Phase Change Material Heat Sink Research Articles

Design and performance assessment of a solar photovoltaic panel integrated with heat pipes and bio-based phase change material: A hybrid passive cooling strategy

This study investigates the effectiveness of an indirect passive cooling solution for photovoltaic (PV) panels using flattened heat pipes (FHPs) and phase change material (PCM). An innovative passive cooling design is proposed to cool a PV panel using multiple FHPs with a thin graphite sheet between the PV panel and the FHPs. Five experimental cases are examined under varying heat flux loads. Case O serves as the baseline with no cooling system, while Cases 1 to 4 feature different configurations of FHPs and aluminum sheets, with PCM heat sinks added in Cases 2 and 4. The investigation focuses on temperature profiles, temperature reductions, and final temperatures of the PV panel, especially at the end of a 4-hour experimental period when the PCM is fully melted. The results show significant temperature reductions in Case 1 compared to the baseline, with further improvement in Case 2 due to the PCM heat sink. Temperature reductions in Cases 2 and 4 are consistently higher than in Cases 1 and 3, demonstrating the enhanced cooling potential of PCM. Case 4 achieves the highest temperature reduction of 37.0 °C, followed by Case 2 with 34.9 °C under a radiative heat flux of 1000 W/m2. Using 4 FHPs (Cases 1 and 2) is economically justified, offering comparable cooling performance to 8 FHPs (Cases 3 and 4), thus ensuring cost-effectiveness and reducing material usage by over 50 %. A maximum enhancement in PV electrical efficiency of 17.3 % is achieved in Case 2 during PCM phase change with a radiative heat flux of 1000 W/m2.

Design and performance assessment of a triply-periodic-minimal-surface structures-enhanced gallium heat sink for high heat flux dissipation: A numerical study

This study numerically investigates a phase-change material heat sink using gallium and Primitive Triply Periodic Minimal Surface (TPMS) cells structure as in-fill for applications requiring high heat-flux dissipation, e.g., electronics. Initially, we used only gallium without thermal conductivity enhancers, relying solely on buoyancy-driven circulations of melted gallium for the convective cooling of a hot sink base. However, this study aims to surpass gallium’s innate heat-dissipation capability. Therefore, the sink is enhanced with a high conductivity Primitive TPMS cells structure. Hybridization of conduction and convection heat dissipation enhancements is accomplished by using only one layer of the TPMS cells installed at the hot sink base. Comparison with the full TPMS structure filling option is made. In the full TPMS structure filling option, the sink relies mainly on conduction through the TPMS structure’s body and less on natural convection. However, equipping the sink with TPMS structures reduces the overall latent heat storage capacity. Therefore, additional gallium is added to the sink to match the overall gallium content in the baseline case without TPMS structures. Furthermore, the effect of the boundary conditions applied at the wall is explored. The results show considerable improvements in heat dissipation and peak temperatures with the TPMS cells, where by the time 100 s (about 20 s post complete melting) peak temperatures are about 13 percent lower than in the case without TPMS structures. Furthermore, the full structure filling option demonstrates superior performance over the partially filled ones, highlighting the importance of conduction through TPMS cells over convection in the free gallium space. Unlike the partial filling option, conduction in the full filling option has a continuous favorable impact on heat dissipation from the onset of the heating process.

3D transient numerical analysis of PCM dendritic cylindrical heat sinks designed by constructal theory

The phase change material (PCM) heat sink represents an important cooling tool for many applications. The presence of a heat sink in devices requires additional space to occupy it. This led to modeling this space to obtain the highest thermal performance with the smallest size. Among the modern modeling methods is constructal theory. This work presents a numerical modeling of the performance of cylindrical phase change material heat sinks with branched heat transfer fluid tubes in the manner of arterial and venous according to constructal theory. The aim of numerical simulations is to demonstrate the effect of growth in design by increasing the number of branches on thermal performance and melting time and the extent to which this is reflected in pressure drops. Several branching configurations are studied for comparison purpose. The governing continuity, momentum and energy equations were solved using the computational fluid dynamics method. Three-dimensional transient simulations of the melting process of phase change materials were performed using an enthalpy and porosity model. Four combinations of constructal dendritic tubes were considered. The results show that the proposed dendritic PCM heat sink significantly reduces the melting time of PCM compared to the traditional heat sink consisting of a shell and single tube up to 69.1 %. The drop in heat transfer fluid temperature at the outlet decreased by up to 51.7 %. The results proved also the heat transfer enhancement is governed with pressure drop increase because of changing branches configuration. Finally, this paper demonstrated the ability of constructal theory to provide promising solutions for cylindrical heat sinks of phase change materials in various applications.

