Heat Transfer Capacity Research Articles

Investigation on the heat transfer characteristics of rotor-stator cavity with different disk roughness

In this study, we numerically investigated the rotor-stator cavity for different disk surface roughness (rough rotor-RR, rough stator-RS, and rough rotor & stator-RRS) with the aim of determining the effect of surface roughness on the heat transfer characteristics of the disk cavity over a range of parameters. First, we experimentally verified that the numerical simulation has high accuracy. Next, the third-generation vortex identification method-Ω vortex identification method is used to preliminarily analyze the effect of different disk cavity roughness on the heat transfer in the rotor-stator cavity. The results indicate that the roughness of the rotor surface plays a dominant role in influencing the flow in the disk cavity. Third, we qualitatively and quantitatively analyzed the temperature field in the disk cavity. Interestingly, we discovered that the roughness of the stator decreases the temperature in the disk cavity to some extent. Thus, we judged the effect of stator surface roughness on the flow in the disk cavity based on the pressure variation in the rotor-stator cavity and gave an optimal roughness range for the stator. This will help to improve the cooling effect in the disk cavity. Finally, we investigated the effect of roughness on the rotor-stator heat transfer capacity. The effect of roughness on overall heat transfer in disc cavities is quantified based on average local heat transfer coefficient. It was concluded that the local heat transfer coefficient of the disk cavity is sensitive to the wall roughness, even for small wall roughness. We then added a roughness term to our previous work on average Nusselt number predictions for disk cavities. This provides a more accurate prediction of the heat transfer capacity of the disk cavity. On the basis of our results, it can provide some assistance to the relevant designers to quickly and accurately predict the heat transfer capacity of the rotor-stator cavity.

Numerical investigation of MHD mixed convection in an octagonal heat exchanger containing hybrid nanofluid

Nowadays, the advancement of heat transmission for the heat exchanger device is an important field of research for many researchers. In this work, a numerical study has been conducted to investigate the thermal performance of a mixed convective flow through the octagonal heat exchanger covered by hybrid nanofluid (Cu-TiO2-H2O). A magnetic field has been introduced inside the cavity to investigate the mixed convective hydrodynamics heat flow characteristics. The nanofluid cores absorb/release energy to manage heat transmission by increasing or decreasing inside the cavity domain as the host fluid and dispersed hybrid nanofluid circulate within the cavity. After transforming the governing equations into a generalized, non-dimensional formulation, the finite element approach is utilized to solve the associated equations. Additionally, response surface methodology is also applied to test the responses of the associated factors. Heat transport was examined in relation to the effects of nanofluids fusion temperature, boundary wall properties, Reynolds number, Hartmann number and nanoparticle volume fractions. The outcomes of this study are analysed by measuring streamline profiles, isotherms, average Nusselt number, velocity profile, and 2D and 3D response surfaces of the computational domain. The underlying flow controlling parameters for instance Reynolds number (10 ≤ Re ≤ 200), Hartmann number (0 ≤ Ha ≤100), and nanoparticle volume fractions (0 ≤ ϕ ≤ 0.1), the influences have been considered. The findings also reveal that the thermal performance is being boosted due to augmentation of Re and ϕ, but reverse behavior is noticed for Ha. Furthermore, the response surfaces obtained from response surfaces methodology express that the Re and ϕ have shown positive influence, and Ha has shown negative influence on Nuav. Utilizing a hybrid nanofluid of Cu-TiO2-H2O increases the heat transfer capacity of water to 25.75 %. Moreover, the findings could guide to design of a mixed convective heat exchanger for industrial purposes.

Experimental and numerical investigation of flow and heat transfer characteristics of teardrop and circular pin fins in a wedge channel

ABSTRACT Pin fin arrays, which have a high heat transfer capacity and minimal pressure loss, are currently being used as the primary cooling technique for the turbine trailing edge cooling channel used in modern gas turbines. To enhance the heat transmission efficiency of the channel, this study proposes the use of a circular-shaped pin and a teardrop pin, through both experimental and numerical investigations. The numerical simulations conducted in the Reynolds number range of 10,000 to 80,000 are used to investigate and compare the flow and heat transfer parameters of a wedge channel which has three rows of staggered circular-shaped and teardrop-shaped pin fins with a diameter of 12 mm. The experiment showed that teardrop pin fns with staggered arrangement has different effect on flow pattern and heat transfer characteristics. Heat transfer is increased by 10.45% when compared to the circular pin fins and the pressure drop of teardrop pin fins is reduced by 54.6%.Therefore thermal performance factor exhibits a 25.4% increase when compared to circular fins.

