Thermal Resistance Model Research Articles

Self-Heating Characterization and Thermal Resistance Modeling in Multitube CNTFETs

The thermal resistance, thermal capacitance, and thermal time constant have been experimentally extracted for the first time for a multi-tube multi-finger carbon nanotube FET (CNTFET) from trap-free high-frequency characteristics by following a methodology based on temperature-dependent two-port network analysis. The extracted short thermal time constant confirms the thermal stability for this emerging technology. A lumped-element electro-thermal model for multi-tube CNTFETs has been developed and proven with experimental data.

Development of acoustic and diffuse mismatch models for predicting the Kapitza resistance

This paper is devoted to the acoustic mismatch model and diffusion mismatch model of Kapitza thermal resistance. We consider that diffusion in the transition layer can be represented by variable composition and finite thickness instead of previous assumptions of a “black box” approximation. The effect of heat flow on the interface is reviewed in the acoustic mismatch model where energy is transferred between two different materials and the critical incident angles are taken into account. Finally we provide calculations of the Kapitza resistance for several interfaces (Metal-Sapphire and Metal-Silicon).

Coupling Analysis of Multi-Physical Field of High-Speed Motorized Spindle Based on Fractal Contact Theory

In order to improve the modeling accuracy of the motorized spindle, a comprehensive thermal contact resistance (TCR) modeling method was proposed. The fractal theory was introduced to calculate the joint thermal contact resistance. The W-M function and the M-B fractal model were established to characterize the microscopic contour of the rough surface. The bulk thermal resistance, constrained thermal resistance, micro-gap thermal resistance and overall thermal contact resistance of the rough surface of different materials were discussed. The finite element method(FEM)was used to establish the multi-physics coupling analysis model of the motorized spindle, adding the theoretical calculation of thermal contact resistance in the joint surface of the motorized spindle. The temperature rise and deformation variation of the motorized spindle were simulated under the condition of thermal contact resistance. The simulation results demonstrate the influence of thermal contact resistance on the temperature and thermal deformation of the motorized spindle. The results show that when the thermal resistance of the high-speed motorized spindle is considered, the temperature rises and the deformation increases, and the accuracy of the model is more accurate, which is closer to the actual processing.

Inverse optimization of building thermal resistance and capacitance for minimizing air conditioning loads

Aiming at reducing the heating and cooling loads for built environments, the thermal resistance and capacitance (RC) model has widely been acknowledged as an effective method for predicting the heat flux through building walls by simplifying wall structures and their properties into R and C allocations. This paper demonstrates an inverse optimization method based on particle swarm optimization (PSO) for determining the optimal RC allocation that minimizes the heat flux through building walls. A thermal RC model with three resistances and two capacitances was used as an example to search for the optimal building RC allocation in the hot summer and warm winter zone of China. The inverse optimization could be efficiently accomplished in 2.5 h with an ordinary computer, approximately 0.12% of the time consumed by using the exhaustive search method. The optimized RC allocation was composed of three resistances of 0.43, 0.18 and 0.39 and two capacitances of 0.50 and 0.50. Compared to the three typical thermal insulation (e.g., internal, external, and internal/external), the optimal RC allocation could reduce the heat flux into/from buildings by 17.3%–44.3%. The proposed inverse PSO method shows an effective and efficient capacity in searching for the optimal RC allocation of thermal RC models.

Energy flow-based method for analysis and optimization of evaporative cooling and ventilation systems

Physical and mathematical models significantly affect the ease of system analyses and optimization. This contribution presents a modified thermal resistance model for an evaporative cooling process and establishes an energy flow model analogous to an electrical circuit for an indirect evaporative cooling and ventilation (IECV) system based on the overall energy transport. The system modeling equations based on Kirchhoff's laws are a set of linear algebraic equations that characterize the relationships between each component in the system. They are applied as system constraints in the Lagrange multipliers method to optimize the design. The optimization minimizes the total thermal conductance for a fixed cooling capacity and total circulating water mass flow rate. The solutions of the optimization equations for a typical IECV system give a set of Pareto frontiers that reflect the trade-off between the thermal conductance and the mass flow rate, which represent the investment cost and the operating cost. Optimizations with various cooling capacities, indoor temperatures and ambient air conditions reveal their impacts on the optimal parameter allocations. Therefore, this application of the energy flow model shows its advantages for both performance analyses and system optimization.