Long-Lasting Heat Dissipation of Flexible Heat Sinks for Wearable Thermoelectric Devices.

Flexible wearable thermoelectric (TE) devices hold great promise for a wide range of applications in human thermal management and self-powered systems. Currently, the main challenge faced by flexible TE devices is the inadequate dissipation of heat, which hinders the maintenance of significant temperature differences over prolonged periods. Most existing heat sinks, being rigid in nature, compromise the overall flexibility of the device. Therefore, the challenge lies in maintaining device flexibility while ensuring effective heat dissipation. In this study, we developed a flexible phase-change material (FPCM) heat sink to address this issue and enhance the heat dissipation capabilities of TE devices (FPCM-TED). When used as a thermoelectric cooler (TEC), the FPCM heat sink efficiently absorbs heat from the hot end, enabling long-lasting and high-performance cooling of the TEC. This capability effectively reduces body temperature by up to 11.21 °C and can be sustained for at least 300 s. Additionally, when employed as a thermoelectric generator (TEG), the FPCM absorbs heat at the cold end, thereby increasing the temperature difference between the hot and cold ends and enhancing the output performance of the device. By integrating FPCM-TED into a fabric wristband, we successfully developed a self-powered wireless pedometer sensing system. This breakthrough lays a solid foundation for the application of wearable, smart clothing.

Waste heat management in electric motors using thermoelectric generator integrated with phase change material and metal foam-embedded heat sink

The waste heat management process from various thermal sources is associated with promising results in the energy conversion field. Thermoelectric generators integrated with phase change materials containing metal foams are useful means for recovering waste heat and converting it into electrical energy. Installing these hybrid cases on common heat sources and providing a practical strategy for waste heat management addresses a significant research gap in this field. The aim of this study is to manage waste heat from a three-phase asynchronous electric motor of a milling machine for the first time using a novel prototype thermoelectric system. Four thermoelectric modules (connected electrically in series) with zero-cooling energy phase change material and copper foam heat sink were embedded on the motor body. Hence, continuous and fluctuating loads were imposed on the motor, starting from ambient temperature. This caused the motor body to heat up and transfer the wasted heat to the module and the environment. The results of this study show that the proposed system was successfully started via the waste heat of the motor body. Thermal energy was absorbed from the hot side of the module, and the hybrid heat sink controlled the temperature of the cold side. Moreover, an appropriate temperature difference was provided across the module, and the system produced electricity for a long time during milling operation. The maximum output voltage in constant and periodic loads, with on/off durations of 180 s and 360 s, was recorded as 960 mV, 1280 mV, and 1440 mV, respectively. The mentioned hybrid thermoelectric system provides a unique solution for waste heat management in industrial applications, improving economic savings.

Experimental study on a rectangular evaporator loop heat pipe with a phase-change material heat sink

To satisfy the heat dissipation requirements of high heat flux electronic devices in extreme conditions where no suitable heat sink exists, such as in the flight process of hypersonic aircraft and the re-entry process of spacecraft, a rectangular evaporator loop heat pipe (LHP) with a phase-change material heat sink was designed and developed. Extensive experimental studies on the thermal control performance of the LHP have been performed, mainly including the startup performance, maximum temperature control time, dynamic response to varying heat load, and the heat transfer limit. Experimental results showed that the LHP could successfully realize the startup at a small heat load as low as 5 W. Under 100 W heat load, the LHP can keep operating for 4 h and 16 min at most with the operating temperature lower than 50 °C, including 2 h and 40 min of quasi-stable operation. The heat transfer limit of the LHP could reach up to 200 W, corresponding to a heat flux of 13.3 W/cm2 at the evaporator. In addition, the LHP exhibited excellent dynamic response characteristics to varying heat loads, holding great application potential in future thermal control tasks in extreme conditions.

Optimizing Waste Heat Conversion: Integrating Phase-Change Material Heatsinks and Wind Speed Dynamics to Enhance Flexible Thermoelectric Generator Efficiency.