Electrohydrodynamic characteristics in parallel-fin channels and enhanced heat transfer performance of an ionic wind heat sink

High heat flux density may lead to a decline in the performance of highly integrated electronic components, which presents a major challenge to thermal management strategies. This work developed ionic wind heat sinks with parallel-fin channels for cooling high-power chips. The study examined the effects of intake air velocity, number of electrodes, and discharge spacing on the distribution of ionic wind flow and the improved heat transfer performance of the ionic wind heat sink. The findings suggest that the ionic wind heat sink with wire electrodes perpendicular to the fin channels can withstand higher operating voltages and generate more reliable corona discharges. The improved heat transfer capabilities are achieved with reduced inlet air velocity. The heat transfer enhancement factor (HTEF) of the ionic wind heat sink decreases as the discharge spacing increases, leading to a reduction in the peak value of the body force. The heat transfer capacity declines as the number of wire electrodes increases, because marginal effects lessen disruption to the thermal boundary layer. An effective airflow is achieved when wire electrodes are positioned upstream of the heat sink and run parallel to the fins, ensuring a steady and efficient cooling process. The design effectively disrupts the thermal boundary layer, reducing momentum loss in the flow and increasing the HTEF value by 21.2%. This improvement significantly enhances the heat dissipation capacity. The structurally optimized heat sink demonstrates excellent overall performance and is a viable option for improving heat dissipation in electronic devices.

Performance optimization of a printed circuit heat exchanger for the recuperated gas turbine

To further improve the thermal efficiency of gas turbines, the recuperator needs to be employed and the printed circuit heat exchanger with airfoil fins meets the recuperator's requirements of high heat transfer capacity, low flow resistance, and high reliability. However, the effect of airfoil fin pitches is not clear and the structure optimization method should be developed. In this study, the heat transfer quantity and pressure drop per length of the flue gas in the airfoil channels are numerically investigated under different Reynolds numbers and airfoil fin pitches. The results show that the effect of the airfoil transverse pitch has a great effect on the performance of the flue gas and the heat transfer quantity is increased by 82.39 %–96.08 % when the transverse pitch is decreased from 6.0 mm to 1.2 mm. At the same time, the pressure drop per length is increased to 189.39–842.47 Pa/m. The heat transfer performance is varied not obviously when the airfoil longitudinal pitch is varied from 4 mm to 15 mm. Based on the numerical data, the multiple-objective genetic algorithm combined with the backpropagation neural network is proposed for the performance predictions and optimizations. The corresponding Pareto front is obtained and the technique for order preference by similarity to the ideal solution method is employed to obtain the optimal point. Under the current conditions, the heat transfer quantity of the optimal point is 521.25 kW/m2, which is decreased by 34.5 % compared to the highest value, and the pressure drop per length of the optimal point is 108.45 Pa/m, which is decreased by 85.2 % compared to the highest value.

Mechanical–thermal coupling in micro-nanocavity graphene/paraffin phase change energy storage materials for heat management

Combining the superior thermal conductivity of graphene and the outstanding heat storage of paraffin, micro-nanocavity graphene/paraffin nanocomposites (MNGPNs) have recently served as promising thermal management materials in high-power microelectronic devices. However, current evaluations of the thermal management performances of MNGPNs are restricted in the lab condition, deviating from the complex mechanical–thermal coupling environment in practical scenarios. Here, we have investigated the structural and thermal management properties of MNGPNs with varying mechanical loads by in situ electron microscopy and in situ thermal characterizations. Our results reveal distinct mechanical–thermal coupling effects along in-plane and out-of-plane directions of MNGPNs. Specifically, mechanical loading reduces the porosity and enhances the heat transfer capacity of MNGPNs in the out-of-plane direction, while mechanical loading along the in-plane direction causes local damage to the graphene structure and weakens the heat transfer capacity of MNGPNs. Since the heat management performance of MNGPNs is dominated by the in-plane thermal transport, MNGPNs with mechanical loading show a delayed phase transition response time and unchanged phase transition enthalpy. This work provides in situ mechanical guidance for the practical application of MNGPNs for heat management.

