Estimation Of Temperature Distribution Research Articles

Estimation of Temperature Distribution in the Brain Using the Temperatures of Blood Inflow and Outflow for Brain Temperature Control

Brain cells can be damaged by higher temperature in the brain, and brain temperature distribution monitoring system is required from the perspective of brain preservation. Brain tissue can be further damaged by direct measurement of temperature using some sensors. Therefore, indirect methods of measuring temperature are required. In this study, we propose a method for estimating the average metabolic rate of the entire brain based on the difference between the observed and estimated blood flow temperatures that can be measured during selective brain hypothermia. Our mathematical simulator can calculate the brain temperature distribution based on the estimated average metabolic rate, taking into account other parameters like heat transfer, metabolic heat of individual tissues, heat‐washout by blood flow, and environmental temperature. The algorithm for estimating the metabolic rate of mathematical master model substituted as a human head is confirmed using the mathematical slave model on the simulator. It is possible to present the temperature distribution by estimating metabolic heat production in the brain, considering the equilibrium between heat wash‐out by the blood flow and heat transfer. In addition, an appropriate initial value of brain temperature enables the accurate temperature management enough for clinical use even in the process of temperature estimation. The development of our proposed method will make it possible to construct a non‐invasive monitoring system that presents the estimated temperature distribution in the brain instead of the conventional invasive method. The new system is expected to be utilized in a various treatments related to some brain disorders. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Estimating temperature distribution and heat quantity of spindle shaft for machining centers

Estimating temperature distribution and heat quantity of spindle shaft for machining centers

Prediction of the efficient heat flux to get an accurate thermal and clad geometry characteristic during laser cladding

The prediction of the accurate thermal and clad geometry characteristics plays a significant role in obtaining a better metallurgical bond between the cladding material and the substrate. The estimation of temperature distribution is difficult experimentally within the melt pool. A suitable and accurate heat flux is needed to apply during the numerical modeling to get clear and accurate process parameters before conducting the actual experiments. Therefore, different heat flux is used to get the best-suited heat flux which gives an accurate response during the laser cladding. The same processing parameters were considered during the simulation for the different heat sources. In all the cases, the maximum temperature was obtained at the center of the melt pool and decreased when moving away from the center of the melt pool in-depth and across the scanning speed direction. A similar shape of the melt pool is formed when three-dimensional volumetric Gaussian heat flux and conical heat flux are used, which gave best suited and efficient heat flux for the numerical simulation before actually conducting experiments. When egg-shaped heat flux is applied, an insufficient temperature was reached at the interface of the powder and substrate, whereas more dilution appeared for parabolic heat flux.

Monte Carlo simulation of phonon transport from ab-initio data with Nano-κ

Understanding of heat transport in nanodevices is a challenging issue for several new technologies. It requires specific modelling approaches and dedicated simulation tools. Yet the latter are not numerous, and are often adapted to some “classic” materials or restricted to simple geometries (i.e. thin films, nanowires). Looking to address this deficiency, the present work brings Nano-κ, a Python code to simulate the phonon transport in nano and micro scale devices from ab-initio phonon data. The code has personalizing capabilities that allow to simulate several geometries and materials, offering insights of temperature distribution, heat flux, thermal conductivity, and mode contribution to energy transport. In the present work, a detailed description of the physical model implementation is provided and several simulation test cases are discussed. Nano-κ provides reliable predictions of the thermal conductivity in different materials, and is able to correctly predict the relative effect of size, temperature, and surface roughness on thermal transport properties. Program summaryProgram Title: Nano-κCPC Library link to program files:https://doi.org/10.17632/tr29mhkjh8.1Developer's repository link:https://github.com/brunohs1993/NanokappaLicensing provisions: MITProgramming language: PythonNature of problem: The estimation of heat conduction at nanoscales depends on the estimation of phonon transport, since Fourier's law may not be valid in these situations. The phonon transport is described by the Boltzmann Transport Equation (BTE), that needs to be solved for each phonon mode separately, while estimating temperature distributions that depends on all modes at the same time. The phonon data can be retrieved from ab-initio simulations. Some BTE calculations have been already done through the years for simple geometries, but there is no publicly available code that allows enough flexibility to be used by the scientific community.Solution method: Some previous works [1-3] have had success in applying the Monte Carlo method to solve the BTE for phonon transport. In the more recent works, the ab-initio data is retrieved from density functional theory (DFT) simulations [4-5]. Nano-κ is a Python code built on the same theoretical basis of previous developments, but adds more flexibility so that it can be open for public research use.