Flexible thermoelectric generators (FTEGs) have garnered significant attention for their potential in harnessing waste heat energy from various sources. To optimize their efficiency, FTEGs require efficient and adaptable heatsinks. In this study, we propose a cost-effective solution by integrating phase-change materials into FTEG heatsinks. We developed and tested three flexible phase-change material thicknesses (4 mm, 7 mm, and 10 mm), focusing on preventing leaks during operation. Additionally, we investigated the impact of wind speed on the output performance of FTEGs with a flexible phase-change material heatsink. The results indicate that the appropriate flexible phase-change material thickness, when integrated with considerations for wind speed, demonstrates remarkable heat-absorbing capabilities at phase-change temperatures. This integration enables substantial temperature differentials across the FTEG modules. Specifically, the FTEG equipped with a 10 mm thick flexible phase-change material heatsink achieved a power density more than four times higher when the wind speed was at 1 m/s compared to no wind speed. This outcome suggests that integrating phase-change material heatsinks with relatively low wind speeds can significantly enhance flexible thermoelectric generator efficiency. Finally, we present a practical application wherein the FTEG, integrated with the flexible phase-change material heatsink, efficiently converts waste heat from a circular hot pipe into electricity, serving as a viable power source for smartphone devices. This work opens exciting possibilities for the future integration of flexible thermoelectric modules with flexible phase-change material heatsinks, offering a promising avenue for converting thermal waste heat into usable electricity.

Experimental and numerical study on temperature control performance of phase change material heat sink

With the increasing power consumption of electronic products, the rising temperature leads to the deterioration of working environment and the reduction of service life. In order to control the temperature rise of electronic products, in this paper, the heat sinks with phase change material (PCM) and honeycomb metal were designed. And their performance was compared with that of the original heat sink (without PCM and honeycomb metal) then studied under various working conditions. Paraffin (n-eicosane) and prepared low melting point alloy were filled into the heat sink with honeycomb metal. The temperature control performance of heat sink was tested experimentally under different heating power. A two-dimensional heat transfer mathematical model of honeycomb metal PCM heat sink was established and solved numerically. The numerical results were compared with experimental data to verify the mathematical model. The results demonstrate that PCM heat sinks effectively controls the temperature of electronic devices and the low melting point alloy makes heat sink better performance than paraffin. Honeycomb metal further decreases the temperature of the paraffin heat sink by up to 3.6 °C, and extends the effective working time of the alloy heat sink by 14 %. The performance of the low melting point honeycomb metal heat sink is superior to that of the paraffin honeycomb metal heat sink at high heating power, and is close to the latter at low heating power. The effective working time of PCM honeycomb metal heat sink is significantly extended when the PCM melting point is close to the limit temperature, especially at high heating power and for the PCM with low thermal conductivity. This study provides valuable reference for temperature control design of electronic products.

Effect of fin geometry on the thermal performance of a phase change material heatsink

This paper presents an experimental and computational study to optimize a novel folded fin phase change material (PCM) heatsink. An experiment was conducted on a custom heatsink assembly. The results were used to validate a finite element model created in ANSYS fluent. This model utilized solidification/melting calculations in Fluent to study the thermal performance of the heatsink assembly with an applied power ranging from 16 to 48 W, varying fin gaps between 2.32 and 5.52 mm, and fin wall thickness of 0.8–2.4 mm. This study revealed that the proposed fin design provides increased thermal effectiveness for applied power up to 48 W. It was also found that that a fin wall thickness of 0.8 mm increased the time required to fully melt the PCM by 17% compared to the 2.4 mm thick fins. A fin gap of 5.52 mm resulted in an 11% increase in melt time when compared to the smallest gap studied of 2.32 mm.

