Research Article www.acsami.org
Efficient Solar-Thermal Energy Harvest Driven by Interfacial Plasmonic Heating-Assisted Evaporation Chao Chang, Chao Yang, Yanming Liu, Peng Tao,* Chengyi Song, Wen Shang, Jianbo Wu, and Tao Deng* State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, P.R. China S Supporting Information *
ABSTRACT: The plasmonic heating effect of noble nanoparticles has recently received tremendous attention for various important applications. Herein, we report the utilization of interfacial plasmonic heating-assisted evaporation for efficient and facile solar-thermal energy harvest. An airlaid paper-supported gold nanoparticle thin film was placed at the thermal energy conversion region within a sealed chamber to convert solar energy into thermal energy. The generated thermal energy instantly vaporizes the water underneath into hot vapors that quickly diffuse to the thermal energy release region of the chamber to condense into liquids and release the collected thermal energy. The condensed water automatically flows back to the thermal energy conversion region under the capillary force from the hydrophilic copper mesh. Such an approach simultaneously realizes efficient solar-to-thermal energy conversion and rapid transportation of converted thermal energy to target application terminals. Compared to conventional external photothermal conversion design, the solar-thermal harvesting device driven by the internal plasmonic heating effect has reduced the overall thermal resistance by more than 50% and has demonstrated more than 25% improvement of solar water heating efficiency. KEYWORDS: solar-thermal energy, photothermal conversion, plasmonic heating, interfacial evaporation, phase change
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INTRODUCTION Pressed by an increasing energy consumption demand and rising environmental concerns of using fossil fuels, utilization of abundant clean solar energy has been considered as one of the most promising strategies to realize sustainable development of human society.1 In general, solar energy can be converted into electricity, fuels, and thermal energy via photovoltaic, photochemical, and photothermal processes.2 Among them, solarthermal energy obtained through converting solar energy into heat has emerged as an efficient, economical, clean, and direct way to provide space and water heating, and drive steam turbines in generating electricity.2−5 Efficient solar-to-thermal energy conversion and rapid transfer of collected thermal energy to the target application terminals are critical for widespread utilization of solar-thermal technology.6 To harness solar-thermal energy, in the past, intensive efforts were devoted to developing high-performance light-to-heat converting materials through delicately tuning the composition of intrinsic solar absorbing materials, designing multilayer coating structures, and complicated surface structure engineering.7−10 However, in conventional solar-thermal collection design, the solar absorbing materials were coated on the external surface of the solar collector.6,11 Such a design usually leads to high surface temperatures, which in turn not only cause serious radiation loss of the converted thermal energy but also © 2016 American Chemical Society
impose strict demands on the thermal stability of the photothermal converting materials.12 Efficient and timely transport of the converted thermal energy to desired locations for the target specific application is another important aspect. To improve thermal energy transfer performance, previous attention was mainly focused on improving thermophysical properties of the transportation fluids, for example, through addition of high thermal conductivity nanofillers13−15 and accelerating the flow of thermal fluids with mechanical pumping methods.16,17 Compared to single-phase thermal transport, liquid/gas phase-change-based heat-transfer technology has demonstrated superior effective thermal conductivity, larger heat-transfer capability, higher transfer rates, and smaller temperature drops.18 In recent years, the plasmonic heating effect of noble metal nanoparticles has attracted great research attention.19 Under resonance excitation, collective oscillation of numerous free electrons leads to a light absorption cross section much larger than the physical size of nanocrystals. Meanwhile, noble metals generally have an extremely low optical quantum yield, meaning nearly 100% photothermal conversion efficiency, Received: July 3, 2016 Accepted: August 18, 2016 Published: August 18, 2016 23412
DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
Research Article
ACS Applied Materials & Interfaces
Figure 1. Schematic design and working principle of solar-thermal energy harvest driven by interfacial plasmonic heating within a sealed chamber.
