Fin Configuration Research Articles

Energy storage performance improvement of phase change materials-based triplex-tube heat exchanger (TTHX) using liquid–solid interface-informed fin configurations

The future of power generation is predicted to be greener with greater uptake in renewable energy which will be more intermittent and make matching demand harder. Latent thermal energy storage using phase change materials (PCMs) could provide a solution to that problem. PCMs can store large amounts of energy in small volumes, however, the main issue is the low conductivity of PCMs, which limits the rate that energy can be stored due to the slow melting and solidification processes. In the present study, we design and optimise a flow structure-informed fin configuration for triplex-tube heat exchangers (TTHXs) that accelerates the PCM melting process to allow for faster energy storage rates. The computational fluid dynamics modelling is developed to evaluate different TTHX geometries and find the most efficient fin geometries. The results show that an optimal fin geometry can provide a 57.4 % reduction in melting time, which demonstrates that fins offer a very effective way of reducing the melting times of PCMs without taking up much volume. We also found that fins in the lower half of the PCM are more effective in reducing total melt time than fins in the upper half. It is revealed that curved fins offer better performance when compared to similar straight fins. Lastly, it is observed that horizontal or angled surfaces allow for more natural convection in TTHX. The findings can be used to inform future studies on energy storage performance improvement of PCMs.

Numerical Analysis of an Aerofoil Fin Integrated Double Pass Solar Air Heater for Thermal Performance Enhancement

The Solar Air Heater (SAH) is considered to be one of the promising devices for the utilization of solar radiation. Extracting more heat to the flowing air is the focus of researchers, and many novel ideas are adopted to improve the efficiency of such collectors. The objective of the present work is the enhancement of thermal performance using a numerical analysis of a single flow double pass solar air heater with two types of arrangements of aerofoil fin configurations. The effect of the aerofoil fin configurations and the height of the fin are investigated for their thermal and thermohydraulic efficiencies. The height of the fin varied parametrically for the Reynolds number ranging from 3000 to 24,000 by keeping the axial pitch of the fin as a constant. It is found that the thermal efficiency increases with the increase in fin height due to an increased flow turbulence causing more absorption of heat to the working fluid. However, it is seen that the varying height of the fin beyond a certain height has yielded an adverse effect in terms of lesser thermal efficiency due to the expected flow blockage in the main stream. The thermohydraulic efficiency increases as the height of the fin decreases. The Computational Fluid Dynamics (CFD) results revealed that the optimum aerofoil fin configuration yields approximately a 23.24% higher thermal efficiency when compared with that of the single pass solar air heater (base model). The thermohydraulic efficiency exceeds the optimum aerofoil fin configuration compared with the base model by approximately 20.94%.

Experimental evaluation of the effect of perforated spiral fins on the thermal performance of latent heat storage units

The spiral fins are widely employed as an innovative fin configuration in latent heat storage units (LHSU) to improve the poor thermal conductivity of Phase Change Material (PCM). Its persistent annulus promotes heat exchange in PCM, but still interferes with buoyancy-driven natural convection. Perforation is a potential solution to facilitate natural convection. Based on this, the thermal properties of the punctured spiral finned LHSU were experimentally studied. An experimental setup was constructed with three spiral finned LHSUs, two of which were installed with perforated spiral fins with 16 mm and 12 mm perforation diameters. The axial and radial temperature distribution, heat transfer characteristics and efficiency were evaluated for three LHSUs. Experimental results showed that the thermal performance of LHSU was improved remarkably by using perforated spiral fins with higher heat benefits achieved at lower heat transfer areas. The thermal efficiency and average heat flux reached 63.4 % and 1370.7 W/m2 respectively, while the average Nusselt number was 44.0 % higher than that of the solid fin. For the same perforation area, fins with higher diameter perforations achieve superior thermal properties and stronger convective heat transfer, while fins with lower diameter perforations continue to limit natural convection.

