Distribution Of Joule Heating Research Articles

A modeling method for thermal steady-state simulation of the four-layer printed circuit board.

Thermal simulation of a Printed Circuit Board (PCB) can help identify potential overheating risks in the circuit. The proposed modeling method combines analytical temperature solutions and numerical approximations. Only Fourier-series analytical solutions related to the prepreg-layer surfaces need to be calculated, rather than the entire structure. Heat transfer through the lateral sides of a PCB is approximately considered as part of the compensated heat flux of the insulating-layer surface boundaries. Heat diffusion within or between metal layers is numerically approximated using the finite volume method. The core layer is treated as "thermally-thick". Temperature-dependent boundary conditions are considered through iterations. A test solver was developed based on the method. The modeling accuracy was validated by comparison with COMSOL Multiphysics for a four-layer structure with a moderate degree of discretization. Additionally, a PCB for generating DC 3.3V was designed, tested, and modeled, with the modeling results confirmed by the thermal images. The electro-thermal analysis of the distribution of electric potential and Joule heating in traces and vias was integrated into the PCB model. The layout maps of the PCB were further adjusted to reduce Joule heating in the output circuit, and the improvement on reducing the IR drop and hotspot temperature was examined.

A Comparative Assessment of the Distribution of Joule Heating in Altitude as Estimated in TIE‐GCM and EISCAT Over One Solar Cycle

AbstractDuring geomagnetically active times, Joule (or frictional) heating in the Lower Thermosphere‐Ionosphere is a significant source of thermal energy, greatly affecting density, temperature, composition and circulation. At the same time, Joule heating and the associated Pedersen conductivity are amongst the least known parameters in the upper atmosphere in terms of their quantification and spatial distribution, and their parameterization by geomagnetic parameters shows large discrepancies between estimation methodologies, primarily due to a lack of comprehensive measurements in the region where they maximize. In this work we perform a long‐term statistical comparison of Joule heating as calculated by the NCAR Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIE‐GCM) and as obtained through radar measurements by the European Incoherent Scatter Scientific Association (EISCAT). Statistical estimates of Joule heating and Pedersen conductivity are obtained from a simulation run over the 11 year period spanning from 2009 until 2019 and from radar measurements over the same period, during times of radar measurements. The results are statistically compared in different Magnetic Local Time sectors and Kp level ranges in terms of median values and percentiles of altitude profiles. It is found that Joule heating and Pedersen conductivity are higher on average in TIE‐GCM than in EISCAT for low Kp and are lower than EISCAT for high Kp. It is also found that neutral winds cannot account for the discrepancies between TIE‐GCM and EISCAT. Comparisons point toward the need for a Kp‐dependent parameterization of Joule heating in TIE‐GCM to account for the contribution of small scale effects.

Analysis of Nonuniform Contact Resistivity Distribution on No-Insulation HTS Racetrack Coil

This paper presents a numerical analysis and experiment to investigate a contact resistivity distribution of a no-insulation (NI) high-temperature superconductor (HTS) racetrack coil. Since the racetrack coil consists of straight and curved sections with continuously varing curvatures, the local inhomogeneity of contact resistivity can occur. We adopt a partial element equivalent circuit (PEEC) method to investigate this inhomogeneity. A 50-turn NI HTS single pancake test coil is fabricated to figure out the discrepancy of contact resistivity, and the coil is charged up to 100 A in a liquid nitrogen bath. Voltage profiles between inserted voltage taps and the magnetic fields at the coil center are measured and compared with two simulation cases: 1) uniform contact resistivity; 2) nonuniform contact resistivity distribution. The results indicated that nonuniform distribution of contact resistivity may exist. Lastly, the current and Joule heat distribution during the ramping process is analyzed by the PEEC model.