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which has been confirmed experimentally.20 Previously, this efficient, instant, intense plasmonic heating had been mainly employed for biomedical applications such as cancer therapy and photothermal imaging.21 More recently, this effect has been used for steam generation,22−24 distillation,25 microfluid modulation,26 nanofabrication,27 chemical reaction,28 thermal storage,29 seawater catalysis, and desalination.30 In these cases, gold nanoparticle (Au NP) dispersions were directly illuminated by laser or solar light to convert optical energy into thermal energy to heat the bulk fluid. In this volumetric solarthermal harvesting method, however, external pumping and circulating of the hot fluid is needed to transport the collected thermal energy to specific usage terminals. Compared with bulk plasmonic heating, we recently demonstrated that localized plasmonic heating by direct solar illumination onto the assembled Au NP thin films and composites at the air−water interface had much higher evaporation efficiency, better reusability and broader performance tunability.31−36 In this work, we report a facile and effective route to harvest solar-thermal energy, including solar-thermal energy conversion and transportation of converted thermal energy by integrating interfacial plasmonic photothermal conversion and phasechange-based heat-transfer within a sealed chamber. Upon solar illumination, the plasmonic photothermal conversion effect of the airlaid paper-supported Au NP films (PANF) was immediately activated to generate a significant amount of thermal energy. The generated thermal energy was instantly absorbed by water to produce hot vapors which quickly travel to the application terminal and condense into liquid to release the carried thermal energy. Integration of the PANF inside the heat-transfer system greatly reduces thermal energy transfer resistance, improves efficiency, and avoids potential overheating in the energy conversion region. The phase-change-based heattransfer design also enables fast delivery of the collected solarthermal energy from the plasmonic energy conversion process. The whole solar-thermal energy conversion and transportation processes are highly efficient, fast, and self-powered without requiring any external pumping. Compared to conventional solar-thermal harvesting design, we demonstrate that the thermal resistance of the reported device was reduced by more than 50% and the solar water heating efficiency was increased by more than 25%.
EXPERIMENTAL SECTION
Materials. Trisodium citrate dehydrate (99%), tetrachloroauric acid (∼49−50% Au basis), and potassium peroxodisulfate (99.5%) were purchased from Aladdin Reagent Co., Ltd. (Shanghai, China). Formic acid (≥88%) and potassium hydroxide were ordered from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China). Preparation of Photothermal Converter. An aqueous solution of Au NPs with an average diameter of 10 nm was synthesized by boiling the mixed 50 mL solution of 1 mM tetrachloroauric acid and 5 mL of 38.8 mM sodium citrate for 15 min. To prepare Au NP films, in the first step, 10 mL of as-synthesized Au NP solution was added into a 50 mL beaker. A piece of airlaid paper (45% polyester, 55% cellulose) with a diameter of 6.5 cm was placed at the bottom of the beaker. This beaker and a Petri dish filled with 10 mL of formic acid were then put into a Vaseline-sealed desiccator. After sitting at room temperature for 48 h, Au NPs self-assembled into a film floating at the air/water interface. The excessive aqueous solution was removed by a syringe to facilitate the integration of the assembled Au NP film with the airlaid paper substrate. The as-prepared PANF was finally dried at 60 °C for 24 h. Solar-Thermal Harvesting Device Fabrication. The device was fabricated by attaching a hydrophilic copper mesh onto a copper plate supporting substrate and placing PANF on top of the copper mesh at the solar-thermal energy conversion section followed by mounting with a transparent quartz cover. The hydrophilic copper mesh was prepared through subsequent washing of commercial copper meshes (300-mesh, Shanghai Hengxin Wire and Mesh Co., Ltd.) in 4 M HCl aqueous solution for 15 min, immersing the washed mesh into a mixed solution of 0.065 M K2S2O8 and 2.5 M KOH for 1 h at 60 °C, and finally rinsing with deionized (DI) water and drying.37,38 The whole device was then pumped to a vacuum of 0.01 Torr, backfilled with different volumes of DI water working fluid, and fully sealed. In a control experiment with a conventional design, the device with only the hydrophilic copper mesh was sealed and loaded with DI water. The PANF was bonded with thermal grease (HZ-KS101, Wuxi Taobo Technology Co., Ltd.) on the back surface of the copper plate at the same thermal energy conversion region in the control device. Characterization and Property Measurement. The microstructure of PANF and hydrophilic copper mesh was characterized by a field-emission scanning electron microscope (SEM, Sirion 2000, FEI). An X-ray diffractometer (Shimadzu, LabX XRD-6000) and X-ray photoelectron spectrometer (XPS, Kratos, AXIS UltraDLD) were used to analyze the structure and composition of the base-treated hydrophilic copper meshes. A three-dimensional (3D) digital microscope (Keyence VHX-S50) was used to collect 3D optical microscope images of PANF. A solar simulator (TRM-PD, Jinzhou Sunshine Technology Co., Ltd.) with adjustable power densities and a xenon lamp (JYANG HID) were used as the light source. Temperature distribution of the device was measured by K-type thermocouples 23413
DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
Research Article
ACS Applied Materials & Interfaces (Omega SMPW-TT-K, resolution ∼0.1 °C) that were connected to a multichannel data acquisition system (Agilent 34972A, Agilent Technologies Inc.). To evaluate the solar-thermal energy harvesting performance of the device, a cold block was attached to the copper plate at the thermal energy release section, and a cooling bath (Shanghai Bilon Equipment) was used to provide circulated running water at a consistent temperature of 20 °C. For solar water heating applications, the temperature evolution profiles of a tank containing 20 mL of water at 20 °C were measured.