Augmentation of Plate-Fin Heat Exchanger Performance with Support of Various Types of Fin Configurations

A plate fin heat exchanger PFHE is a form of compact heat exchanger CHE containing of a block of alternating layers of fins and flat separators known as parting sheets. In this paper, 3-dimensional incompressible laminar flow and heat transfer in a (PFHE) has been investigated numerically. The influences using different fin configurations and the effect of the offset of these fins, on thermal and hydro-dynamic fields are presented. The cases of study for the PFHE are established, by using the fins with different configurations (plain rectangular (PR) and it's offset (OR), plain triangular (PT) and it's offset (OT) which is a novel shape, and a novel combination of a two fin shapes, between rectangular and triangular (ORT)). The upper and lower plates are exposed to a constant heat flux and the working fluid is air where chosen under a laminar range of (Re) number (600 to 1400). The laminar flow and heat transfer is governed by continuity, momentum and energy equations. ANSYS FLUENT (2021 R1) is used to get the numerical results, based on finite volume method. One of the most utilized fins for a PFHE is the offset fin arrangement due to its higher heat change amount, adjustable structure, and enhances flow turbulence and heat transfer coefficient by interrupting the thermal boundary layer. The obtained results of using of the offset configuration increases the Nusselt number by 20.32% and 17.82% for OSF rectangular and OSF triangular, respectively as compared with the with plain configurations, as a result, a significant heat transfer enhancement is observed. And significant increase in the friction-factor is found to be 79.8% and 48.7% for OT and ORT, as compared with the PT. It can be observed that use of the OSF configuration leads to greater f-factor for triangular configuration values. In addition, the temperature fields for the primary and secondary flows were showed in a contour diagram.

Experimental Analysis of Nano-Enhanced Phase-Change Material with Different Configurations of Heat Sinks.

The demand for high-performance and compact electronic devices has been increasing day by day. Due to their compactness, excessive heat is generated, causing a decrease in efficiency and life. Thermal management of electronic components is crucial for maintaining excessive heat within the limit. This experimental research focuses on the combined effect of nano-enhanced phase-change material (NePCM) with different configurations of heat sinks for cooling electronic devices. Multi-walled carbon nanotubes (MWCNTs) are used as nanoparticles with concentrations of 3 wt% and 6 wt%, RT-42 as the phase-change material (PCM), and aluminum as the pin fin heat sink material. Different configurations of the heat sink, such as circular, square, and triangular pin fins, are used against the fixed volume fraction of the fins. It is found that the square configuration has the highest heat transfer with and without PCM. A maximum base temperature reduction of 24.01% was observed in square pin fins with RT-42 as PCM. At 6 wt% of NePCM, the maximum base temperature lessened by 25.83% in the case of a circular pin fin. It is concluded from the results that a circular pin fin with NePCM is effective for base temperature reduction, and all fin configurations with NePCM collectively reduce the heat sink base temperature.

Melting expedition in horizontal triplex tube heat exchangers via radial and combined radial-axial fins

The effects of using radial fins on the melting of a Phase-Change Material (PCM) inside a horizontal Triplex Tube Heat Exchanger (TTHX) are investigated in this study. To this aim, several configurations of radial fins and their combination with conventional axial fins are considered. First, the melting in a TTHX equipped with axial fins is simulated to assess the validity of the solver. The numerical predictions agree well with the experimental data. Next, the melting process in a TTHX equipped with different configurations of radial fins is simulated to compare their thermal performance with that of the longitudinal fins. Effects of multiple parameters are investigated, such as the fin radii and number, replacing full circle fins with arc fins, and axial distribution of the fins. The results indicate that inserting arc fins in the lower section of the PCM enclosure improves the thermal performance significantly. This leads to an 18 % reduction in melting time when their axial spacing is non-uniform. Also, combined radial-axial configurations, considered in the present research for the first time, greatly accelerate the melting if the axial fins are located on the inlet side of the PCM enclosure and the radial fins are located on the other half.

Enhancement Of Plate-Fin Heat Exchanger Performance with Aid of Various Types of Fin Configurations: A Review

This study is a review of recent studies on heat transfer enhancement in plate fin-heat exchangers (PFHE) with plain and offset (OSF) fins. Thermal designing parameters such as the coefficient of heat transfer, Nusselt number, hydraulic diameter, Colburn factor (j), friction factor (f) and Reynold's number of PFHE was presented in this review for both straight and offset types. According to the results, by replacing plain fins into OSF, the pressure increases because of the increasing of f-factor, while there is a significant increase in Nusselt number and then the heat transfer. The j & f factors, are the most essential two parameters of researching the heat exchanger that were represented as functions of Reynolds number and other geometrical parameters. At the same Reynolds number, the J-factor declines and the friction factor f increases as the fin pitch increases for the same fin height and fin thickness.