Fast multilayer temperature distribution estimation for lithium-ion battery pack

Fast and accurate temperature estimation is crucial for ensuring battery packs' safety and operation performance. However, the full-scale online temperature estimation is still challenging. In this work, a novel reduced-order multi-physics model for a lithium-ion battery pack is proposed for real-time temperature distribution estimation, containing the distributed equivalent circuit model, the three-heat-source thermal model, and the flow resistance network model. The proposed model is conducted on a direct contact liquid-cooled battery pack composed of three modules connected in series. An online parameterization methodology with a closed loop observer is designed, and the key parameters can be automatically identified and corrected. The validation results suggest that the multilayer temperature distribution of cell, module, and pack levels can be commendably described under both steady and transient conditions, where the maximum error can be controlled within 2.8 °C. Besides, the temperature variation of the coolant can be estimated during the operation. The proposed model shows excellent potential in onboard temperature estimation with tens of milliseconds for each temperature update.

A High-Resolution Analytical Thermal Modeling Method of Capacitor Bank Considering Thermal Coupling and Different Cooling Modes

Thermal stress is of crucial importance to capacitor reliability. However, for a capacitor bank, on spatial scale, the complex heat transfer modes are not clearly illustrated; and on time scale, the ESR aging is neither fully discussed in current evaluation methods. These could lead to a glaring error in the prediction of temperature distribution and lifetime estimation. Therefore, this paper proposed an analytical thermal modeling method with high-resolution for the capacitor bank, considering the thermal coupling effect between individual capacitors, as well as different cooling conditions and the heat variation caused by ESR aging. Firstly, the improved thermal state-space modeling method is proposed to universally describe a multiple heat source system. Then, based on heat transfer and fluid mechanic theories, the characterization method of thermal coupling effect in different cooling modes is discussed. Furthermore, the ESR aging model is applied in the electro-thermal analysis of capacitor bank, aiming to improve the accuracy of thermal calculation in long time scale. Finally, to alleviate the uneven temperature distribution in an in-line designed capacitor bank, a staggered design method is proposed followed by a case study, where a nine-capacitor bank is presented to validate the corresponding modeling method and optimization.

Estimating the thermal conductivity of plutonic rocks from major oxide composition using machine learning

SUMMARY The accurate estimation of temperature distribution in the earth's crust and modelling of heat-related processes in geodynamics requires knowledge of the thermal conductivity of plutonic rocks. This study compiled an extensive data set of 530 representative plutonic rock samples, including thermal conductivity, major oxide composition and (for two subsets of data) modal mineralogy. For the first time, three machine learning algorithms (ML; i.e. support vector regression, random forest and extreme gradient boosting) were employed to estimate the thermal conductivity of plutonic rocks using the major oxide composition feature as input variables. The performance of these ML-based models was evaluated against a geochemically compositional model and eight mineral-driven physically based empirical mixing models. Results show that the means of predicted thermal conductivity by the ML-based models and the geochemically compositional model are not significantly different from the measured thermal conductivity at a significance level of 5 per cent. However, the ML-based models outperformed the best-performing non-ML model, the geochemically compositional model. The highest prediction accuracy was achieved by extreme gradient boosting, which reduced the mean absolute percentage error and root mean square error by more than 50 per cent. Furthermore, SiO2 is confirmed as the most important independent variable, followed by Al2O3, TiO2, CaO and K2O. The turning point observed in the thermal conductivity trend with SiO2 wt per cent may be primarily attributed to variations in mineral composition within the subgroup of igneous rock types classified based on SiO2 wt per cent. This study explores, for the first time, the use of ML algorithms to estimate the thermal conductivity of plutonic rocks from their major oxide composition.