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RESULTS AND DISCUSSION Figure 1 presents the schematic design and working principle for utilization of the interfacial plasmonic heating effect to efficiently harvest solar-thermal energy. The whole device has a sealed chamber and a transparent quartz cover, allowing for direct incidence of solar irradiation. The PANF prepared by depositing an assembled Au NP film on a porous hydrophilic airlaid paper is placed at the solar-thermal energy conversion region to instantly and continuously convert incident solar energy into thermal energy. The generated plasmonic heat rapidly vaporizes the liquid water at the air/liquid interface. The hydrophilic paper substrate favors wetting of PANF with the water working fluid, thus promoting timely storage of converted heat as latent heat of the working fluid. The porous airlaid paper substrate also facilitates continuous water supply through the numerous pores within the paper. This unique interfacial evaporation design eliminates the potential overheating issues in conventional photothermal conversion processes. Driven by the pressure difference, the hot vapor then quickly moves to the cold terminal end and condenses into liquid water, releasing the carried thermal energy. Meanwhile, the condensed water is pumped back to the thermal energy conversion region with the assistance of the capillary force from the hydrophilic copper mesh attached on the surface of the supporting copper plate, thereby completing the whole cycle of solar-thermal energy conversion and transportation. Rather than relying on complex fabrication of solar absorbing coatings,39 we utilized PANF as the photothermal converter to convert solar irradiation into plasmonic heating. As shown by the TEM image in Figure 2a, spherical Au NPs with an average diameter of ∼10 nm were synthesized by a simple single-step citrate reduction method. The aqueous solution of Au NPs exhibits a pink color due to the strong plasmonic absorption effect. This paper-based converter is flexible, reusable, and can be ready fabricated on a large scale by directly transferring assembled Au NP films onto the airlaid paper substrate. Figure 2b shows that PANF with a diameter of 6.5 cm can be easily prepared, and the resultant PANF has a dark purple appearance. The prepared PANF showed broad absorption of the solar light (Figure S1).32 The SEM images in Figure 2c display uniform distribution of Au NPs on the porous fibrous airlaid paper substrate. Unlike dispersed individual particles, in our case, the Au NPs were self-assembled through interparticle attraction into a thin film. As shown by the FTIR spectra (Figure S2), the Au NP films synthesized from the aqueous route could easily integrate with the hydrophilic airlaid paper substrate. The 3D optical microscope observation indicates a rough surface structure of the PANF, and the height difference reaches more than 300 μm (Figure 2d). Such a highly porous rough structure not only imparts the PANF with good wettability for water but also enhances the light absorption capability. Unlike the flat surface, which directly reflects the incident light, the porously structured airlaid paper fibers can
Figure 2. (a) TEM image of as-synthesized Au NPs. The inset shows the pink-colored dispersion of Au NPs within DI water. (b) Photograph of prepared PANF with a diameter of 6.5 cm. (c) SEM images of PANF at low and high magnifications. The inset image at a higher magnification shows homogeneous distribution of Au NPs on paper fibers. (d) 3D optical microscopic image of PANF. (e) SEM images of the superhydrophilic Cu mesh obtained through treatment with strong bases.