Numerical Simulation of Multi-Physics Fields in Fused Magnesia Furnace

In this paper, a 3D transient multi-physical field model is developed to capture the complex processes inside a fused magnesia furnace. The multi-physics model integrates electromagnetism, thermodynamics, decomposition reactions, and flow. The three-phase submerged magnesia furnace includes an arc, magnesite ores, a melting pool, and a solidification ingot. For a more comprehensive analysis of the optimal design of industrial operations, the influence of the key index of electrode insertion depth on temperature and reaction is also discussed. The results show that the current density in the fused magnesia furnace is almost the same as the joule heat distribution, and there is an obvious area of low energy density affected by the skin effect, which leads to the waste of electric energy. The temperature at the center of the arc reaches 12,000 K, and the plasma areas formed at the end of the three electrodes are connected to each other to form a closed current path, which provides energy for the process of melting magnesia. The arc region is an ellipsoid with a length of ~30 mm and a diameter of ~49 mm. The decomposition reaction of magnesite mainly occurs in the arc area, and the radiation heat provided by the high-temperature arc is used as the heat source. There is almost no magnesite in the molten pool, and the molten pool only provides energy for the melting process of magnesia. When the electrode insertion depth is 0.4, 0.5, 0.6, and 0.7 m, the arc length is 0.049 m, 0.066 m, 0.068 m, and 0.059 m, respectively. According to the simulation results, there is an optimal electrode insertion depth.

Research on Reliability of Ni/Sn/Cu(Ni) Copper Pillar Bump Under Thermoelectric Loading

Abstract With the development of packaging devices toward high performance and high density, electronic devices are subjected to thermo-electric stresses under service conditions, which has become a particularly important reliability problem in micro-electronics packaging. The reliability of the chip under thermo-electric stresses is studied in this paper. First, thermo-electric coupling experiments were carried out on two solder joint structures of Ni/Sn3.5Ag/Cu and Ni/Sn3.5Ag/Ni. The interface evolution of solder joints under different current densities was analyzed. The reliability of the two structures under thermo-electric stresses was compared and analyzed. After that, three-dimensional finite element analysis was employed to simulate the current density, Joule heat, and temperature distribution of the flip chip. Finally, through the combination of experiment and simulation, the distribution of Joule heat and temperature of the chip was analyzed. The results show that the Ni/Sn3.5Ag/Ni structure has better reliability than the Ni/Sn3.5Ag/Cu structure under thermal–electric coupling. In addition, when the Ni layer was used as the cathode side, the constant temperature applied on the chip was 150 °C, and the current density was higher than 5 × 104 A/cm2, the dissolution failure of the Ni layer occurred in two structures. Because the higher current density generated a large amount of Joule heat where the current was crowded, resulting in excessively high temperature and rapid dissolution of the Ni barrier layer.

Ion migration behavior and its interaction with sintering environment in cation conductor during flash sintering

Flash sintering has been reported in various ceramics. Nevertheless, anion and cation conductors exhibit different flash-sintering behaviors, and the interaction mechanism between the conductive species and the sintering environment has remained unclear. Herein, we report the flash-sintering phenomena of a typical cation conductor, Na3Zr2(SiO4)2(PO4) with anode region surrounded by air and NaNO3 environments. The results prove that the ionic behavior and joule heating distribution can be controlled by changing the electrode environment. Four possible scenarios describing the ion migration behavior and interaction with the environment are proposed for providing a guidance for controlling the ion interaction behavior during flash sintering.

Refined microstructure and dispersed precipitates in a gradient rolled AZ91 alloy under pulsed current

Pulse current assisted treatment has gained more attention in metallic materials, which is efficient and energy-saving, as compared with traditional heat treatment. However, the microstructural evolution of magnesium alloys with varied pre-deformation under pulsed current is still unclear. In this work, AZ91 alloy is subjected to gradient rolling and pulse current treatment (∼40 s). After gradient rolling, a transition zone from the initial to deformed microstructure was obtained in the sample, and the evolution of phases and twins can be analyzed precisely and continuously. Due to the difference in the Joule heat distribution of pulse current, a large number of fine Mg17Al12 phase are precipitated and dispersed, the precipitation and dissolution process of Mg17Al12 phase occur simultaneously. The region with moderate deformation has the largest recrystallization fraction, and the {101¯1}−{101¯2} double twins and {101¯1} compression twins are the preferred nucleation sites in the early stage of pulse current treatment. The weaken of texture is due to the newly formed grains with non-basal orientations. This work provides a new insight into the microstructural control of pre-deformed magnesium alloys under pulse current assisted treatment.