Gaussian process optimization of phase change material heat sink design

Thermal management strategies based on phase change materials (PCMs) offer promising alternatives to conventional approaches, owing to their ability to absorb transient heat flows by melting. However, the design of PCM heat sinks is challenging due to the nonlinear interactions between heat flow and phase change during melting and solidification. This paper presents the design optimization of PCM heat sinks using a Gaussian Process (GP) method. We show that the GP method offers a significant decrease in computational intensity compared to conventional approaches used for optimization. We apply our method to optimize the design of a PCM-integrated heat sink for a gallium nitride (GaN) device that operates under a pulse train heat profile. Field’s metal-infused copper foam is used as the PCM. We used a reduced order model (ROM) for the PCM-integrated device, which is validated through experimental measurements and finite element simulations. We coupled the ROM with the GP optimizer to determine PCM heat sink design parameters, including geometric dimensions and the composition of the composite PCM, which minimizes both the GaN maximum junction temperature and junction temperature swing. We tested the GP optimizer under various conditions, encompassing GaN device power levels ranging from 1 to 4 W, pulse widths spanning 1 to 10 s, and duty cycles ranging from 10 to 90%. The GP optimizer produced nearly identical results to particle swarm optimization, with a mean absolute error <0.2 °C for optimal thermal performance and a reduction in computational time of 39×. Overall, our design method offers a computationally efficient approach to optimizing PCM-integrated heat sinks for the transient thermal management of electronic devices.

Effect of T-shaped fin arrangements on the temperature control performance of a phase change material heat sink

The control of operating temperature in phase change material (PCM) heat sinks is restricted by their low thermal conductivity. The present study proposes a novel T-shaped fin strategy, targeting to improve the thermal management capability of PCM heat sinks in the field of electronic devices, i.e., the originality behind is that heat flux from the heated surface can be transported to the solid phase region by T-shaped fins over a longer distance. Based on the background of photovoltaic cell thermal management, a numerical calculation was conducted to investigate the temperature control performance of PCM heat sinks with different T-shaped fin layouts, which was compared with heat sinks without fins and with rectangular fins. The key discoveries indicate that the melting front in the heat sink cavity was severely influenced by the fins, which first suppressed and then enhanced natural convection in the melting process and improved the PCM temperature uniformity. Compared to the unfinned and rectangular fin systems, the employment of T-shaped fins could reduce melting time respectively by up to 25.5% and 14.5% (achieved by case 8), and lower wall temperature respectively by maximum values of 18.9 °C and 4.9 °C (obtained by case 12).

The impact of different fin configurations and design parameters on the performance of a finned PCM heat sink

This work builds on our recent research on finned phase change material (PCM) heat sinks, where we proposed a novel Gallium based PCM heat sink concept that counter-intuitively incorporated fins detached from the hot sink base instead of being fully attached to it. The detached and fully attached fin configurations studied utilized the same overall fin size and material resources. The attached fin approach offered less outer fin surface area exposed to the ambient surroundings and less PCM capacity compared with the detached fin approach. However, the attached fin approach facilitated a more direct path for the heat dissipation into the ambient surroundings via the fin body. As an extension of the previous work, the present work explores finned heat sinks that combine the advantages of the above two approaches. First, we present results for two limiting baseline cases of the two finning categories: attached fins with lower outer fin surface area and less PCM and detached fins with a larger exposed fin area and more PCM. Next, we study a heat sink case with attached fins tall enough to have a total outer fin surface area equivalent to the outer surface area of the detached fins case but with less PCM content. Subsequently, we consider cases of fully attached fins with the same total outer fin area and the same total PCM capacity as the detached fins baseline case. Here, we achieve the same PCM content in the sink while still having fully attached fins simply by increasing the overall heat sink size to accommodate additional PCM. This is done in two ways: (1) by expanding the heat sink size in the horizontal direction (i.e., increasing the heat sink width) at constant heat sink height, and (2) by expanding the heat sink height at constant heat sink width. In this work, we propose the best way to utilize the resources in terms of used PCM and used fin content in the heat sink space to achieve the ultimate goal of attaining lowest peak temperatures.

A novel method to improve the performance of PCM thermal energy storage units using a small oscillator plate-numerical analysis

Employing a small oscillator plate is proposed as a novel idea to improve the performance of phase change material (PCM) based thermal energy storage unit. This idea could make mixing heat flow toward the PCM solid-liquid interface to hasten the melting and heat transfer rates. Opposite to the vibration of the whole PCM heat sink suggested in the literature, it needs very slight mechanical energy for oscillation. The oscillator plate was installed at three positions for the horizontal and vertical PCM heat sink: i) the middle of the hot plate, ii) the bottom of the hot plate, and iii) the corner of the heat sink. A computational fluid dynamics model has been employed to model the PCM melting process and evaluate the induced mixing heat flow and its effect on natural convection. A new mechanical method using vibration energy accelerates heat flow to improve heat transfer and thermal energy absorption. The results reveal that in the best case with transversal oscillation at the corner of the heat sink, the melting rate and heat transfer rate (Nusselt number) increase by 39 % and 64.2 % compared to no vibration case, respectively. Also, the absorbed heat energy rate (AHR) within the PCM heat sink is elevated from 0.51 to 0.79 (54.9 %), while the oscillator just consumed as small as 438 mJ of mechanical energy, reflecting this mechanical approach's uniqueness.

