Thermal Circuit Model Research Articles

Thermal Circuit Model to Calculate the Heat Losses from the Frontal Surface of a Photovoltaic-Thermal System

The structure of a flat-plate photovoltaic-thermal system and its thermal circuit are considered. A method is proposed for the determination of heat losses and the temperatures of the front layers of a photovoltaic-thermal system with the specified operation conditions and a known temperature of the absorbing surface.

Reduction of self-heating effect using selective buried oxide (SELBOX) charge plasma based junctionless transistor

A junctionless transistor (JLT) having high doping concentration of the channel, suffers from the threshold voltage roll-off because of random dopant fluctuation (RDF) effect. RDF has been minimized by using charge plasma based JLT. Charge plasma is same as a workfunction engineering in which work function of the electrode is varied to create hole/electron plasma and induce doping in the intrinsic silicon. N-type doping is induced at the source and drain side due to difference of workfunction of silicon wafer. In this paper, charge plasma based junctionless MOSFET on selective buried oxide (SELBOX-CPJLT) is proposed. This approach is used to reduce the self-heating effect presented in SOI-based devices. The proposed device shows better thermal efficiency as compared to SELBOX-JLT. 2D-Atlas simulation revealed the electrostatics and analog performance of both the devices. The SELBOX-CPJLT exhibits better electrostatic performance as compared to SELBOX-JLT for the same channel length. The analog performance such as intrinsic gain, transconductance generation factor, output conductance and unity gain cut-off frequency are extracted from small signal ac analysis at 1 MHz and compared to SELBOX-JLT. The analysis of the thermal circuit model of SELBOX structure is also performed.

A Spatially-Reduced Dynamic Thermal Model for Liquid Cooling Lithium-Ion Battery Pack

In electric vehicles, thermal management of a battery pack is becoming critical as both excessive and low temperature may affect the overall battery life and even trigger disastrous damage to a battery pack. Therefore, estimating the temperature distribution and its variation over time is an essential requirement to ensure safe and provide design guidance for control strategy. This study carries out a transient thermal model to predict the thermal behavior of a square lithium-ion battery pack with liquid cooling thermal management system. Different from Equivalent thermal circuit (ETC) model, which can only predict a lumped temperature of a battery cell, a one-dimensional thermal model was built in this study to estimate the temperature distribution throughout the cell and its variation over time according to the structural feature and the liquid cooling mode. The model is based on the Green function method, capable of calculating one-dimensional thermal dynamics and achieving high accuracy with low calculation requirements, making it suitable for real-time control. A second order equivalent circuit model was used in the approach to predict the dynamics of the cell voltage and SOC in relation with the current. Then the electric model is coupled with a lumped thermal model to describe the dynamics of internal temperature distribution of one cell. Based on this cell model, a coupled flow-electro-thermal model for a battery pack was built, which was able to predict the uneven heat generation during the charge and discharge procedure under different cooling conditions. 3D CFD calculation was conducted for the model calibration and validation results are presented to support the proposed modeling approach.

An Investigation Into the Coupling of Magnetic and Thermal Analysis for a Wound-Rotor Synchronous Machine

This paper is dealing with magnetic and thermal analysis coupling of a wound-rotor synchronous machine (WRSM) based on the equivalent circuit methods. The main objective of this work is to introduce the principles of both magnetic equivalent circuit (MEC) and thermal equivalent circuit (TEC) models, as well as the importance of their coupling. The results of nonlinear MEC are compared to 2-D finite-element analysis results obtained by the magnetic field analysis software JMAG while the results of TEC coupled with MEC are compared with the experimental thermal test results.

Convective melting and freezing of phase change materials encapsulated within small diameter polymer tubes

This work characterizes the inward melting and freezing of phase change materials (PCMs) within small diameter polymer tubes under convective boundary conditions. Using air as the heat transfer fluid, a custom-built experimental apparatus was used to control the convective heating and cooling of vertically oriented PCM-filled tubes with an outer diameter of 3.175 mm. Various air speeds and air temperatures were investigated, as well as the effects of wall thickness and material properties, using three different polymer encapsulant tubes. Volume fraction, latent heat transfer rate, and the associated overall heat transfer coefficient have been measured experimentally during the transient melting and freezing processes. Using a commercially available paraffin-based PCM with a nominal melting temperature of 35 °C, phase change times ranging from 50 s to 180 s were recorded with air speeds and air temperatures of 4.7–15.3 m/s and 25.3–62.6 °C, respectively. Overall latent heat transfer coefficients as high as 200 W/m2 K were measured and shown to decay with time as the PCM changes phase during inward melting and freezing. For the thinnest encapsulants tested here, the results were consistent with a simplified one-dimensional quasi-steady-state thermal circuit model. Deviations from this model were observed and explained, including the importance of the wall thickness and thermal conductivity of the encapsulant.