The evaluation of power generation performance of variable cross section thermoelectric generator based on new thermoelectric material parameter measurement method

ABSTRACT This paper mainly study the feasibility of anew method of measuring thermoelectric material parameters and several TEGs with variable cross-sectional legs. The corresponding experimental system was established, and the thermoelectric material parameters were obtained according to the experimental data and measurement theory. ATEG model containing 127 pairs of thermocouples was established to verify the accuracy of the parameters. Then, the models with different leg shapes were established to study the corresponding internal resistance, Joule heat generation and power generation performance. The results showed that the maximum relative error between the model and the experimental data was not exceed 5%, which verified the feasibility and accuracy of the measurement method. The shape of the legs affected the internal resistance, current and Joule heat distribution of the models. The Joule heat of Model 1 accounts for up to 4.86% of the hot side heat flow. Among several models, Model 4 provides the smallest internal resistance, the largest output current and power generation performance. Compared with the regular-leg of Model 1, the maximum output power and efficiency of the convex-leg of Model 4 were increased by 14.2% and 3%. The results of this paper can provide reference for designing variable leg geometry of thermoelectric modules.

A numerical method for spatially-distributed transient simulation to replicate nonlinear ‘defect-irrelevant’ behaviors of no-insulation HTS coil

This paper presents a numerical method, based on the partial element equivalent circuit (PEEC) technique, for spatially-distributed and time-varying simulation to analyze nonlinear ‘defect-irrelevant’ behaviors of a no-insulation (NI) high temperature superconductor (HTS) coil. We suggest a resistivity parameterization approach in combination of the PEEC method to replicate electromagnetic dynamics of an NI HTS coil containing multiple ‘defects.’ The proposed method is adopted to investigate ‘defect-irrelevant’ behaviors of an NI single pancake coil having lap joints as a form of artificial defects. To validate our approach, electromagnetic characteristics of the NI test coil are measured in a bath of liquid nitrogen at 77 K and compared with four key simulation results: (a) local voltages; (b) current distribution; (c) magnetic field;and (d) Joule heating distribution. Experimental measurements of local voltages and the magnetic field are compared to the simulation results to validate our numerical method.

Liquid Metal Welding to Suppress Li Dendrite by Equalized Heat Distribution

AbstractIt is important to understand the growth mechanism of Li dendrites for the protection of Li metal anodes. Herein, joule heat as another inducing mechanism for Li dendrites is proposed and demonstrated by experiments and theoretical simulations. A nonuniform interface structure can lead to disordered surface thermal distribution based on joule heat theory, which may induce chaotic nucleation and growth of dendrites. Based on this concept, a new strategy of liquid metal welding is explored to overcome such joule heat distribution issue. This strategy is universally compatible with other traditional protection routes such as solid electrode interphase films, charging protocols, and electrolytes. Multistrategy synergetic protection strategies result in remarkable performance.

Novel Paradigm of Subdural Cortical Stimulation Does Not Cause Thermal Damage in Brain Tissue: A Simulation-Based Study.