Online temperature distribution estimation of lithium-ion battery considering non-uniform heat generation characteristics under boundary cooling

Lithium-ion batteries (LIBs) generate a lot of heat in the course of use, which will lead to a highly uneven distribution of the temperature, thus affecting the accuracy of battery modeling, parameter estimation and thermal management. In order to solve this potential threat, an on-line temperature distribution estimation method of LIB considering non-uniform heat generation under boundary cooling is proposed in this paper. Firstly, a thermal model of tab area is constructed by using lumped parameter method based on the analysis of the heat generation and heat transfer mechanism, and this tab thermal model is regarded as the first kind of boundary condition of the cell core. Secondly, a difference equation of the temperature distribution of the core area is constructed by using the heat balance method, and the boundary conditions and convection coefficient model are also deduced. Finally, a disturbance observer is designed to estimate the state and disturbance simultaneously to further improve the accuracy of temperature estimation. Additional stability analysis shows the convergence of the proposed disturbance observer. Experiments and verification demonstrate that the proposed method is effective and has better estimation performance compared with the other traditional methods under four different cycles, and the estimation error is less than 1.5 °C.

Estimation of laser light propagation in biological tissue during laser-tissue bonding using Monte Carlo simulation

Monte Carlo simulations are an elementary approach towards modeling light propagation in tissues. The detection of subsurface temperature in tissues during laser mediated therapies and microsurgeries is crucial for estimating associated thermal damage. MC simulation provides with the possibility to optimize the process. The approach has been used to model light propagation, associated energy deposition, and the temperature distribution inside the tissue. Understanding the extent of laser light transmittance and heat distribution within the tissue is crucial for minimizing damage to the adjacent biological tissues. The total photon weight absorbed estimates the total heat distribution within the volume. A three-layer heterogeneous tissue was specified consisting of only the epidermis, dermis, and the subcutaneous fat tissue. The hop, drop, and spin trail of photons depends on the optical properties of these layers. The energy deposition and temperature distribution estimation are obtained by the MC simulation method. A real-time measurement of the temperature profile was also performed. The experimental results were in close congruence with the simulation result. The simulation results show good reproducibility of the real temperature distribution. Monte Carlo method can, thereby, be used in estimation and optimization laser induced processes.

Temperature-related thermal properties of paving materials: experimental analysis and effect on thermal distribution in semi-rigid pavement

ABSTRACT Thermal properties of paving materials are essential for estimating temperature distribution in semi-rigid pavements. Literature reported that the thermal parameters varied widely and were most independent of temperature. This paper proposed an innovative test setup to determine the thermal conductivity and diffusivity of hot mix asphalt (HMA) and cement-treated base (CTB) materials. The experimental results indicated that the thermal properties of the paving materials linearly increased with surface temperature. Field temperature monitoring in semi-rigid pavement was also conducted at different depths of HMA and CTB. The heating rate of any location inside the pavement was found approximately twice the heat release. Such obtained thermal parameters and the pavement surface temperature from field monitoring served as inputs for numerical simulations based on ANSYS programme. Using temperature-related thermal properties in the modelling exhibited higher accuracy in predicting temperature distribution in the semi-rigid pavement than those independent of temperature from the literature.

Bistatic Radar Tomography of Shear Margins: Simulated Temperature and Basal Material Inversions

A significant portion of the sea level contributions of Antarctica and Greenland comes from ice streams, but the physical processes controlling ice stream width are poorly understood, especially when topographic controls are absent. Recent modeling studies have indicated that ice stream width may be controlled by elevated temperatures inside ice stream shear margins. While radio echo sounders can provide measurements of englacial water storage and subglacial conditions, existing radar-sounding techniques cannot measure temperature profiles at the scale required to test this hypothesis. We propose using a wide-angle radar survey and tomographic inversion to resolve temperature profiles, gradients, and anomalies at the scale required to study the thermophysical controls on shear margins. Recent work produced a bistatic radar system capable of obtaining the long offsets required for well-constrained inversions; however, shear-margin-specific temperature inversion techniques have not been developed for this system. In this article, we develop Newton’s method and alternating direction method of multipliers’ inversions for estimating temperature distribution and basal material across ice stream shear margins. We evaluate the performance of these inversion techniques on simulated bistatic radar-sounding data. Our results suggest that bistatic radar tomography experiments should be able to produce temperature maps on 50 m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times50$ </tex-math></inline-formula> m grids with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.83~^{\circ} \text{C}~\pm ~0.084~^{\circ} \text{C}$ </tex-math></inline-formula> mean temperature error, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.58~^{\circ} \text{C}~\pm ~0.20~^{\circ} \text{C}$ </tex-math></inline-formula> maximum temperature error, and an error in relative basal permittivity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.63~\pm ~0.08$ </tex-math></inline-formula> for a 4-km transect.