Hydraulic control system design for a PHEV considering motor thermal management

In this paper, a design method for a PHEV hydraulic control system was proposed considering motor thermal management. Dynamic models of the target PHEV were developed including the hydraulic system, which consists of one mechanical and one electric oil pump. The required motor cooling flow was designed based on the motor temperature, which was obtained from a one-dimensional thermal equivalent circuit model including the heat source and oil spray cooling. Combining the PHEV powertrain model, hydraulic control system model, and the motor thermal model including the cooling system, an integrated simulator was developed for the target PHEV. Using the integrated simulator, the temperatures of MG1 and MG2 were investigated for various motor cooling flow rates when the PHEV underwent a highway driving cycle. The energy consumption of the hydraulic control system was also evaluated. It was found from the simulation results that a hydraulic control system of the target PHEV could be designed that satisfied the required flow for the motor cooling, lubrication and brake control using the design procedure proposed in this study.

Effect of grafted chains on the heat transfer between carbon nanotubes in a polyamide-6.6 matrix: A molecular dynamics study

By employing reverse non-equilibrium molecular dynamics simulations in a united-atom resolution, the influence of grafted polyamide-6,6 (PA) chains on the heat transfer between two parallel carbon nanotubes (CNTs) in a PA matrix is analyzed by calculating the thermal resistance. We show that grafted chains can reduce the thermal resistance between the CNTs significantly. Specifically, the thermal resistance between the CNTs decreases continuously with the grafting density and grafting length. In addition, the thermal resistance between the CNTs gradually increases with the increase of the distance between the CNTs. When the CNTs are directly linked by PA chains, the thermal resistance is even more reduced. The number of linking PA chains is the main factor that controls the thermal resistance, rather than their length. The relationship between the thermal resistance and the different parameters (grafting density, grafting length, number of linking chains, the intertube distance) can be described by an empirical equation. The heat transfer process from one CNT to another can be approximately described by a thermal circuit model between the CNTs. For the grafted CNTs, the model underestimates the simulated thermal resistance, whereas for the PA-linked CNTs, it overestimates it. However, for the grafted CNTs with very high grafting density and very short grafting length, the model significantly underestimates the simulated thermal resistance because of the appearance of a new interface between grafted PA and free PA.

Circuit modeling of the electro-thermal behavior of nanoscale bulk-FinFETs

Because the selfheating effect (SE) influences the performance and reliability of gate oxide and interconnect lines, and SE is affected by circuit operation such as operating frequency, the spatial distribution and dynamic behaviors of SE are important in a robust circuit design. In this work, we propose new thermal equivalent circuit model of ITRS roadmap based 5 nm bulk-FinFETs, which is based on analysis of the Boltzmann phonon transport and commercial 3D-technology computer-aided design simulation. By implementing the proposed model into a SPICE circuit simulator, circuit designers can co-optimize the electro-thermal behaviors of nanoscale bulk-FinFETs at the circuit level.

An Improved Dynamic Thermal Circuit Model for Transformers and its Application to Evaluate Capacity Increase

The thermal circuit model is widely used in the estimation of transformer temperature, especially the hot-spot temperature which is extremely challenging to be acquired. In this paper, a dynamic thermal circuit model for calculating the transformer internal temperatures is established considering actual operating conditions and environmental factors synthetically. In our model, load losses are calculated according to the operation currents and the tap positions, while the effects of sunshine and wind are reflected in thermal resistances. The parameter-estimation methods are also analyzed to solve the problem of information incompleteness in practice. To implement and verify the dynamic thermal circuit, the real-time loss and cooling thermal resistance of a transformer are calculated first. Then, the hot-spot temperature based on the average oil temperature is calculated for a period of 24 hr. The calculated results were compared with the temperature-rise test result and practically measured data. The comparison shows that the estimation accuracy of the proposed model is satisfactory. The model is then used to evaluate the feasibility of increasing operating capacity and the maximum safe load factor for a long-term operation.

Section Selection Software Design for Submarine Cables

In order to improve the efficiency and accuracy of ampacity calculation and submarine cable’s section selection, this article improved the shortage of IEC(International Electrotechnical Commission) norms when calculating the ampacity of submarine cables, developed hierarchical principles and established accurate thermal circuit model of the various types of cables. This article realized accurate calculation of ampacity and achieved the ampacity calculation software module’s design. Finally this article firstly developed a section selection software for submarine cables combined with the heat-stable calibration module. After verified the accuracy and effectiveness of software in the typical layout conditions, this software can provide good guidance for practical engineering.