Parametric study and optimization of H-type finned tube heat exchangers with honeycomb arrangement using Taguchi method

Enhancing the efficiency of flue gas waste heat utilization is an important way to achieve carbon peaking and carbon neutrality goals. In this paper, a three-dimensional numerical model of an H-type finned tube heat exchanger with honeycomb arrangement is developed. Firstly, the effects of five parameters are analyzed using the control variable method, including the oblique tube pitch, the ratio of fin height to oblique tube pitch, fin pitch, fin thickness and slit width. Then, the Taguchi method was used to investigate the interaction effects of the five geometric parameters. Numerical simulations of 27 cases with different parameter combinations were carried out and the heat transfer and flow friction characteristics and their overall performance were discussed in detail. The results show that oblique tube pitch has the most significant effect on heat transfer capacity, fin pitch has the most significant effect on overall performance, and slit width has the least effect on both. Finally, the optimum parameter combinations were obtained. When inlet velocity ranges from 5 m/s to 10 m/s, heat transfer performance is increased by 46.3 %-52.1 %, pressure drop is increased by 5.7 % − 11.3 %, and the overall performance PEC is improved by 63.5 %-105.9 %. The results of the study contribute to the development and optimization of new flue gas heat exchangers.

Three-dimensional numerical simulation of two-phase flow in a proton exchange membrane electrolysis cell and study of the effect of flow channel depth

Abstract The flow channel play a critical role in water-gas transfer within an electrolysis cell, directly impacting its mass and heat transfer capacity. While most studies concentrate on the overall shape and structure of the flow channel, limited attention has been given to its dimensions. This paper investigates the influence of various operational conditions and changes in flow channel depth on the electrolytic cell using a three-dimensional numerical model of PEMEC. Results indicate that higher temperatures enhance electrolysis cell performance, whereas the impact of water inlet velocity on the polarization curve is insignificant. Under constant inlet velocity, increasing the depth of the flow channel improves mass and heat transfer as well as electrolysis performance, whereas, under constant water flow rate, changes in inlet velocity have a greater effect than alterations in flow channel depth.

Heat transfer, crack, and wear resistance of a newly designed heat-treated Ni/Cr multilayer composite coating for strip casting rolls

A new heat-treated Ni/Cr multilayer composite coating for strip casting rolls was designed in this contribution. The results revealed that the addition of the middle layer of the Ni layer was conducive to enhancing the heat transfer capacity. Insignificant improvement was found in the crack resistance of the Ni/Cr coating when compared to the Cr coating. However, the heat-treated Ni/Cr coating exhibited remarkable cracking resistance due to intensified binding force with the matrix. Also, the wear resistance of Ni/Cr and heat-treated Ni/Cr was superior to that of Cr coating.

Cooling air flow field in the primary mirror temperature control system of a solar telescope

The temperature distribution and the difference with the ambient temperature of the primary mirror are crucial factors affecting the observational quality of the solar telescope. We designed a flow field structure of the primary mirror temperature control system based on the 2.5-meter Wide-field and High-resolution Solar Telescope(WeHoT), analyzed the flow conditions and heat transfer capacity of the overall flow field, and then carried out five stages of optimization iteration and simulation guided by the analysis results. A flow field structure for the primary mirror temperature control system with high efficiency and high uniformity is summarized. The simulation results for the final solution indicate an average surface temperature of the primary mirror at 20.064°C, with a maximum temperature difference within the reflective surface of 0.809°C, and a reduced difference with the ambient temperature of 0.411°C. Surface thermal deformation is less than 0.2 μm, with an RMS value of 18.05 nm, achieving the ideal state. This work can provide a theoretical foundation and valuable insights for future research on the temperature control system of the primary mirror in large-aperture solar telescopes.