Experimenting and Modeling Thermal Performance of Ground Heat Exchanger Under Freezing Soil Conditions

Many studies have investigated the thermal performance of ground heat exchangers (GHEs) under normal conditions with inlet temperatures above 0 °C, but the freezing soil condition has been absent. We conducted a three-month test to investigate the heat transfer of GHE with inlet water-glycol temperatures of −7~0 °C. An improved thermal resistance and capacity (RC) model was developed to investigate the heat transfer between vertical single U-tube GHEs and the frozen soil. After validating with experimental results and CFD simulations, the RC model was applied to analyze GHEs’ thermal performance under different freezing soil conditions. It shows that the frozen soil increases GHE’s heat transfer capacity by 30% and the freezing inlet temperature has limited impacts on temperature distribution around the exchanger (with < 4 m influence radius). The GHEs’ heat transfer rate remained at 75~80 W/m throughout the three-month test, which is surprisingly high to ensure the normal operation of the ground source heat pump (GSHP). These findings can be references for designing and operating GSHP systems in cold and severe cold climate zones, and the RC model can be applied to analyze future GHEs performance with phase change processes.

Thermal error controlling for the spindle in a precision boring machine with external cooling across coated joints

Spindles in precision boring machines usually operate without internal cooling, and thermal error in such spindles is nonnegligible and can severely affect the end-processing quality of the machines. This study aims to investigate the effects that external cooling exerts on the thermal behavior of such spindles. A helical tube cooler is taken for external cooling. An analytical thermal resistance model for the grease-coated cooler-housing joint surface, which considers the pressured cambered-flat contact pair and rough metal surface-grease contact, is presented and validated, and a numerical thermal–fluid–solid coupling model for the cooler-spindle system is then established. An evaluation method is put forward to obtain the stability of the thermal error, which determines the boring processing accuracy and thermal equilibrium time, from experimental data. Then, the external cooling was optimally designed based on the simulation results from the numerical model. Experiments show that the designed cooler reduced the thermal equilibrium time by 47.13% and the maximum thermal error by 81.7%, and the proposed model can accurately predict the cooling effect on the spindle thermal behavior. This study not only provides a thermal error control method for the spindle but is expected to advance the theoretical basis of cooling design for complex electromechanical systems.

Simulation of the Thermal Contact Resistance Characteristics on Rod Fastening Rotor

The thermal contact resistance model of the rod fastening rotor is improved, which can be more suitable for the engineering condition. By means of numeric simulation, the relationships between characteristics of the heat transfer between contact interfaces and the pre-tightening force of the tie rod, the surface roughness and the temperature of the contact interface are revealed intuitively. The simulation results show that the coefficient of contact heat transfer between the contact interfaces will increases with the pre-tightening pretension of the tie rod, will decreases with the increase of the surface roughness, and will increases with the increase of the surface temperature. It is also shown that the thermal contact resistance between the contact interfaces will have an important influence on the overall temperature distribution and heat transfer of the rod fasten rotor, and the thermal contact resistance between the interfaces must be considered when the temperature field distribution of the rod fastening rotor are accurately researched.

Comparison and parametric study of two theoretical modeling approaches based on an air-to-water thermoelectric generator system

Numerical model and thermal resistance model are two commonly used modeling approaches to analyze the performance of thermoelectric devices. However, a great number of assumptions and simplifications are made in previous researches. This work presents a steady state and fluid-thermal-electric multi-physical numerical model and improves the conventional thermal resistance model to investigate the performance of an air-to-water thermoelectric generator system. In considering the multi-physical field coupling effects and temperature dependent thermoelectric material properties, the comparison of these two theoretical models and parametric investigation on the thermoelectric generator system are conducted. The results indicate that the thermal resistance model can be used to preliminarily evaluate the performance of thermoelectric generator system with acceptable accuracy at appropriate working conditions, but more precisely, the numerical model should be adopted. Besides, the heat losses should not be omitted in the theoretical analysis, and an optimal load resistance must be chosen between the maximum power one and the maximum conversion efficiency one. The findings of this work can guide the future theoretical analysis of the thermoelectric generator system by numerical model or thermal resistance model.

