness was observed at a heating power of 16 W (Ra*c;bf ¼ 7.2 107e1.17 108). For a fixed heating power, different cold-wall temperatures affected the average heat transfer effectiveness at the cooling section inlet. In particular, different trends occurred at 4 W compared to other power inputs. At 4 W (Ra*c;bf ¼ 1.15 107e1.75 107), lower coldwall temperatures were associated with lower heat transfer effectiveness. Some of the nanocapsule suspensions exhibited lower heat transfer effectiveness than water at cold-wall temperatures of 4 C (Ra*c;bf ¼ 1.15 107) and 10 C (Ra*c;bf ¼ 1.32 107) and only
achieved heat transfer coefficients similar to that of water at a coldwall temperature of 15 C (Ra*c;bf ¼1.75 107). Due to these viscosity effects, at 4 C, the 1% suspension exhibited a lower heat transfer coefficient than the 0.1% suspension. At 16 W, the 0.5% capsule suspension could not provide sufficient cooling to achieve a steady state, and the effectiveness of the 1% and 0.1% suspensions decreased to less than 1.1. This result indicates that an increased concentration of PCM may improve thermal performance at high heating powers. Similar to the results for the thermal resistances of the hot wall, larger modified Rayleigh numbers were associated with lower thermal resistances of the cold wall, as shown in Fig. 9. However, the thermal resistances of the hot and cold walls differed with respect to change trends and the proportion of flow and fin thermal resistances. The flow thermal resistance (Rc,flow) (Fig. 9, right) decreased as the modified Rayleigh number increased, and the suspension concentrations had little effect on the results, accounting for approximately half of the total thermal resistance. This proportion is lower than the corresponding proportion for the hot wall (the flow thermal resistance accounted for two thirds of the overall thermal resistance in the heating section). Consequently, the contribution of the fin thermal resistance (Rc,fin) (Fig. 9, left) to the overall thermal resistance was greater in the cooling section than in the heating section. Appearance of jagged local extremes in the fin thermal resistance was observed. These local extremes were more obvious at high power compared to
Fig. 8. Relation of the average heat-transfer effectiveness at the cooling section inlet εh with the modified Rayleigh number Ra*c;bf for various heating powers qh and nanocapsule c;itd suspension (up).
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revealed that for a given heating power, compared to water, the phase-change suspensions could reduce the hot-wall temperature, decrease the hot-/cold-wall temperature difference, and reduce the system thermal resistance. However, the phase-change suspensions gradually became less effective as the power increased due to insufficient PCM concentrations. 4. Conclusions This study experimentally investigated the thermal performance of a natural circulation loop with a mini-channel heat sink and heat source using water-based suspensions of phase-change nanocapsules as the working fluid. The major findings can be summarized as follows:
Fig. 10. Variations of the thermal resistances of the system Rsys with the modified Rayleigh number Ra*bf for various nanocapsule suspension (up).
low power. A detailed examination of the data revealed that relative maxima for these jagged fin thermal resistances were obtained at a cold-wall temperature of 4 C (8 W (Ra*c;bf ¼ 2.87 107); 12 W (Ra*c;bf ¼ 4.7 107); 16 W (Ra*c;bf ¼ 7.2 107)). Because the temperature difference between the inlet and outlet of the cooling section is quite large at low cold-wall temperatures, the viscosity has a significant influence, thereby reducing the effects of natural convection. In contrast, relative minima in the fin thermal resistance were obtained at a cold-wall temperature of 15 C (4 W (Ra*c;bf ¼ 1.75 107); 8 W (Ra*c;bf ¼ 4.6 107); 12 W (Ra*c;bf ¼6.7 107); 16 W (Ra*c;bf ¼1.17 108)). A comparison of working fluids with different nanocapsule concentrations revealed that pure water typically exhibited a higher thermal resistance than the various capsule suspensions. Only some of the flow thermal resistances for the water were lower than those of the suspension cases. Fig. 10 presents the thermal resistance of the system. For pure water, the system thermal resistance decreases with increases in the modified Rayleigh number, i.e., increasing flow rates for a greater temperature difference. Subsequently, the results for different suspension concentrations were analyzed. These analyses
(1) The dispersion of phase-change nanocapsules in water in a natural circulation loop with a mini-channel heat sink and heat source can reduce the hot wall temperature and achieve heat convection enhancement, except some cases at the cooling section at 4 W heating. The 0.5% capsule suspension was most prominent in the hot wall temperature reduction. (2) At the mini-channel heat source: (a) Higher modified Rayleigh numbers were associated with smaller thermal resistances. The flow thermal resistance constituted approximately two-thirds of the total thermal resistance. (b) The average Nusselt number increased with increases in the modified Rayleigh number and more phase-change nanocapsules. (c) The heat-transfer effectiveness increased with decreases in the modified Rayleigh number and more phasechange nanocapsules. For a given power, the effectiveness increased with decreases in the cold-wall temperature. (3) At the mini-channel heat sink: (a) Larger modified Rayleigh numbers were associated with lower thermal resistances. The flow thermal resistance and fin thermal resistance accounted for approximately half of the total thermal resistance. Jagged local extremes in the fin thermal resistance were observed. (b) The average Nusselt number increased with increases in the modified Rayleigh number; for a given modified Rayleigh number, higher cold-wall temperatures were associated with greater Nusselt numbers. At a heating power of 4 W, the average Nusselt numbers for the 0.1%
Fig. 9. Variations of the thermal resistances of the cooling section Rc with the modified Rayleigh number Ra*c;bf for various nanocapsule suspension (up).