Experimental study on the flat loop heat pipe with minichannel wick under low heat flux

Stable operating under low heat flux condition is crucial for loop heat pipe. To investigate the performance of the flat loop heat pipe under low heat flux, a visual structure of evaporator with longitudinal replenishment characterized by minichannel wick is proposed and fabricated. The minichannel wick increases the permeable area and reduces flow resistance to enhance the heat transfer capacity. However, under low heat flux condition, excessive liquid permeation into the vapor line and the local reverse vapor flow may deplete the liquid storage in the compensation chamber, resulting in a wick temperature increase of 4.7 °C under extreme condition. Lowering the heat sink temperature does not necessarily lead to a lower stable wick temperature in specific cases but rather poses operational challenges and further raises the stable wick temperature by 9 °C. By visualizing the flow structure, it is found that arduous vapor–liquid prestart distribution leads to prolonged circulation establishment time and higher wick temperature, resulting in a higher stable wick temperature. As the heat flux increases, the effect of prestart distribution on the stable wick temperature weakens as the redistribution capability improves.

Study of heat transfer and hydrodynamic processes in a full-size thermosyphon installation under the influence of solar radiation with coolant

Abstract This article discusses the theoretical background and results of the study of heat exchange and hydrodynamic processes occurring in a thermosiphon installation. One of the important characteristics of the operation of thermosiphons is their ultimate heat transfer capacity, the calculation of which allows us to create a reliable, highly efficient heat exchange device. For optimal design and improvement of the technical and economic indicators of a thermosiphon installation, it is necessary to develop and improve scientifically based methods for calculating the processes occurring in the elements of its design. The purpose of the experimental part of the work was to test the selected theoretical model and more accurately determine the physical picture of the processes occurring in full-scale thermosiphon installations by measuring not only integral, but also local characteristics of the installation. There is intense heating of the liquid in the collector in the first half of the day (from 11 to 13 hours) and a slowdown in the rate of increase in temperature at the outlet of the collector in the second half of the day. A drop in the level of solar radiation in the second half of the day does not lead to a significant decrease in the temperature at the outlet of the collector, which is obviously explained by an increase in the temperature of the liquid at the inlet to the collector during the period under consideration. The presence of a long period of lag in the increase in the temperature of the liquid at the inlet to the collector compared to the temperature at the outlet is associated with the inertia of thermal processes in the system. The time interval from the beginning of the experiment to the beginning of the increase in the temperature of the liquid at the inlet to the collector coincides with the period of a single circulation of the liquid in the system.

Simulation of the effect of the structure and location of non-closed droplet microchannel on flow/ thermal performance

In order to investigate the effects of geometric parameters and flow modes on the fluid flow morphology, resistance and heat transfer effect in the non-closed droplet pin fin array, in this manuscript, a numerical simulation has been conducted under Re = 100–700 with different pin fin heights (Hp = 0.3 mm, 0.5 mm, 0.7 mm) and pin fin densities (β = 0.046, 0.059, 0.072), with different flow directions under heat flux (10 W/cm2 – 50 W/cm2) studied as well. It is discovered that increasing the height and density of the non-closed droplet pin fin increases the interference with the fluid, resulting in a greater flow resistance phenomenon. However, the enhancement of turbulence not only exacerbates the flow instability in microchannels, but also further promotes the mixing of hot and cold fluids, making the internal temperature distribution more uniform. In which way, the effect of optimizing heat transfer performance achieves. In addition, as q > 20 W/cm2, the overall heat transfer capacity of flow direction B (the tip of the pin fin as upstream fluid direction) is better than that of flow direction A (the cavity of the pin fin upstream as upstream fluid direction). When q = 30 W/cm2, there is a process transferring from single-phase flow to two-phase flow along with the direction of working fluid flow in the microchannel. Under this condition, the local maximum heat transfer coefficient is 15,502.4 W/(m2·K) in flow direction A and 16,094.8 W/(m2·K) in flow direction B. Furthermore, the comprehensive evaluation concludes that the channel flow/thermal performance is the best with Hp = 0.7 mm, β = 0.046.

Numerical study on a new spiral fin heat Exchanger's thermal-hydraulic performance

This study presents a numerical investigation of a novel spiral finned heat exchanger (SFHE). The primary objective is to optimize the heat transfer efficiency of micro gas turbine recuperators by employing a spiral fin model. Through computational simulations (CFD), the study examines the variations in the Colburn j factor and Fanning friction f factor as the spiral fins alter. The results demonstrate that the SFHE exhibits superior heat transfer capacity and overall heat transfer performance compared to wavy fin models. At a Reynolds number of 1000, the JF factor of the spiral fin 35_125 is 70.47 % higher than that of a wavy fin at the same Reynolds number, and 34.03 % higher when the Reynolds number increases to 5000. The study also reveals that the cutting thickness of the top and bottom, denoted as C1, does not significantly impact the variable j, f. However, increasing the cut thickness C2 on the left and right sides results in a more compact model, leading to higher values of f, but the j-factor is almost unchanged. While decreasing the wavelength of the spiral fins can improve heat transfer efficiency, it also increases pressure loss, necessitating careful selection of wavelength for optimal SFHE design.