Investigation on the Melting Performance of a Phase Change Material Based on a Shell-and-Tube Thermal Energy Storage Unit with a Rectangular Fin Configuration

A case study on the melting performance of a shell-and-tube phase change material (PCM) thermal energy storage unit with a novel rectangular fin configuration is conducted in this paper. Paraffin wax and circulated water are employed as the PCM and heat transfer fluid (HTF), respectively. It can be observed that the melting performance could be significantly improved by using rectangular fins. Melting photographs demonstrate that the melting of the PCM is firstly dominated by heat conduction; then, the melting rate is improved further due to natural convection. Moreover, the results illustrate that the influence of the inlet HTF temperature on the melting performance is significantly greater than that of the inlet HTF flow rate. The liquid fraction of paraffin wax in the PCM unit with a higher inlet HTF temperature is always higher than that with a lower inlet HTF temperature at the same time. The total charging time is reduced by 62.38% and the average charging rate is increased by 165.51% when the inlet HTF temperature is increased from 57 °C to 68 °C. As a result, a higher value of the inlet HTF temperature and a lower value of the HTF flow rate are able to improve the energy efficiency of the PCM unit with a rectangular fin configuration.

Numerical investigation on cooling performance of oil cooled PMSM jacket design with vertical straight fin design

Cooling has been an important parameter to extend the high-speed generator operating conditions. Literature highlights the high speed generator jacketjacket of generator is a crucial part that need to be cooled down to dissipate the coil temperature to ensure the performance of the Permanent magnet synchronous machine (PMSM). Research shows there are work done on the internal jacket design to improve cooling. This research work focuses on further enhancement of more design parameters for the internal oil flow jacket space design to dissipate heat better. The vertical straight fin configurations were deployed to investigate the effect of heat transfer with same cooling medium, Oil. The numerical analysis using ANSYS-FLUENT was completed, converged and mesh independent results were presented. The vertical straight fins improve heat transfer more than triple as compared to the baseline. This will be used as base for future enhancement in PMSM jacket cooling for high speed generator.

Impacts of non-adsorbable gas on the adsorption-based desalination and cooling system with fin branch configurations

Non-adsorbable gas can significantly deteriorate the adsorption dynamics of the adsorption-based desalination and cooling system. In this study, an alternative complete computational fluid dynamic model involving non-adsorbable gas transportation is established. The impacts of non-adsorbable air originating from the incomplete degassing or leakage in the evaporator on the heat and mass transfer characteristics in the adsorbent bed and the performance of the adsorption-based desalination and cooling system are analyzed. Non-adsorbable air can significantly hinder the system performance due to weakened adsorption dynamics and induced additional mass transfer resistance. Moreover, a finned-tube bed attached with branched fins is employed to improve the heat transfer and adsorption dynamics. The impacts of fin configurations on the system performance with non-adsorbable air considered are systematically investigated. Machine learning is employed to construct the quantitative relationship between the fin configuration parameters and the total system throughput. And the optimal fin configuration is further identified via the genetic algorithm. The optimal fin configuration with the fin number of 12 and fin branch angle of 64.4° renders a 24.6% augmentation in the total cooling power and a 20.4% increase in total daily water production, respectively.

Numerical analysis of the effect of the iso-surface fin redistribution on the performance enhancement of a shell-and-tube latent heat thermal energy storage unit for low-temperature applications