Thermal resistance capacity model for short-term borehole heat exchanger simulation with non-stiff ordinary differential equations

In the present study, a new thermal resistance capacity circuit for the heat transfer modeling in borehole heat exchanger with low computation time is developed. Generally, the thermal circuit models result in sets of ordinary differential equations which are solved numerically. The system of equations derived from the traditional thermal resistance capacity model (TRCM) are usually stiff and lead to unstable results unless for a very small time steps which can increase the computation time significantly. Meanwhile, the system of ordinary differential equations derived from the present model is non-stiff and there is no time step limitation for the stability of the results. It is shown that the present model yields accurate and stable results even for large time steps. Finally, the two-dimensional model is extended to the three-dimensional model. The results of the three-dimensional solution of the present model are in good agreement with the numerical results and experimental measurements reported in the literature.

Underground MV power cable joints: A nonlinear thermal circuit model and its experimental validation

The analysis of the thermal stress of underground MV power cable joints under different environmental conditions, both in normal operation and during faults, is crucial to assess any correlation between the occurrence of overheatings and the anomalous increase of failures (two to three times compared to previous years) which have been observed in the Italian distribution network during summer 2015 (the hottest year ever since 1880). In order to perform this analysis, we have developed a nonlinear circuit model that is able to estimate, both in stationary conditions and in transient ones, temperature profiles inside MV joints, referring to different environmental conditions and with current flowing both in the core conductor and in the metallic shield. The model has been implemented in the Simulink environment and then it has been validated with a set of experimental tests, specifically set up in order to check its performance in steady state and during transients. The numerical results were always in good agreement with the measurements. Subsequently, the circuit model has been employed to perform a predictive analysis of the joint internal temperatures, which may be achieved in operation and during faults by varying the ambient temperature. In all cases, the temperature limits tolerated by insulations have never been exceeded.

Thermal Circuit Model of Gas-insulated Transmission Line Based on the Finite Element Method

Based on the finite element method and thermoelectric analogy theory, the steady-state equivalent thermal circuit model of Gas-insulated transmission line(GIL) is established to calculate the temperature of its tank and conductor, and the transient model is established as well. The losses of tank and conductor are solved by analyzing the electromagnetic field of GIL using the finite element method. Steady-state equivalent thermal circuit model is framed for solving temperature, based on the heat transfer characteristics of GIL. Introducing thermal capacity, transient thermal characteristics of its tank and conductor are solved by simplified transient thermal circuit model. Compared with experimental data and the finite element simulation data, the accuracy of this thermal model of GIL is verified and a theoretical basis is also provide for temperature prediction of GIL.

Experimental verification of a thermal equivalent circuit dynamic model on an extended range electric vehicle battery pack

Abstract The development of a dynamic thermal battery model for hybrid and electric vehicles is realized. A thermal equivalent circuit model is created which aims to capture and understand the heat propagation from the cells through the entire pack and to the environment using a production vehicle battery pack for model validation. The inclusion of production hardware and the liquid battery thermal management system components into the model considers physical and geometric properties to calculate thermal resistances of components (conduction, convection and radiation) along with their associated heat capacity. Various heat sources/sinks comprise the remaining model elements. Analog equivalent circuit simulations using PSpice are compared to experimental results to validate internal temperature nodes and heat rates measured through various elements, which are then employed to refine the model further. Agreement with experimental results indicates the proposed method allows for a comprehensive real-time battery pack analysis at little computational expense when compared to other types of computer based simulations. Elevated road and ambient conditions in Mesa, Arizona are simulated on a parked vehicle with varying quiescent cooling rates to examine the effect on the diurnal battery temperature for longer term static exposure. A typical daily driving schedule is also simulated and examined.

Thermal nexus model for the thermal characteristic analysis of an open-type air-cooled induction motor

A new thermal nexus model (TNM) is introduced to enhance the existing thermal circuit models by compensating for the modeling of heat transport by air flow. The concepts of unit structure as well as body and surface thermal resistances, which are the most basic components of the thermal nexus, are defined. The thermal circuit for heat transport by air flow is expressed using the capacity thermal resistance and a temperature fitting constant. An iteration algorithm for the temperature fitting constant is suggested to improve the accuracy of the thermal nexus model. The thermal characteristic analysis for an open-type, air-cooled induction motor was performed using the proposed model. Based on the results, the feasibility of the thermal nexus model is examined. The thermal nexus model had an error of less than 2°C for stator and winding temperatures, compared with the CFD and experimental results.