Enhancement of Thermo-Physical Properties of Form-Stable Nano-Enhanced Phase Change Materials: Advancing Maritime Sustainability

This paper explores the application of novel, form-stable eutectic mixtures in thermal energy storage systems for maritime environments. These advanced materials present a significant leap forward, addressing critical challenges faced by conventional phase change materials (PCMs) in marine environments. The stability, eliminating leakage and fluidity issues encountered with liquid PCMs are ensured by incorporating 2-hydroxypropyl ether cellulose (HPEC) as a gelling agent. Additionally, the thermal properties and heat transfer capacities were significantly enhanced, and eventually, overall system efficiency improved by including nano-graphene platelets (NGPs). Notably, NGPs effectively suppress supercooling, minimizing energy losses and guaranteeing consistent performance at elevated temperatures. Further, the eutectic mixture demonstrates exceptional durability through an accelerated thermal reliability test, guaranteeing optimal performance over a projected seventy-year lifespan. This enhanced thermal performance, and enduring stability combination establishes the form-stable eutectic mixture with NGPs as an up-and-coming solution for diverse maritime applications requiring efficient and reliable thermal energy storage. This research provides a compelling case for implementing form-stable eutectic mixtures with NGPs in maritime thermal energy storage systems. Its superior performance and sustainability offer significant advantages for diverse shipboard and offshore applications, contributing to improved energy efficiency, environmental sustainability, and operational resilience within the maritime sector.

Numerical study and experimental validation of heat transfer capacity of flat-type divertor for fusion reactor

The divertor must simultaneously withstand unprecedented high heat fluxes of up to 20 MW/m2 and high-energy neutron irradiation of 14-MeV during fusion reactor operation. Accordingly, it is necessary to simultaneously meet the excellent heat dissipation capacity of the divertor and maintain good material performance in harsh neutron irradiation environments. The flat-type divertor demonstrates better heat transfer performance compared to monoblock divertor. Nevertheless, under the condition of a heat flux of 20 MW/m2, the heat transfer and thermal fatigue performance of flat-type divertor using advanced materials are still unidentified. In this study, we conducted a thorough analysis of the heat transfer capabilities and thermal fatigue characteristics of potassium-doped tungsten (KW)/Cu/Oxide dispersion strengthened copper (ODS-Cu)/reduced activation ferritic/martensitic (RAFM) divertor mockup adopts hypervaportron (HV) structure by numerical simulations combined with experiments. The numerical results indicate that the flat-type KW/Cu/ODS-Cu/RAFM divertor mockup expresses excellent heat transfer capacity. The contact area between the edge of the fins and the bottom surface of the ODS-Cu heat sink induces a significant increase in water flow velocity to ∼15 m/s. The peak temperature of loaded KW surface is only ∼985 °C under the flow rate of 5 t/h and inlet temperature of 20 °C. During the high heat flux tests, the prepared flat-type divertor mockup successful endured 1000 cycles of 20 MW/m2 with the peak temperature of 883 °C, and the surface temperature experienced a fluctuation of 2.4 % during the thermal fatigue tests. This study can provide a strong data reference and technical support for the development of fusion reactors, and is of great significance in advancing the commercialization of fusion energy.

Development and application of data-driven CHF model in system analysis code

In nuclear reactor systems, when the fuel rods reach the critical heat flux (CHF), a sharp increase in fuel temperature occurs due to a drastic reduction in heat transfer capacity, thus posing a considerable risk to the reactor’s safety. Consequently, accurate CHF prediction holds paramount importance in accurately simulating accident scenarios and enhancing the overall safety of reactor systems. To tackle the challenge of limited prediction accuracy in existing CHF models, this study initially established a comprehensive database by utilizing available experimental data and lookup tables. Subsequently, various methodologies, including the Back Propagation Neural Network (BPNN), Random Forest (RF), and Physics-Informed Machine Learning (PIML), were employed to develop multiple CHF prediction models, and their performance was thoroughly evaluated. Furthermore, the optimal CHF model was integrated into the self-developed analysis code ARSAC, which was then validated using the ORNL-THTF experiment. The results indicated that the BPNN-based model not only demonstrated exceptional prediction accuracy but also exhibited rapid calculation speeds. Notably, the average relative error between the experimental data points and the calculation results of the modified code is 3.64%, while for the original code, it is 22.84%. This study effectively leverages the strengths of data-driven approaches, providing a robust technical solution for high-precision, efficient, and adaptive numerical prediction and analysis of reactor accidents.