Mathematical Modeling of Contact Thermal Resistance for Elastostrained Solid Bodies by the Methods of Multiphase Systems Mechanics

A new nonstationary conjugate mathematical model of thermal and stressed-strained state in loaded joints of metal elements in the presence of nonideal thermal contact has been formulated. A one-dimensional approximation of the model in a stationary case has been obtained. A numerical investigation of the approximate mathematical model has been carried out. Satisfactory agreement has been shown between the calculated values of thermal resistance of the contact of plane rough surfaces and the experiential data.

Computational fluid dynamics study to reduce heat losses at the receiver of a solar tower plant

Today, renewable energy systems are developing rapidly and are reaching economic competitiveness with conventional power plants. Due to their ability to efficiently integrate energy storage systems, concentrated solar power plants are ascribed a high potential for energy generation. Typically, the usage of molten salt as heat transfer fluid in the receiver reaches thermal efficiencies of 80–88% (de Meyer et al., 2016. Thermal Resistance Model for CSP Central Receivers). Placing the dome on top of the tower may be a measure in order to reduce the heat losses at the receiver. In the presented work, a computational fluid dynamics 11Computational fluid dynamics.(CFD) study with the commercial simulation package STAR-CCM+ 22Simulation of Turbulent flow in Arbitrary Regions - Computational Continuum Mechanics - C++ based.(Simulation of Turbulent flow in Arbitrary Regions - Computational Continuum Mechanics, C++ based) was executed to investigate the impact of placing the dome geometry on top of the solar tower. Mainly the potential to reduce convective and radiative heat losses at the molten salt receiver at various wind loads was analyzed. The respective Crescent Dunes plant in Las Vegas (Nevada) with an electrical net power of 110 MW was chosen as reference for generating the required input data for the simulations. Overall six simulation models were set up: two geometries, one with and one without a dome, and each of the geometries with three variable wind loads (Beaufort Number (BN 33Beaufort Number.) 2, 4 and 6). In the main part, the radiative and convective heat losses at the receiver were analyzed for the BN 4 and afterwards compared to the results with the models BN 2 and BN 6. The construction of the dome reduced the heat losses at the receiver by 1.92 MW (BN 4) with the radiation energy savings (1.32 MW) being higher than the reduction of convective losses (0.60 MW). Furthermore, the reduced heat losses are 1.79 MW for BN 2 and only 0.43 MW for BN 6. Besides in the last case, the convective losses actually rise and the function of the dome turns out as counterproductive. Nevertheless, the results can be fundamental for further research projects as the dependence of the heat losses on variations of the dome form and the installation of components to disturb or eliminate a convective heat flow at the receiver can be essential to future studies. However, each concept must be seen in terms of economic and technical feasibility.

Effect of the Inclination Angle on the Steady-State Heat Transfer Performance of a Thermosyphon

A two-phase closed thermosyphon is an efficient heat transfer element. The heat transfer process of this type of thermosyphon includes conduction and convective heat transfer accompanied by phase changes. Variations in the inclination angle of a thermosyphon affect the steady-state heat transfer performance of the device. Therefore, the inclination angle is an important factor affecting the performance of a thermosyphon. In this paper, an equation for the actual heating area variations with respect to the inclination angle is deduced, and a model for the areal thermal resistance of a thermosyphon is proposed by analyzing the main influence mechanisms of the inclination angle on the heat transfer process. The experimental results show that the areal thermal resistance, which accounts for the effect of the actual heating area, does not change with respect to the inclination angle and exhibits a linear relationship with the heat transfer rate. The thermal resistance equation is fit according to the experimental data when the inclination angle of the thermosyphon is vertically oriented (90°), and the predicted values of the thermosyphon’s thermal resistance are obtained when the thermosyphon is inclined. The deviations between the experimental data and predicted values are less than ±0.05. Therefore, the theoretical equation can accurately predict the thermosyphon’s thermal resistance at different inclination angles.