further scatter the reflected light to the surface of Au NPs, thus increasing the absorption probability and photothermal conversion by the Au NPs. Figure 2e presents the microstructure of the hydrophilic Cu mesh that was employed to transport the condensed water back to thermal energy conversion region. After treatment with strong bases, the surfaces of Cu meshes were decorated with a thin layer of hydrophilic CuO, which was identified by both X-ray diffraction (Figure S3) and XPS (Figure S4). The observed petal-like nanostructure further improved the mesh wettability with water, offering strong capillary pumping forces within the solarthermal harvesting device. To investigate the solar-thermal energy harvesting performance of the fabricated device, as shown in Figure 3a, two thermocouples were placed to monitor the real-time temperature at the solar-thermal energy conversion section (Tc) and the thermal energy release section (Tr). Figure 3b presents the temperature evolution profiles with illumination time at different illumination power densities. Once the light is incident on the PANF, the plasmonic heat conversion effect is immediately activated, leading to gradual rise of all the measured temperatures. At low illumination power densities, both Tc and Tr increased only slightly, implying that only a small amount of thermal energy was generated by PANF, and thus, vapor generation was limited. When the solar illumination power density reached 5 W/cm2, Tc and Tr rose from 25 to 60 and 45 °C, respectively, suggesting the relatively large amount of heat produced through the solar-thermal conversion by the PANF and also the effective heat transfer to the thermal energy release region in the device. In addition, the immediate temperature increase upon switching to higher illumination 23414
DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
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ACS Applied Materials & Interfaces
Figure 3. (a) Solar-thermal harvesting experimental setup. (b) Temperature evolution of solar-thermal harvesting device at conversion (Tc) and releasing (Tr) sections with increasing illumination power densities.
Figure 4. Thermal resistance of solar-thermal harvesting devices with (a) different illumination power densities loaded with 16 mL of water and (b) different volumes of water working fluid illuminated at 5 W/cm2.
power densities indicates that the device has a rapid response to solar illumination. This should be related to the combined advantages of the ultrafast plasmonic light-to-heat conversion process by the PANF and the rapid phase-change-based heattransfer process.19,40 During our repeated solar illumination tests for more than 100 h in total, it was found the PANF system had excellent stability in solar-thermal conversion and vapor generation, as we reported previously.32 In the interfacial evaporation system, the floating PANF achieved high evaporation efficiency through localizing photothermal conversion at the evaporation interface. Such efficient evaporation, in turn, timely removed the generated heat, which could help avoid the potential overheating damage of the PANF.41 Thermal resistance (R), here defined by R = Q/(Tc − Tr) (Q is the illumination power), is a well-established performance indicator that has been frequently utilized to characterize the solar-thermal energy harvesting process. Figure 4a shows that with lower power inputs the device presented a relatively high thermal resistance due to the fact that at low light power densities, most of the thermal energy produced by the PANF was stored as sensible heat by slightly increasing the water
temperature, and the collected heat was delivered to the heatrelease end by heat conduction through the supporting copper plate rather than phase-change-based heat transfer. With high incident light intensities, the whole cycle of liquid vaporization and vapor condensation can be realized, leading to lower thermal resistance. Therefore, when the illumination power density was increased to more than 3 W/cm2, the change in the resistance became smaller. In the solar-thermal harvesting process, water plays an important role, as the medium to store converted thermal energy as latent heat and to deliver thermal energy to the application terminal. Thus, the amount of water loaded in the device is critical to its proper functioning and energy collection performance. By varying the volume from 4 to 20 mL, we investigated the effect of water content on the solar-thermal harvesting performance of the device. Figure 4b shows that the thermal resistance varies with the amount of water from 4 to 20 mL under the same illumination power density of 5 W/cm2. Due to the lack of enough working liquid, the device loaded with 4 mL of water had a larger thermal resistance. Increasing the water content to 8 and 16 mL reduced the thermal resistances, but when further working 23415
DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
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ACS Applied Materials & Interfaces
Figure 5. (a) Schematic of solar-thermal harvest through external photothermal conversion in the conventional design. (b) Schematic of solarthermal harvest through internal photothermal conversion in the new design. (c) Temperature evolution profiles of Tc and Tr. (d) Comparison of thermal resistance of solar-thermal harvesting devices. (e) Schematic of heat-transfer paths in the conventional design. (f) Schematic of heat-transfer paths in the new design.