The thermal effect of a novel effective electrical stimulation mapping (ESM) technique using an Ojemann's stimulation electrode in open craniotomy areas causes a nondestructive local increase in temperature. Another type of stimulating electrode is a subdural strip, routinely used in intraoperative electrocorticography (ECoG), which applies ESM in a covered subdural area over the motor cortex. ECoG electrode geometry produces a different electrical field, causing a different Joule heat distribution in tissue, one that is impossible to measure in subdural space. Therefore, the previous safety control study of the novel ESM technique needed to be extended to include an assessment of the thermal effect of ECoG strip electrodes. We adapted a previously well-validated numerical model and performed coupled complex electro-thermal transient simulations for short-time (28.4 ms) high-frequency (500 Hz) and hyperintense (peak 100 mA) ESM paradigm. The risk of heat-induced cellular damage was assessed by applying the Arrhenius equation integral on the computed time-dependent spatial distribution of temperature in the brain tissue during ESM stimulation and during the cooldown period. The results showed increases in temperature in the proximity around ECoG electrode discs in a safe range without destructive effects. As opposed to open craniotomy, subdural space is not cooled by the air; hence a higher - but still safe - induced temperature was observed. The presented simulation agrees with the previously published histopathological examination of the stimulated brain tissue, and confirms the safety of the novel ESM technique when applied using ECoG strip electrodes.

Role of saline concentration during saline-infused radiofrequency ablation: Observation of secondary Joule heating along the saline-tissue interface

Infusion of saline prior to radiofrequency ablation (RFA) is known to enlarge the thermal coagulation zone. The abundance of ions in saline elevate the electrical conductivity of the saline-saturated region. This promotes greater electric current flow inside the tissue, which increases the amount of RF energy deposition and subsequently enlarges the coagulation zone. In theory, infusion of higher concentration of saline should lead to larger coagulation zone due to the greater number of ions. Nevertheless, existing studies on the effects of concentration on saline-infused RFA have been conflicting, with the exact role of saline concentration yet to be fully elucidated. In this paper, computational models of saline-infused RFA were developed to investigate the role of saline concentration on the outcome of saline-infused RFA. The elevation in tissue electrical conductivity was modelled using the microscopic mixture model, while RFA was modelled using the coupled dual porosity-Joule heating model. Results obtained indicated that the presence of a concentration threshold to which no further elevation in tissue electrical conductivity and enlargement in thermal coagulation can occur. This threshold was determined to be at 15% NaCl. Analysis of the Joule heating distribution revealed the presence of a secondary Joule heating site located along the interface between wet and dry tissue. This secondary Joule heating was responsible for the enlargement in coagulation volume and its rapid growth phase during ablation.

Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators.

The efficiency of a thermoelectric (TE) generator for the conversion of thermal energy into electrical energy can be easily but roughly estimated using a constant properties model (CPM) developed by Ioffe. However, material properties are, in general, temperature ()-dependent and the CPM yields meaningful estimates only if physically appropriate averages, i.e., spatial averages for thermal and electrical resistivities and the temperature average (TAv) for the Seebeck coefficient (, are used. Even though the use of compensates for the absence of Thomson heat in the CPM in the overall heat balance, we find that the CPM still overestimates performance (e.g., by up to 6% for PbTe) for many materials. The deviation originates from an asymmetric distribution of internally released Joule heat to either side of the TE leg and the distribution of internally released Thomson heat between the hot and cold side. The Thomson heat distribution differs from a complete compensation of the corresponding Peltier heat balance in the CPM. Both effects are estimated quantitatively here, showing that both may reach the same order of magnitude, but which one dominates varies from case to case, depending on the specific temperature characteristics of the thermoelectric properties. The role of the Thomson heat distribution is illustrated by a discussion of the transport entropy flow based on the plot. The changes in the lateral distribution of the internal heat lead to a difference in the heat input, the optimum current and thus of the efficiency of the CPM compared to the real case, while the estimate of generated power at maximum efficiency remains less affected as it is bound to the deviation of the optimum current, which is mostly <1%. This deviation can be corrected to a large extent by estimating the lateral Thomson heat distribution and the asymmetry of the Joule heat distribution. A simple guiding rule for the former is found.