Construction of gradient structure C/C–ZrC–SiC composites with good ablation resistance

With the upgrade of aircraft and the increasingly harsh service environment, it is urgent to develop high-performance thermal structural materials. In this study, inspired by foliar and root water uptake of trees, we propose a one-step facile method to achieve an autonomous gradient in C/C–ZrC–SiC sharp leading edge composites. The gradual increase of SiC content from top to bottom is beneficial to improve the heat transfer capacity of the composites. After oxyacetylene ablation for 60 s, the mass and linear ablation rates of the samples with gradient structure are 0.83 mg/s and 0.5 μm/s, 35 % and 83 % lower than conventional samples. The composites with gradient structure of ZrC and SiC are favorable to the formation of a compact and smooth ZrO2 oxide protective layer, which not only protects the composites from further penetration of O2, but also resists the mechanical denudation. The novel gradient structure composites with enhanced ablation resistance show a bright application prospect in next-generation thermal protection systems.

Simulation study on the dynamic characteristics of natural circulation coupled phase change material for equal height difference passive containment cooling system

The passive containment cooling system (PCCS) plays a significant role in ensuring the safety of nuclear power plants. To further reduce peak pressure in the containment during a loss of coolant accident (LOCA), phase change materials (PCMs) are utilized to improve the system’s cooling effectiveness. The dynamic simulation model of PCCS has been developed using Apros software. This article focuses on examining the system’s dynamic characteristics related to various tube startup methods and comparatively analyzing the impact of different PCM thicknesses on heat transfer capacity. The results indicate that post-accident, PCM significantly suppresses peak pressure in the containment. Under the full tube startup method with 4 mm PCM, the peak pressure decreases to 1.75 MPa, whereas under the empty tube startup method, it is reduced to 1.69 MPa. With natural circulation empty tube startup method, PCM can reduce pressure change intensity in the containment but negatively affects natural circulation heat transfer. Although the full tube startup method underperforms the empty tube startup method on suppressing peak pressure, PCM can positively affect natural circulation heat transfer in the early stages of the accident. Empty tube startup offers the advantages of higher heat transfer capacity and lighter weight, making it the optimal choice for ocean nuclear platforms. Additionally, the higher peak power of PCM heat transfer under the empty tube startup method indicates that system can withstand larger thermal shocks.

A novel coaxial heat pipe with an inner vapor tube for cooling high power electronic devices

Improving heat transfer limit of heat pipe is important for their application in high-power equipment system. Shear stress at the liquid–vapor interface affects the heat transfer capacity of heat pipe. In this study, a novel coaxial heat pipe is designed to eliminate vapor entrainment from interfacial shear stress for the first time. An inner thin-walled tube is sintered with the powder wick in the adiabatic section by one-step sintering process. The effects of filling ratio and powder size of sintered wick on the thermal performance of coaxial heat pipe are investigated experimentally. The results indicate that the optimal powder size range for the sintered wick of coaxial heat pipe is 106–125 μm, while the optimal filling ratio is about 125 %. It means that the sintered wick with 106–125 μm powder can achieve better trade-off between capillary performance and permeability. The coaxial heat pipe can operate at heat loads of 70 ∼ 140 W with the total thermal resistance less than 0.06 °C /W. Moreover, compared with the normal heat pipe, the heat transfer capacity of coaxial heat pipe is increased by 57 %, while the evaporation temperature is decreased by 9.6 ∼ 19.1 °C and the total thermal resistance is decreased by 41 %∼320 %. The inner tube can improve the replenishment efficiency of working liquid by eliminating interfacial shear stress, resulting in the significant heat transfer improvement. The design of coaxial heat pipe is an effective and low-cost solution to improve the thermal performance of heat pipe.