A Multiphysics Design Methodology Applied to a High-Force-Density Short-Duty Linear Actuator

This paper presents a coupled electromagnetic and thermal design methodology which addresses the problem of balancing accuracy against computation time. A case study on a short-duty permanent-magnet (PM) linear actuator is used to illustrate the approach. The proposed method employs a two-dimensional electromagnetic finite-element (FE) model coupled with a detailed thermal equivalent circuit (TEC) model which is automatically constructed and parameterized using geometric and material data. A numerical method of estimating the equivalent thermal properties of the winding amalgam is used along with published empirically derived convection and radiation heat transfer correlations. The relatively high number of network nodes and more accurate thermal material properties minimizes model calibration and allows improved temperature prediction, including winding hot spots, while maintaining a low computational cost for both steady-state and transient analyses. A comparison between experimental and theoretical actuator performance shows that the design methodology provides good accuracy electromagnetic and transient thermal performance predictions without the need for direct model calibration and can yield an optimized design within an acceptable time frame.

Kapitza resistance and the thermal conductivity of amorphous superlattices

We report on the thermal conductivities of amorphous Stillinger-Weber and Lennard-Jones superlattices as determined by non-equilibrium molecular dynamics simulations. Thermal conductivities decrease with increasing interface density, demonstrating that interfaces contribute a non-negligible thermal resistance. Interestingly, Kapitza resistances at interfaces between amorphous materials are lower than those at interfaces between the corresponding crystalline materials. We find that Kapitza resistances within the Stillinger-Webber based Si/Ge amorphous superlattices are not a function of interface density, counter to what has been observed in crystalline superlattices. Furthermore, the widely used thermal circuit model is able to correctly predict the interfacial resistance within the Stillinger-Weber based amorphous superlattices. However, we show that the applicability of this widely used thermal circuit model is invalid for Lennard-Jones based amorphous superlattices, suggesting that the assumptions made in the model do not hold for these systems.

Study on the Thermal Transient Response of TSV Considering the Effect of Electronic-Thermal Coupling

The transmission performance of TSV considering the effect of electronic-thermal coupling is an new challenge in three dimension integrated circuit. This paper presents the thermal equivalent circuit (TEC) model of the TSV, and discussed the thermal equivalent parameters for TSV. Si layer is equivalent to transmission line according to its thermal characteristic. Thermal transient response (TTR) of TSV considering electronic-thermal coupling effects are proposed, iteration flow electronic-thermal coupling for TSV is analyzed. Furthermore, the influences of TTR are investigated with the noncoupling and considering coupling for TSV. Finally, the relationship among temperature, thickness of SiO₂, radius of via and frequency of excitation source are addressed, which are verified by the simulation.

Thermal characterization and modeling of ultra-thin silicon chips

Manufacturing ultra-thin chip is an emerging field in semiconductor technology that is driven by 3-D integrated circuits and flexible electronics. Unlike bulk silicon (Si) chips with thickness greater than 400μm, the thermal management of ultra-thin Si chips with thickness smaller than 20μm is challenging due to the increased lateral thermal resistance implying stringent cooling requirements. Therefore, a reasonable prediction of temperature gradients in such chips is necessary. In this work, a thermal chip is implemented in an ultra-thin 0.5μm CMOS technology to be employed in surface steady-state and transient temperature measurement. Test chips are either packaged in a Pin Grid Array (PGA) ceramic package or attached to a flexible polyimide substrate. The experimental results show an on-chip temperature gradient of ∼15°C for a dissipated power of 0.4W in the case of the PGA package and ∼30°C for the polyimide substrate. The time constants are ∼50s and ∼1s for the PGA and the polyimide packages respectively. The measurements are complemented by FEM simulations using ANSYS 14.5 workbench and spice simulations using an equivalent lumped-component thermal circuit model. The lumped-element thermal circuit model is then used for the surface temperature prediction, which is compared to measurement results.

A thermal circuit model consistent with integral energy balance for internal forced convection in a circular tube

The equivalent thermal resistance circuit based on integral energy balance of thermally developing forced convection in a circular tube is derived describing the heat flow path between the heated tube wall and inlet fluid. The axial heat conduction of the flow is assumed to be negligibly small. To validate the thermal circuits developed, numerical simulations have been performed for laminar thermally developing forced convection of water in a circular tube with an imposed constant heat flux or constant wall temperature. The overall thermal resistances for the convective circuit separating the heated tube wall and inlet fluid are simply the convection thermal resistances due to the local/average heat transfer coefficients, respectively, defined based on the difference between local/average tube wall temperature and inlet fluid temperature. Applications of the convection thermal circuit derived have been demonstrated for direct or indirect evaluation of the pertinent heat transfer parameters of technical interest characterizing the forced convection heat transfer of thermally developing fluid flow in the iso-flux or iso-thermally heated tube.