Statistical Analysis of Joule Heating and Thermosphere Response During Geomagnetic Storms of Different Magnitudes

AbstractDuring a geomagnetic storm, the energy deposition from magnetosphere to thermosphere through Joule heating leads to variations in the total mass density of thermosphere. In this study, measurements obtained from the Challenging Minisatellite Payload and Gravity Recovery and Climate Experiment satellites between 2002 and 2008 are used to study the response of thermospheric density during geomagnetic storms of different magnitudes inferred from the Dst index. Based on the height‐integrated Joule heating with data derived from the Defense Meteorological Satellite Program spacecraft, we statistically analyze 265 geomagnetic storm cases to study the characteristics of Joule heating distribution and its influence on thermospheric density. The results show that between thermospheric density and Joule heating during weak and moderate geomagnetic storms, the time lag is only about 0–2 hr, while the same for intense storms is 3–5 hr. This indicates that the time lag is positively correlated with the intensity of geomagnetic storms. Besides, it is found that the peak duration of Joule heating increases for more intense geomagnetic storms.

Effect of Electrode Immersion Depth on the Electrical Resistance and Heat Generation in the Electroslag Remelting Process

A numerical simulation based on the coupling of electromagnetic-fluid-thermal analysis was developed to investigate the effects of electrode immersion depth (EID) on the electrical resistance and heat generation in the electroslag remelting (ESR) process. The total electric current was obtained by integrating the current density at the slag/metal interface, and the electrical resistance is the ratio of potential to current. It indicates that the EID variation changes the shape, size, and current path of the slag pool, and, as a result, the current density, heat generation, and melting power are directly proportional to the EID, while the electrical resistance of the slag pool is inversely proportional to the EID. The distance between the electrode and the molten-metal pool and the contact areas between the electrode and the slag are the main factors affecting the distribution of voltage, current density, Joule heating, and temperature in the slag pool of the ESR process. A change in the current density affects the electrical resistance and heat generation, which has a direct effect on the ESR process.

Effects of Electropulsing Treatment on the Element Diffusion Between Ti6Al4V and Commercially Pure Titanium

AbstractPrevious studies show that the phase transition temperature of Ti6Al4V can be effectively reduced by electropulsing treatment, which may be related to the promotion effect of current on element diffusion. In order to verify the above conjecture, the diffusion experiments of the Ti6Al4V-pure titanium system under the action of electropulsing and heat treatment are carried out. The results show that the current can effectively improve the diffusion coefficients of aluminum and vanadium, and the promotion effect has no relationship with the direction of the current. Considering the inhomogeneity of the Joule heat distribution of the microscopic scale of the material, the hypothesis of “local hot spot” is proposed to explain the experimental phenomena. It is found that the hypothesis can make effective predictions of diffusion coefficients and explain the promotion effect of electropulsing on Ti6Al4V phase transition reasonably.

Numerical simulation of heat distribution in RGO-contacted perovskite solar cells using COMSOL

A 3D simulation of optical photogenreation, electrical characteristics, and thermal/heat distribution across the structure of a perovskite solar cell with a reduced graphene oxide (RGO) contact is presented. COMSOL Multiphysics package has been used to solve the coupled optical-electrical-thermal modules for this hybrid cell where the RGO added as the bottom electrode instead of a conventional metallic contact to enhance the heat dissipation towards a higher device stability. The Wave Optic module, Semiconductor module, and Heat Transfer in Solid module were coupled and solved for the proper input parameter values taken from relevant literature. The optical photogeneration, current-voltage characteristics, electric-field and the thermal maps of the cell are presented. The RGO contact doesn’t significantly impact on the optical and electrical output of the cell, but it accelerates the heat dissipation. The heat is mainly generated across the cell from the light absorption, Shockley-Read-Hall non-radiative recombination, and Joule heating. Compared to the cell with the Au electrode, the RGO contacted cell is showing a minimized heat accumulation and gradient at the bottom junction of the RGO/Spiro interface which promises a thermal stability of the cell. The nan-radiative and joule heat distribution also show a moderated density for the RGO contacted cell which are assigned to the high heat conductivity of the RGO layer compared to traditional metallic electrodes. Our simulations results are of the rarely presented thermal simulations for such devices and prove the superiority of graphene over plane metallic contacts for heat dissipation and thermodynamic aspect of a solar cell.