In the present study, the melting and solidification processes of a Phase Change Material (PCM) are numerically carried out in eight geometrical configurations of horizontal Latent Heat Thermal Energy Storage (LHTES) units for low-temperature applications. The PCM considered in this study is water undergoing solidification below its density-temperature inversion point (T < 4 °C) at atmospheric pressure, and the Heat Transfer Fluid (HTF) considered is a water/glycol mixture solution. Among the eight geometrical configurations studied, four are made of longitudinal finned tubes and a shell and the other four are made of radial finned tubes and a shell. All the geometrical configurations studied have the same PCM volume, compactness and total heat transfer surface. The objective of the study is to compare their thermal performances in order to highlight the most efficient configurations during melting and solidification processes. Effects of fin redistribution at a constant total heat transfer surface on the local melting and solidification mechanisms are investigated. Variations in the solid volume fraction during melting and solidification and the associated kinetics are compared and subjected to quantitative analysis. Natural convection and its effect on the melting and solidification mechanisms are studied and analysed using the commercial CFD code Star CCM + V12.02. This study shows that increasing the number of fins, at a constant PCM volume, compactness and total heat transfer surface, reduces the thermal performance of the heat storage unit when complete melting or solidification is desired. The opposite behaviour is observed at low melting/solidification rates. Among the configurations studied, the best thermal performances at the end of the melting/solidification phases are obtained in heat storage units with a smaller number of fins. A solidification rate higher than 82 % was reached with the 4 longitudinal fins configuration, compared with 75.7 % with the 8 longitudinal fins configuration, 63.3 % with the 16 longitudinal fins configuration and 55 % with the 32 longitudinal fin configuration after 4 h of solidification process. A similar succession of solidification rates was observed with radial fin configurations. During the melting process, the same trends that had been observed during the solidification process were noted: better performance from configurations with 4 longitudinal or radial fins than from the other configurations with larger numbers of fins after 4 h of the melting process. Conversely, at the very beginning of the melting/solidification process, better performances were obtained in the configurations with the largest number of fins. Therefore, for given values of heat transfer surface augmentation and PCM volume, in shell-and-tube storage units used for low-temperature applications, it is recommended to prioritize finned-tube configurations with small numbers of tall fins rather than those with large numbers of short fins when complete melting or solidification is desired.

Numerical Study of Heat Transfer Enhancement by Arc-Shaped Fins in a Shell-Tube Thermal Energy Storage Unit

Latent heat thermal energy storage (LHTES) technology can alleviate the mismatch between the supply and demand of solar energy and industrial waste heat, but the low thermal conductivity of phase change materials (PCMs) is an issue that needs to be solved. In this work, the effects of the bifurcated fins on melting and solidification are studied, and local and global entropy generation are discussed. The radial lag time and the circumferential lag time were defined to evaluate thermal penetration and thermal uniformity. Subsequently, a novel arc-shaped fin configuration was proposed to further enhance the heat transfer. The results showed that attaching the bifurcated fins could effectively reduce the global entropy generation. Increasing the trunk fin length was beneficial to enhance the thermal uniformity and promote the melting process, while increasing the branch fin was more effective in the solidification process. Overall, thermal uniformity determined the phase change process. More importantly, the concentric arc-shaped fins significantly reduced the heat transfer hysteresis region, showed better thermal performance than straights fins, and the energy storage and release time were reduced by 52.7% and 51.6%, respectively.

Performance enhancement of triplex tube latent heat storage using fins, metal foam and nanoparticles

The inherent low thermal conductivity of latent heat storage materials hinders its effective use due to quite long charging/discharging process. Heat transfer enhancement techniques are promising solutions to overcome this major drawback. In this study, the effect of combining heat transfer techniques including fins of different arrangements, fins-nanoparticles, and fins-metal foam is numerically examined and compared for latent thermal energy storage in a triplex tube. Two fin configurations are examined uniform as well as non-uniform. The predictions of the numerical model are validated by comparisons with experimental data available in the literature. The transient liquid fraction, temperature distribution, and interface position are analyzed for the considered cases. Results show that the non-uniform fin arrangement contributes to improving the thermal energy storage. The non-uniform fin distribution expedites the melting rate by 56.45%. Furthermore, it is shown that the combination of fins-metal foam outperforms the fins-nanoparticles configuration. The time needed for full charging and discharging reduces with fin-metal foam by up to 80.12% and 90.04%, respectively, depending on the fin arrangement. The proposed storage model and results are useful for designing efficient thermal energy storage units.

Parametric investigation of internal Y-shaped fin configurations under natural convection in a concentric annulus