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and 1% cases were lower than that of pure water, due to the high viscosity of the nanocapsule suspension. (c) The heat-transfer effectiveness displayed a convex trend with increasing modified Rayleigh numbers and improved effectiveness was observed as the heating power increased to 8 and 12 W, and a slow decrease was observed at a heating power of 16 W. At 4 W, some of the nanocapsule suspensions exhibited lower heat transfer effectiveness than water at cold-wall temperatures of 4 C and 10 C and only achieved heat transfer coefficients similar to that of water at a cold-wall temperature of 15 C. (d) Higher PCM concentrations were required to achieve adequate heat transfer enhancement in increased wattages. Acknowledgements Support from the National Science Council of ROC through Grant No. NSC100-2221-E006-190 is gratefully acknowledged. References [1] C.J. Ho, S.P. Chiou, C.S. Hu, Heat transfer characteristics of a rectangular natural circulation loop containing water near its density extreme, Int. J. Heat Mass Tranfer 40 (1997) 3553e3558. [2] P.K. Vijayan, M. Sharma, D. Saha, Steady state and stability characteristics of single-phase natural circulation in a rectangular loop with different heater and cooler orientations, Exp. Therm. Fluid Sci. 31 (2007) 925e945. [3] M. Misale, P. Garibaldi, J. Passos, G.G. de Bitencourt, Experiments in a singlephase natural circulation mini-loop, Exp. Therm. Fluid Sci. 31 (2007) 1111e 1120. [4] J.F. Lin, A.S.Y. Chiu, C.J. Ho, Conjugate heat transfer simulation of a rectangular natural circulation loop, Heat Mass Transfer 45 (2008) 167e175. [5] S. Küçüka, T. Bas¸aran, Laminar flow modelling of a thermosyphon loop at specified wall temperatures, Heat Mass Transfer 43 (2007) 1293e1302. [6] M. Misale, P. Garibaldi, L. Tarozzi, G.S. Barozzi, Influence of thermal boundary conditions on the dynamic behaviour of a rectangular single-phase natural circulation loop, Int. J. Heat Fluid Flow 32 (2011) 413e423. [7] B. Swapnalee, P. Vijayan, A generalized flow equation for single phase natural circulation loops obeying multiple friction laws, Int. J. Heat Mass Tranfer 51 (2011) 2618e2629. [8] C.M. Lai, R.H. Chen, C.S. Huang, Development and thermal performance of a wall heat collection prototype, Build. Environ. 57 (2012) 156e164. [9] G.H. Tan, C.J. Ho, Experiments on thermal characteristics of a natural circulation loop with latent heat energy storage under cyclic pulsed heat load, Heat Mass Transfer 39 (2002) 11e17. [10] D.B. Tuckerman, R. Pease, High-performance heat sinking for VLSI, Electron Dev. Lett. 2 (1981) 126e129. [11] P.S. Lee, S.V. Garimella, D. Liu, Investigation of heat transfer in rectangular microchannels, Int. J. Heat Mass Tranfer 48 (2005) 1688e1704. [12] X. Zhang, J. Huo, S. Wang, Experimental investigation on temperature oscillation in a miniature loop heat pipe with flat evaporator, Exp. Therm. Fluid Sci. 37 (2011) 29e36. [13] M. Choi, K. Cho, Liquid cooling for a multichip module using Fluorinert liquid and paraffin slurry, Int. J. Heat Mass Tranfer 43 (2000) 209e218. [14] C.J. Ho, J.F. Lin, S.Y. Chiu, Heat transfer of solideliquid phase-change material suspensions in circular pipes: effects of wall conduction, Numer. Heat Transfer A Appl. 45 (2004) 171e190. [15] C.J. Ho, J.B. Huang, P.S. Tsai, Y.M. Yang, Water-based suspensions of Al2O3 nanoparticles and MEPCM particles on convection effectiveness in a circular tube, Int. J. Therm. Sci. 50 (2011) 736e748. [16] F. Dammel, P. Stephan, Heat transfer to suspensions of microencapsulated phase change material flowing through minichannels, J. Heat Transfer 134 (2012) 020907. [17] C.J. Ho, J.B. Huang, C.P. Chen, P.S. Tsai, Y.M. Yang, Forced convection performance of a MEPCM suspension through an iso-flux heated circular tube: an experimental study, Heat Mass Transfer 48 (2012) 487e496. [18] C.J. Ho, S.Y. Chiu, J.F. Lin, Heat transfer characteristics of a rectangular natural circulation loop containing solideliquid phase-change material suspensions, Int. J. Numer. Method Heat Fluid Flow 15 (2005) 441e461.