Modelling the particle contact influence on the Joule heating and temperature distribution during FLASH sintering

FLASH sintering is a field-assisted technique that allows the densification of ceramics in a few seconds at temperatures significantly lower than those of conventional cycles. There is still discussion among the scientific community about the mechanism behind this sintering process, that has been typically attributed to Joule heating, defect creation and movement or liquid phase assisted sintering. Computational modelling can be a powerful tool in helping to explain and predict this process. Using potassium sodium niobate (KNN) as a case study, a lead-free piezoelectric, this work explores Finite Element Modelling to evaluate the dependence of Joule heating generation and temperature distribution as a function of the cubic particle orientation.

Low-voltage and -surface energy SWCNT/poly(dimethylsiloxane) (PDMS) nanocomposite film: Surface wettability for passive anti-icing and surface-skin heating for active deicing

Icing is a multiphase/multiscale/multiparameter physical process, and is of frequent occurrence when suitable conditions with temperature, pressure and humidity are met. In the present work, we prepared a series of PDMS-matrix nanocomposite films with different SWCNT contents, which were endowed with hydrophobicity based on the low-surface-energy PDMS matrix and the conductivity on the SWCNT filler. Furthermore, by etching the pillar-textured structure on its surface, the nanocomposite with 5.0 wt% SWCNT was given the superhydrophobicity. These nanocomposites can be easily switched from a hydrophobic anti-icing mode to an electro-thermal deicing mode by supplying a low voltage. Using non-contact infrared thermometry, we presented an analysis of the freezing phase transition process of a single water droplet on cooling surfaces with different wettability, and investigated their ice nucleation rate and macroscopic growth velocity on these surfaces. The ice-retarding capability of superhydrophobic nanocomposite surface subjected to lots of condensed droplets was also confirmed, and understanding in light of weak contact interaction with droplets. Also under consideration is the icephobicity after freezing in terms of ice shear strength. In addition, we performed a statistical analysis about the Joule heat distribution on nanocomposite surface, the results of which demonstrated that the nanocomposite could supply a suitable heating function for active deicing, demonstrating with an energy-input deicing experiment subsequently.

Effects of Alignment Between Particle Precipitation and Ion Convection Patterns on Joule Heating

AbstractIn the high‐latitude thermosphere and ionosphere the Joule (frictional) heating rate is related to both conductivity and electric field. Thus, an accurate calculation of the Joule heating rate requires self‐consistent specifications of high‐latitude particle precipitation and ion convection patterns. However, general circulation models usually use uncorrelated empirical models to specify high‐latitude particle precipitation and ion convection separately and independently. Here, studies have been conducted to examine the significance of the appropriate spatial alignment of the precipitation and ion convection patterns to the energy input estimation for the upper atmosphere. As shown in Defense Meteorological Satellite Program satellite observations, a close alignment between the particle poleward boundary (PPB) and the convection reversal boundary (CRB) can be identified when the interplanetary magnetic field is strongly southward. To illustrate the importance of this alignment, a comparison between two Global Ionosphere‐Thermosphere Model runs has been conducted. In the first case, the uncorrelated empirical models were used in Global Ionosphere‐Thermosphere Model to specify the high‐latitude electrodynamics. In the second case, the PPB was adjusted to be approximately coincident with the CRB. The alignment between the PPB and the CRB causes changes in the Joule heating distribution and a 50% enhancement of hemispheric integrated Joule heating under extreme conditions. The effect of the alignment on Joule heating and neutral density has also been investigated preliminarily during the 5 August 2011 geomagnetic storm.