Natural convection heat transfer inside concentric annular enclosures has been well researched for decades. Such enclosures have been employed as intermediate layers between fluid streams in heat exchangers, particularly in latent heat thermal energy storage applications. Convection heat transfer coefficients originating from natural convection are relatively low, which drives the need for heat transfer enhancements by using extended surfaces (e.g., fins, heat sinks). In this study, numerical simulations are performed to investigate the natural convection heat transfer inside a concentric annulus in the presence of Y-shaped fins. Each Y-shaped fin has four important geometric parameters: (i) length of the fin base a, (ii) length of the fin branches b (i.e., the V-section), (iii) primary fin spacing angle θ, and (iv) secondary fin angle or branch angle α. Steady-state simulations are conducted using COMSOL Multiphysics® with constant temperature boundary conditions to generate the laminar natural convection profiles in the enclosure filled with air. The average Nusselt numbers, calculated at both the inner and outer walls of the enclosure, are used to gauge the heat transfer. The model is built with thin layer approximated fins first and subsequently compared to a modified model with fins with finite thickness. The optimized case using the thick fin model is found to yield a percent increase in Nu of 358.8% compared to the case with no fins. Lastly, the entropy generation is considered to determine the second law efficiency of the system, which is approximately 91%.

Twisted-fin parametric study to enhance the solidification performance of phase-change material in a shell-and-tube latent heat thermal energy storage system

Abstract Phase change material (PCM) is considered as one of the most effective thermal energy storage (TES) systems to balance energy supply and demand. A key challenge in designing efficient PCM-based TES systems lies in the enhancement of heat transmission during phase transition. This study numerically examines the privilege of employing twisted-fin arrays inside a shell-and-tube latent heat storage unit to improve the solidification performance. The presence of twisted fins contributes to the dominating role of heat conduction by their curved shapes, which restricts the role of natural convection but largely aids the overall heat-transfer process during solidification. The heat-discharge rate of twisted-fin configuration is increased by ∼14 and ∼55% compared to straight fin and no fin configurations—leading to a reduction in the solidification duration by ∼13 and ∼35%, respectively. The solidification front at various times has also been assessed through a detailed parametric study over the fin height, fin pitch number, and fin thickness. Over the range of values assumed, the fin height is the most dominant parameter – increasing the heat-retrieval rate from 10.0 to 11.4 W and decreasing the discharge time from above 3600 to 2880 s by varying the fin height from 2.5 to 7.5 mm.

Performance enhancement of phase change materials in triplex-tube latent heat energy storage system using novel fin configurations

Phase change material (PCM) has promising applications as an energy storage material in thermal energy storage (TES) systems. However, the low thermal conductivity of PCM limits its applications. To reduce the response time of TES systems, various configurations of fins are used to improve the heat transfer performance of PCM. The Y-structured fins utilize the Y-structure, a common structure in nature, and this study investigates the different structures of Y-shaped fins and the effect of HTF on melting time. A numerical research method based on the enthalpy-porosity method is adopted used for the study. The numerical model of the study is validated using previous experimental data. The simulation results have been obtained, including solid–liquid interface contours, isotherm contours, and evolution of the PCM liquid fraction. The results show that the melting process of the PCM is divided into three main stages and integrated solid fins within the PCM effectively reduce the melting time. Under certain operating conditions, reducing the fin thickness, increasing the fin angle, and increasing the HTF temperature can effectively reduce the PCM melting time. Transient heat transfer rates and dimensionless quantities are analyzed based on numerical results. This study provides potential applications of novel fin structures for new industrial products related to thermal energy storage and management.

Study on heat storage performance of a novel bifurcated finned shell-tube heat storage tank

Improving the heat storage performance of latent heat storage systems plays a crucial role in the utilization of solar energy. In this paper, a vertical shell-tube heat storage tank equipped with a novel set of bifurcated fins has been introduced, and the effects of bifurcation angle, fin number and fin thickness on heat storage performance have been investigated. The results show that the bifurcated fin configuration outperforms the longitudinal fin configuration. The bifurcation angle is not the larger the better, and the bifurcated fins achieve the optimal spatial layout when θ is 60°. The fin number shows a significant effect on the melting process, and the numerical results reveal that the optimum fin number is 6. Moreover, the fin thickness has a certain effect on the heat storage performance, but the enhancement is very weak. Under optimal fin parameters, compared with the finless configuration and the longitudinal fin configuration, the melting time reduction of the bifurcated fin configuration is 65.1% and 33.3%, respectively, and the increase in the average heat storage rate is 174.1% and 48.8%, respectively. The results can provide a certain reference value for the structural optimization of the vertical latent heat storage system.