Three-dimensional Lattice Boltzmann study on structure optimization and heat dissipation performance of pin-fin heat sink integrated with phase change material

Phase change material (PCM) cooling is an excellent approach for reducing the excessive temperature of electronic devices. However, the heat transfer capacity of a heat sink is diminished by the low thermal conductivity of a PCM. Although this issue can be ameliorated by using extended pin-fins and nanoparticles, the latent heat storage capability of a PCM is decreased. To optimize the heat transfer efficiency of PCM heat sink with pin-fins, in this study, the effects of pin-fin shapes (circle, triangle, square, pentagon, hexagon, and octagon), novel arrangements with triangular fins, and the volume fraction of nanoparticles are investigated using the 3D enthalpy-based multi-relaxation time lattice Boltzmann method. The results showed that the PCM heat sink with triangular pin-fins exhibited optimal thermal performance due to the largest heat transmission area between the PCM and pin-fins. After conducting optimization research on triangular pin-fin arrangements, the full melt time was shortened by 14.3 % and the heat dissipation power was increased by up to 15.2 %, when compared with the PCM heat sink with triangular pin-fins. Furthermore, nanoparticles with a volume fraction of <0.1 were beneficial for balancing the elevated heat dissipation capacity and reducing the latent heat duration of the nano-enhanced PCM.

Flexible Thermoelectric Devices with Flexible Heatsinks of Phase-Change Materials and Stretchable Interconnectors of Semi-Liquid Metals.

Flexible thermoelectric (TE) devices offer great potential for wearable thermal management and self-powered systems, but heat dissipation and electrical interconnection remain key challenges. In this study, we address these issues by integrating flexible TE devices with phase-change material (PCM) heatsinks and stretchable semi-liquid metal (semi-LM) interconnectors. The effectiveness of PCMs with varying melting points for temperature regulation in different environmental conditions is demonstrated, delivering cooling effects exceeding 10 °C. Furthermore, the utilization of semi-LMs instead of LMs enables excellent stretchability and efficient heat dissipation. Moreover, the TE devices generate power with a density of 7.3 μW/cm2 at an ambient temperature of 22 °C, making it an ideal power source for a wearable self-powered sensing system. Successful integration into garments and armbands confirms the practicality and adaptability of these flexible thermoelectric devices, establishing them as critical components for future wearables with superior resilience to daily wear and tear.

Phase change heat transfer in a vertical metal foam-phase change material thermal energy storage heat dissipator

A metallic foam heat dissipator for cooling electronic components was addressed. A heat dissipator is a partitioned aluminum container loaded along with aluminum metallic foam and saturated with paraffin wax. A heat flux at a surface contains a basic uniform flux and the step transient raise, which should be managed by a heat dissipator and a Phase Change Material (PCM). The regulating equations for a melting/solidification transfer of heat & momentum transport in a heat dissipator were instituted into a structure of partial differential equations. Then, the vital monitoring equations were converted into a general dimensionless type and solved by the Finite Element Method. A mesh adjustment technique & automated time-step control was employed to control the accuracy & convergence of the result automatically. An adaptation technique controls the mesh resolution at the melting/solidification interface. The dimensionless temperature of fusion is a vital factor in the control of the surface temperature and heat dissipator efficiency. Considering a fixed amount of material for walls, a heat dissipator with thick sidewalls and thin top and bottom walls results in slightly better thermal performance. Using a PCM heat sink could reduce the heated surface temperature by >175 % during the pulse load.