[19] R. Mohamed, Study of phase changing characteristics of granular composites using differential scanning calorimetry, Energy Convers. Manag. 50 (2009) 1210e1217. [20] C.J. Ho, J.B. Huang, P.S. Tsai, Y.M. Yang, Preparation and properties of hybrid water-based suspension of Al2O3 nanoparticles and MEPCM particles as functional forced convection fluid, Int. Commun. Heat Mass Transfer 37 (2010) 490e494. [21] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavines, Principles of Heat and Mass Transfer, seventh ed., John Wiley & Sons, 2013.
Nomenclature Afin: heat transfer area of a single mini-channel (m2) Cp: specific heat capacity (kJ/kg K) Dch: hydraulic diameter of the mini-channel (m) g: acceleration due to gravity (m/s) hc;itd : average heat convection coefficient at the cooling section inlet (W/m2 K) hh;lm : average heat convection coefficient at the mini-channel heat source (W/m2 K) hh;itd : average heat convection coefficient at the heating section inlet (W/m2 K) hitd;bf : average heat convection coefficient with the base fluid (water) (W/m2 K) hitd;nf : average heat convection coefficient with the phase-change nanocapsule suspension (W/m2 K) Hch: height of a single mini-channel (m) k: thermal conductivity of the working fluid (W/m K) ks: thermal conductivity of the copper base (W/m K) lc: length of the cooling section (m) Lht: length of the heating sheets (mm) _ working fluid mass flow rate within the loop (kg/s) m: Nh: total number of flow channels in the heating section Nuc;itd : average Nusselt number at the cooling section inlet ðNuc;itd ¼ hc;itd Dch =kÞ Nuh;itd : average Nusselt number at the heating section inlet ðNuh;itd ¼ hh;itd Dch =kÞ q_ c : cooling power (W) q_ h : heating power (W) Ra*: modified Rayleigh number ðRa* ¼ gbq_ h l4c =nakÞ Rfin: fin thermal resistance of the mini-channel ð ¼ 1=hfin hh;lm Afin Þ (K/W) _ (K/W) Rflow: thermal resistance of the working fluid flow ð ¼ 1=Cp mÞ Rsys: loop system thermal resistance ð ¼ ðT h;w T c;w Þ=q_ h Þ (K/W) Rtot: total thermal resistance of the loop flow (K/W) T: temperature ( C) Tc,in: fluid temperature at the cooling section inlet ( C) Th,in: fluid temperature at the heating section inlet ( C) Th,out: fluid temperature at the heating section exit ( C) T c;w : average surface temperature of the cooling section ( C) T h;w : average surface temperature of the heating section ( C) DTlm: logarithmic mean temperature difference (Eq. (12)) ( C) Wch: width of a single mini-channel (m) Wht: width of the heating sheets (m) Wrib: width of the fin in the mini-channel (m) xloop: dimensionless distance Greek symbols
a: thermal diffusion coefficient (m2/s) b: mal expansion coefficient (1/K) r: density (kg/m3) m: viscosity (N s/m2) n: kinematic viscosity (m2/s) hfin: fin efficiency (hfin ¼ tanh(mHch)/mHch)
εh : heat transfer effectiveness at the channel inlet ðεh
u: weight percentage concentration itd
Subscripts bf: base fluid (water) c: cooling ch: channel fin: fins of the mini-channel h: heating in: mini-channel inlet itd: inlet temperature difference lm: logarithmic mean m: phase-change nanocapsule suspension nf: nanocapsulate fluid p: phase-change nanocapsule pcm: phase change material w: wall
itd
¼ hitd;nf =hitd;bf Þ