Study on effect of tank and fin configurations and operating conditions on performance of thermal storage system

The low thermal conductivity of phase change materials (PCMs) is a crucial challenge in utilizing latent heat thermal energy storage (LHTES) systems. Incorporating fins into LHTES system is an effective approach to overcoming the low thermal conductivity of PCM and enhancing its performance. In the present study, computational fluid dynamics is used to investigate the effects of fin configurations and operating conditions on the performance of a shell-and-tube system assisted by fins. The heat transfer rate and liquid fraction are investigated to evaluate the thermal behavior of the proposed system. The enthalpy–porosity technique is employed to simulate the phase change. The temperature variations over time at different PCM locations are calculated and compared with the measured temperatures. The predicted results show that the fin thickness and the inlet temperature of the heat transfer fluid play a key role in reducing the melting and solidification time. The obtained results indicated that by increasing the fin thickness from 0.5 to 1 mm, the heat transfer rate increased by approximately 17%. Also, increasing the inlet temperature from 60 °C to 65 °C improved the heat transfer rate by 36.2%.

No fins attached? Numerical analysis of internal–external fins coupled PCM melting for solar applications

Thermal energy storage/sink is imperative for any type of solar energy harnessing system/technology. However, the inevitable challenge remains in developing and optimizing a thermal energy storage (TES) system suitable for long cyclic operation. This work numerically analyses the melting characteristics of phase change material (PCM; RT42)-based latent thermal energy storage (LTES) as a two-dimensional rectangular enclosure. The consequence of utilizing internal–external extended surfaces (fins) with realistic convective boundary condition is studied for photovoltaic thermal (PVT) applications. The application of internal–external fins is intended for enhancing the charging (melting) duration according to the long cyclic solar operation and better dissipation of heat after complete melting. Three kind of fins-rectangular, triangular, and Y-type- are investigated for two orientations of storage/sink enclosures-upright ( θ = 90°) and inclined ( θ = 35°). Moreover, three fin configurations are analyzed-equal, decreasing and increasing-stepped-based on the arrangement of fins along the enclosure height. Two-dimensional, transient numerical simulations are conducted for governing PCM melting, contemplating the consequences of natural convection. The performance assessment of each storage unit (orientation/fin-type/fin-arrangement) is made based on parameters such as time enhancement ratio, suppression ratio, liquid fraction, temperature distribution, melt velocity magnitude, storage capacity/rate, and enhancement in Nusselt number. The melting is delayed for triangular and Y-fins enclosures as compared to that for rectangular fins. Equal and increasing-stepped Y-fin arrangements yielded the largest time enhancement ratios of 42.38% and 29.86% for inclined and upright enclosures, respectively. Moreover, Y-fins-based enclosure produced a larger average suppression ratio as compared to other types of fins. A 2.56, 2.67, and 2.64 times enhancement in Nusselt number is observed for increasing-stepped fin arrangement of rectangular, triangular, and Y-finned upright enclosures, respectively. However, for the inclined enclosure, a 2.32 times enhancement in Nusselt number is reported for increasing-stepped Y-fin. • Internal–external fin-coupled thermal storage for cyclic solar PVT applications. • Utilization of rectangular, triangular, and Y-fins in augmenting PCM melting. • Assessment of 3 configurations/fin-immersions for intensifying convection currents. • Effect of cavity inclination on melting characteristics for long duty operation. • Maximum 2.67 times Nusselt number enhancement for increasing triangular fin.

Performance improvement of heat sink with vapor chamber base and heat pipe

The heat sink with vapor chamber heat spreader has been the emerging design as it offers tremendous reduction in spreading resistance. However, this type of heat sinks suffer from the fin side temperature non-homogeneity, which hinders the heat transfer enhancement. The present study aimed to develop parallelogram fins integrated with heat pipes to increase the heat transfer performance of the heat sink with the vapor chamber heat spreader. The experimental and numerical investigations were performed on different heat sinks with different heat spreaders, including flat plate, vapor chamber, and vapor chamber combined with heat pipe. The air-cooled heat sink features a parallelogram fin configuration is proposed to tailor the temperature non-uniformity alongside the fins. The results showed that the overall thermal resistance of the heat sink with the vapor chamber and the vapor chamber combined with heat pipe spreader (no-cut fins) is about 50% and 55% lower than in the flat plate case. The proposed heat sink with vapor chamber combined with heat pipe spreader having a parallelogram fin structure offered about 61% reduction in thermal resistance and 45–50 °C reduction in chip temperature over the heat sink with flat plate heat spreader.