fluids were added, the thermal resistance again increased. When the amount of working fluid is low, there is not enough water to cover the cycling loop within the chamber, and dry-out at the solar-thermal energy conversion section occurs, which results in the large R. The dry-out in turn results in temperature rise of Tc, and in extreme cases, it could damage the PANF converter if the local temperature is close to the melting temperature of the Au NPs.34 On the contrary, if there is too much water, overflooding phenomena would occur.42 In this case, the excessive water blocks the vapor flow and also covers the condensation area; thus, the normal thermodynamic cycle is restricted, and the PANF continues to heat water at the conversion end, resulting in local overheating. In our experiment, 16 mL of water is the optimum volume for the device to show the best thermal performance with the lowest thermal resistance. As shown by Figures 5a and b, we further compared the thermal performance of our device driven by the interfacial evaporation within the chamber with the conventional design in which the photothermal conversion takes place on the outside surface of the chamber. For this controlled design, the only difference is that the PANF was attached onto the copper plate with thermal greases (Figure 5a). Figure 5c shows the temperature evolution profiles of Tc and Tr with illumination time under the same power density of 1.5 W/cm2 generated by a portable xenon lamp. With the conventional design, while Tc rapidly rises from 28 to 40 °C, Tr only increases from 24 to 25 °C, implying that, although PANF can efficiently generate heat at the solar-thermal energy conversion section, the converted heat could not be effectively transferred to the application terminal, implying a large thermal energy transfer resistance in the process. By comparison, in the new design, the heat generated by PANF directly vaporizes the water at the conversion section. The corresponding temperature rise of Tc is smaller (from 26 to 33 °C) than that in the case of the control device. Meanwhile, the temperature difference between
Tc and Tr is much smaller than that in the controlled design, indicating that the converted solar-thermal energy was successfully delivered to the releasing terminal. Figure 5d shows that with the same solar energy input the internal conversion device has a much smaller thermal resistance (0.23 K/W) than that of the control device with the conventional external photothermal conversion design (∼0.77 K/W). The difference in thermal resistances can be understood by analyzing their different thermal-energy transfer paths. As shown by Figure 5e, in the conventional external photothermal conversion design, the thermal energy produced by PANF must pass through a series of interfaces before arriving at the liquid−vapor conversion section. Thus, the overall thermal resistance (Rtot) is the sum of each individual resistance (Rtot = Rcc + Rccs + Rcm + Rcvl + Rrvl + Rrm + Rrcs + Rrc), including the contact resistances (Rcc and Rrc), the copper substrate resistances (Rccs and Rrcs), the mesh resistances (Rcm and Rrm), and the vapor/liquid resistances (Rcvl and Rrvl) at the solar-thermal energy conversion and thermal energy release sections, respectively. On the basis of the similar analysis as shown by Figure 5f, with the internal photothermal conversion design, the thermal energy transfer needs to pass through only ′ to Rrc, and the overall thermal resistance (Rtot ′ ) can be Rcv1 ′ = Rcv1 ′ + Rrv1 + Rrm + Rrcs + Rrc. The heat expressed by Rtot transfer coefficient at the vapor/liquid interface (hδ) can be described by hδ = qδ/(Tv − Tl), where qδ is the latent heat and Tv and Tl are the vapor and liquid temperatures at the interface, respectively. With the internal interfacial evaporation design, the vapor bubbles can easily escape from the liquid water into the chamber; thus, the temperature difference (Tv − Tl) is ′ rather than Rcvl. smaller, which in turn leads to a smaller Rcv1 With the same device, the values of Rcc, Rccs, Rcm, and Rcvl are equal to those of Rrc, Rrcs, Rrm, and Rrvl, respectively. On the basis of this analysis, in ideal cases when the whole loop of liquid vaporization and vapor condensation can proceed ′ is approximately half of Rtot, smoothly for both designs, Rtot 23416
DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
Research Article
ACS Applied Materials & Interfaces confirming the advantage of the new solar-thermal energy harvest design within the chamber. Apparently, the experimentally measured thermal resistance difference between the conventional design and the new design is much larger than theoretically analyzed result. This discrepancy can be ascribed to the fact that, in the conventional external photothermal conversion design, the converted thermal energy tends to be easily lost to the surroundings, which results in a reduced amount of thermal energy for driving the evaporation− condensation cycle in the chamber. By contrast, the new internal photothermal conversion mitigates the heat loss problem by timely utilizing the converted thermal energy to vaporize the fluid. Therefore, the shortened heat-transfer path and reduced heat loss from the internal plasmonic heating together contribute to the decreased thermal resistance of the solar-thermal energy harvesting device. Finally, we utilized the device to apply the collected solarthermal energy for water heating applications. A tank filled with 20 mL of water at 20 °C was connected to the releasing end to receive the harvested solar-thermal energy. We comparatively studied the heating performance of the devices with two different designs by monitoring the temperature rise of the water in the tank. Figure 6 shows that, as soon as the solar light
Compared with the conventional design, the solar-thermal harvest efficiency driven by interfacial plasmonic heating evaporation is increased by 26.2%.