A morphology optimization of enclosure shape of low melting point alloy-based PCM heat sink

The enclosure shape of the phase change material (PCM) container is an important factor affecting the thermal performance of PCM heat sinks. A novel morphology optimization method is developed and used to optimize the enclosure shape of the low melting point alloy (LMPA) based PCM heat sink. The working process of the LMPA heat sink is firstly simulated with a simplified 2D numerical model. Then, morphology operations (erosion and dilation) are performed to update the material distribution in the design domain based on the simulation results. Through alternative execution of simulation and morphology operations, the desired optimal enclosure shape is obtained, and the optimization results are further experimentally validated. It is shown that the proposed optimization method can obtain better optimization results than traditional methods. With a fixed heat flux of 30 kW/m2, the experimental temperature rise rate of the optimized LMPA heat sink is about 1.59 °C/min, which is 57.9 % lower than the theoretical minimum temperature rise rate of the corresponding rectangular LMPA heat sink. The experimental protection time of the optimized LMPA heat sink is about 924 s with a safety temperature of 120 °C, which is 31.3 % longer than the theoretical maximum protection time of the corresponding rectangular heat sink.

Energy impact of heat pipe-assisted microencapsulated phase change material heat sink for photovoltaic and thermoelectric generator hybrid panel

As the importance of energy saving continues to increase owing to climate change, various Internet of Things sensors, related to building temperatures, humidity, and energy usage, are being employed in buildings, such as in building energy management systems. Aiming to satisfy the rapidly increasing electric energy demands of buildings, studies have combined various building-integrated photovoltaic (BIPV) and thermoelectric generators (TEGs) to recover sunlight and heat wasted from building envelopes. However, in most previous studies, active methods for heat rejection were applied to increase the temperature difference between both ends of the TEG and cooling of the solar panel. The actual constructability problems, such as leakage problems, were insufficiently addressed. Therefore, this study proposed a BIPV-TEG system with increased constructability and heat dissipation efficiency using a heat pipe and microencapsulated phase change material (mPCM). In addition, this study analyzed the thermal behaviors and improvements in power generation efficiency through field tests by manufacturing a prototype. The results of the outdoor experiment indicated that the BIPV-TEG-PCM prototype improved power generation efficiency by approximately 2% in the intermediate season and 2.5% in the summer relative to the efficiency of a general PV panel. Moreover, using a single TEG, approximately 3.06 Wh of the heat wasted in the building envelope can be recovered as a form of electricity annually.

THE EFFECT OF USING PHASE CHANGE MATERIALS AND EXAMINING THE ASPECT RATIO IN AN AIR-COOLED SYSTEM OF A PLATE BATTERY CONNECTED TO A SOLAR SYSTEM

Lithium-ion batteries are widely used in the electronics industry to store electrical energy. One of the challenges with these batteries is that they heat up during operation, which can damage the battery. For this reason, this paper simulates the cooling process of a plate-type (BTP) lithium-ion battery pack. To control the temperature of the battery (T-B), a laminar air flow and a phase change material (PCM) are used. The PCM is placed in a heat sink around the battery. This evaluation is performed temporarily for four different dimensions of the PCM pack. The hot outlet of this system is used to provide the thermal energy required for a small residential building (THE) at a mild temperature. The BTP was also simulated using COMSOL. The results show that the use of larger heat sinks can increase the maximum (MAX) and average (AVE) temperature of the battery. The minimum T-B occurs at different times for the smaller PCM heat sinks. Also, when using a heatsink with a larger PCM volume, it takes longer for the PCM to fully solidify. A BTP with 5 or 50 battery cells can provide up to 3% or 30% of the THE required for the building.

Zero-cooling energy thermoelectric system by phase change material heat sink integrated with porous copper foam

Active cooling of thermoelectric generators (TEGs) by fans or water pumps imposes cooling energy reducing net power generation in TEG systems. This study aims to make zero-cooling energy TEG systems by integration of low temperature phase change material (PCM) and porous copper foam on cold side of the TEG. In this design, air fan is eliminated. To study the proposed system under transient heat input, the TEG system was exposed to continues and dynamic heat flows. Results of this study show that, the proposed fanless heat sink is an effective and alternative cooling solution for TEG systems. Utilization of the copper foam in the PCM not only reduced cold side temperature of the TEG by 11.3 %, but it also prevents hot side of the TEG from overheating. With this cooling technique, output power of the TEG increased 53.5 % compared to conventional TEG systems operating with fan. The results of this study provide a guideline for design of self-sufficient and autonomous TEG systems with zero-cooling energy used for energy harvesting for sensors and actuators under dynamic heat sources.