Experimental validation of a TRC model for a double U-tube borehole with two independent circuits

This paper presents an experimental validation of a thermal resistance and capacitance (TRC) model for double U-tube boreholes with two independent circuits. In the TRC model, the borehole cross-section is divided into four quadrants each with two nodes representing the fluid and the grout, respectively. Ground heat transfer is evaluated in each of the n vertical sections using the infinite cylindrical source analytical solution with appropriate temporal superposition. Finally, internal tube-to-tube and tube-to-borehole thermal resistances are evaluated with the multipole method. The TRC model is validated against results obtained using a small-scale borehole (90.39 cm long with a 9.45 cm diameter) positioned in a sand tank of known properties. The borehole is made of ceramic which enabled the precise positioning of thermocouples at the mid-height cross-section. Data are acquired at a high frequency (1 s) to capture transient effects. In the first set of results obtained for a quasi-steady state, isotherms over the mid-height cross-section compare favorably well with the ones obtained using the multipole method. In the other two tests, the borehole is subjected to varying inlet (flow rate and temperature) conditions. It is shown that the TRC model is in good agreement with the experimental data except when there is a severe steep change in inlet temperature or when there is no flow.

Thermal Spreading Resistance in Ballistic-Diffusive Regime for GaN HEMTs

To develop an efficient thermal design for gallium-nitride (GaN) high-electron-mobility transistors (HEMTs) that usually hold a super-high-power density, it is essential to accurately predict the junction temperature. In GaN HEMTs, the heat transfer process is dominated by thermal spreading resistance. Moreover, the phonon mean free paths (MFPs) of GaN are comparable with the channel layer thickness and the heat spot width. Thus, a ballistic effect emerges, resulting in the invalidity of Fourier’s heat conduction law. Therefore, Fourier’s law-based thermal resistance model should be reexamined and modified for this case. In this paper, we used the phonon Monte Carlo (MC) method to investigate the thermal spreading resistance in a ballistic-diffusive regime for GaN HEMTs. Our simulation results indicate that the ballistic effect significantly altered the temperature distributions within channel layers and resulted in a dramatic increase in the thermal resistance when compared with Fourier’s law-based predictions. Furthermore, a semiempirical thermal resistance model with a fitting parameter was derived. This model can accurately address the issues of thermal spreading and the ballistic effect. This paper can provide a more in-depth understanding of the thermal spreading resistance in a ballistic-diffusive regime, and it can be useful for the prediction of junction temperatures and for the thermal management of HEMTs.

Analysis of gravity heat pipe for anti-icing and snow melting on road surface

Road icing is a serious hazard to highway traffic safety, so it is necessary to develop the anti-icing and de-icing technology. In this paper, theoretical and simulation analysis was carried out based on the idea that the gravity heat pipe uses shallow geothermal energy to meet the requirements of highway de-icing. The maximum heat transfer limit of different working media was calculated, and the two-dimensional pavement heat transfer model and thermal resistance model were established. The effect of different pipe diameters, pipe spacing and length of evaporation and condensation section on the heat transfer efficiency of gravity heat pipe to the surface of road was considered. It is concluded that ammonia can maximize the heat transfer limit of heat pipe due to its high latent heat, which is the best working fluid for preventing ice and snow melting of gravity heat pipe. When the pipe spacing is 150mm, the road surface temperature can be more than 2 °C. Considering the maximum heat transfer per unit area, the optimal length of the gravity heat pipe is 30m for the evaporation section and 10m for the condensation section, and the unit heat transfer is 205W/m2.

A Novel Model for Thermal Behavior Prediction of Oil-Immersed Distribution Transformers With Consideration of Solar Radiation

Monitoring the insulation status of a transformer requires the availability of accurate information of the oil temperature at any moment. Considering the importance of oil temperature prediction in oil-immersed transformers and its direct relation with the life of transformer, a novel model is presented in this paper using the concept of thermal resistance with consideration of solar radiation for expressing the heat transfer in distribution transformers. The results of the proposed model are compared and validated with experimental results. These results show that in the studied transformer and rated loading, solar radiation can increase the oil temperature by about 3.7 °C. In this paper, the thermal resistance model with solar radiation is used to predict the thermal behavior of the transformer in overloading condition. Finally, the transformer operation with/without consideration of solar radiation effect is studied and its impact on the transformer's loss of life due to the increase in oil temperature is investigated. In order to consider the effect of solar radiation on oil temperature, new equations using the concept of thermal resistance are presented to calculate the shadow surface created on the fin-folded transformers, and a novel equation is proposed for permissible loading of distribution transformers.