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CONCLUSIONS In this work, we report on the application of the plasmonic heating effect of noble metal nanoparticles for efficient and convenient solar-thermal energy harvesting. The novel design combines the interfacial evaporation driven by plasmonic heating of paper-supported Au NP films under solar irradiation and phase-change-based heat-transfer technology within a sealed chamber. This new approach integrates thermal energy conversion and transportation within a single device and significantly reduces the overall thermal resistance. As a proof of concept application, we demonstrated direct harvesting of solar-thermal energy for efficient hot water generation. The unique device structure design also provides potential for further optimization of the solar-thermal conversion, heat and mass transportation, and thermal energy release processes to speed up solar-thermal energy harvest and explore other thermal-related applications. In the future, more durable substrates made from stable polymers such as polyvinylidine fluoride, mesoporous ceramics, or hybrid organic−inorganic membranes, which have already been used in water treatment systems,43 could potentially be better candidates for long-term usage. This reported system could be further improved by replacing Au NPs with other low-cost solar-thermal converters such as black metal oxide particles or carbon nanomaterials and introducing stronger bonding between the converters and the substrates to explore commercial solar-thermal harvesting applications.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b08077. Absorption spectrum of PANF, FTIR spectra of Au NPs, airlaid paper and PANF, XRD pattern, and XPS spectrum of base-treated copper mesh (PDF)
Figure 6. Solar water heating temperature evolution profiles with conventional and new solar-thermal harvesting designs.
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Corresponding Authors
is shined onto the PANF, the water in the tank warmed immediately. The temperature quickly climbed from 20 to 36 °C within the initial 8 min and then steadily increased to more than 40 °C with prolonged illumination time. In the controlled device, the water temperature increasing rate and final temperature values are much lower, meaning that the interfacial evaporation design had a quicker response and higher energy harvesting efficiency. The overall solar-thermal harvesting efficiency (η) of the device can be calculated by the following equation: η=
cmΔT qAt
AUTHOR INFORMATION
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the National Natural Science Foundation of China (Grants 51403127, 91333115, 51420105009, 51521004, and 21401129), the Natural Science Foundation of Shanghai (Grants 13ZR1421500 and 14ZR1423300), the “Chen Guang” project from Shanghai Municipal Education Commission and Shanghai Education Development Foundation (Grant 15CG06), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the State Education Ministry, the project from Guangdong Provincial Key Laboratory of Materials for High Density Electronic Packaging (Grant 2014B030301014), and the Zhi-Yuan Endowed fund from Shanghai Jiao Tong University for financial support of this work.
(1)
where c is the specific heat capacity of water, m is the mass of water in the tank, and ΔT is the temperature rise of water. With the same solar energy input and the same amount of water in the tank, the relative efficiency increase (ε) can be described by η − η2 ΔT1 − ΔT2 = ε= 1 η2 ΔT2 (2) 23417
DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
Research Article
ACS Applied Materials & Interfaces
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DOI: 10.1021/acsami.6b08077 ACS Appl. Mater. Interfaces 2016, 8, 23412−23418