Dynamic thermal behavior of micro heat pipe array-air cooling battery thermal management system based on thermal network model

An effective battery thermal management system is crucial for electric vehicles because the performance of lithium ion battery is sensitive to its operating temperature. In this study, a thermal management system equipped with micro heat pipe array (MHPA) is designed. An equivalent thermal resistance model is developed for MHPA based on thermal circuit method. The accuracy of the proposed model is validated by comparing the simulation results with experimental data under steady and dynamic and operating condition. A validated lumped thermoelectric model is adopted for prismatic lithium ion battery. The proposed thermal resistance model is combined with the battery model in order to predict the transient temperature distribution of a battery pack based on MHPA cooling. Simulations are conducted for air-cooled MHPA thermal management system. Temperature rise and temperature gradients of the designed cooling system are compared with direct forced convection. Simulation results demonstrate that the MHPA-based battery thermal management provides a quick response to ensure the temperature stability during rapid changing operating condition.

Optimization of Two-Stage Combined Thermoelectric Devices by a Three-Dimensional Multi-Physics Model and Multi-Objective Genetic Algorithm

Due to their advantages of self-powered capability and compact size, combined thermoelectric devices, in which a thermoelectric cooler module is driven by a thermoelectric generator module, have become promising candidates for cooling applications in extreme conditions or environments where the room is confined and the power supply is sacrificed. When the device is designed as two-stage configuration for larger temperature difference, the design degree is larger than that of a single-stage counterpart. The element number allocation to each stage in the system has a significant influence on the device performance. However, this issue has not been well-solved in previous studies. This work proposes a three-dimensional multi-physics model coupled with multi-objective genetic algorithm to optimize the optimal element number allocation with the coefficient of performance and cooling capacity simultaneously as multi-objective functions. This method increases the accuracy of performance prediction compared with the previously reported examples studied by the thermal resistance model. The results show that the performance of the optimized device is remarkably enhanced, where the cooling capacity is increased by 23.3% and the coefficient of performance increased by 122.0% compared with the 1# Initial Solution. The mechanism behind this enhanced performance is analyzed. The results in this paper should be beneficial for engineers and scientists seeking to design a combined thermoelectric device with optimal performance under the constraint of total element number.

Response surface based experimental analysis and thermal resistance model of a thermoelectric power generation system

In this work, a response surface analysis is carried out on an experimental setup of a combined two-phase flow thermosyphon and thermoelectric generator (TEG) system. Three-level Box-Behnken response surface method is adopted for the design of experiments, and analysis of variance is carried out to gauge the contribution of operating parameters on various performance parameters. Effects of operating parameters such as working pressure, filling ratio, evaporator length, and evaporator temperature are studied. The performance of the system itself is gauged concerning the maximum power obtained, open circuit voltage and short circuit current. With an increase in vacuum pressure and evaporator temperature, performance parameters are found to increase. However, performance parameters under the influence of filling ratio and evaporator length first decrease and then increase due to uneven variation in evaporation rate of working fluid. Experiments also reveal that the performance of the thermosyphon-assisted TEG system is mainly governed by pressure and evaporator temperature, whereas filling ratio and evaporator length have relatively lesser influence.

Heat transfer simulation, analysis and performance study of single U-tube borehole heat exchanger

This paper presents the analysis, simulation and performance study of heat transfer in a single U-tube borehole heat exchanger (BHE). Unsteady heat transfer method was used to analyze the heat transfer process of both inside and outside the borehole. Implicit numerical method applied on heat transfer equations obtained from energy balance (accompanied with thermal resistance model) was used to obtain the solution. The variation of mean fluid temperature, average borehole wall, grout and nearby ground temperature as well as borehole loading with borehole depth and time were investigated. Dynamic simulation was also performed to assess the influence of important parameters. The effect of two parameters, fluid mass flowrate and thermal conductivity of grout, on mean fluid temperature, borehole wall, grout and ground temperature as well as on borehole loading and borehole thermal effectiveness were investigated. The outcome of this study can substantially reduce the time devoted for research and to quickly determine the impact of various parameters on performance of vertical single U-tube borehole heat exchanger. Furthermore, the obtained result can be utilized as a reference for the design and optimization of heating and cooling system integrated with ground coupled heat pump system.