Numerical Estimation of SAR and Temperature Distributions inside Differently Shaped Female Breast Tumors during Radio-Frequency Ablation.

Radio-frequency (RF) ablation is a reliable technique for the treatment of deep-seated malignant tumors, including breast carcinoma, using high ablative temperatures. The paper aims at a comparative analysis of the specific absorption rate and temperature distribution during RF ablation with regard to different female breast tumors. In the study, four tumor models equivalent to an irregular tumor were considered, i.e., an equivalent sphere and ellipsoid with the same surfaces and volumes as the irregular tumor and an equivalent sphere and ellipsoid inscribed in the irregular tumor. An RF applicator with a specific voltage, operating at 100 kHz inserted into the anatomically correct female breast, was applied as a source of electromagnetically induced heat. A conjugated Laplace equation with the modified Pennes equation was used to obtain the appropriate temperature gradient in the treated area. The levels of power dissipation in terms of the specific absorption rate (SAR) inside the naturalistically shaped tumor, together with the temperature profiles of the four simplified tumor models equivalent to the irregular one, were determined. It was suggested that the equivalent tumor models might successfully replace a real, irregularly shaped tumor, and the presented numeric methodology may play an important role in the complex therapeutic RF ablation process of irregularly shaped female breast tumors.

Analytical – numerical estimation of temperature distribution in living tissue by the DPL bio-heat model

Here, we used mathematical modeling to predict and simulate the behavior and effect of temperature on human skin, together with studying the effects of the blood perfusion parameters, the time of tissue exposure to the laser, and the effect of the delay times on temperature distribution on living tissue. The model that has been used is a dual-phase lag DPL bioheat transfer model. The solution of the model has been obtained by using the analytical scheme represented by Laplace transforms, as well as the numerical scheme represented by the implicit finite difference method. The paper involves comparing analytical and numerical solutions, a comparison between the temperature distribution according to various bio-heat models and the resulting thermal damage. The results of the DPL bioheat model have been compared with the previous study and it showed. A favorable convergence results have been presented graphically and discussed in detail.

Temperature estimation method for supercapacitor cell and module with less sensors

Temperature monitoring is of great significance for the safe operation and state estimation of supercapacitors in practical applications. As excessive temperature can even cause thermal runaway, it is quite necessary to monitor the temperature of each cell, especially in transportation area. However, there are two problems in the temperature distribution estimation. Firstly, the hot-spot temperature is usually distributed inside the cell and is hard to be measured by sensors. Secondly, applying sensors to each cell in a module requires a large number of sensors, which are difficult and expensive to install. In this paper, aiming at difficulty in cell internal temperature measurement, the closed-loop observer is established which measures the surface and ambient temperature online; aiming at difficulties to reduce sensors in the module, a Long Short-Term Memory (LSTM) network is established to measure a small number of cells to predict the temperature distribution of the whole module, thus a method of hot-spot temperature estimation of supercapacitor is proposed. The result from experiment and estimation shows that the RMSE and MAE of the H-∞ and NN joint filter is <0.4 °C in most situations, and the absolute error of LSTM for module temperature distribution is <0.8 °C, the MAE and RMSE is <0.5 °C.

Reduced order model-based observer design for online temperature distribution estimation in lithium-ion batteries

Time/space separation-based modeling methods have been widely researched for estimating lithium-ion battery (LIB) thermal dynamics. However, these methods have been developed in an offline environment and may not perform well in real-time application since the battery systems in electric vehicles (EVs) are usually subject to external disturbances. Furthermore, the onboard measurements of temperature are often corrupted by significant error. To address these problems, we present a reduced model-based observer design for online temperature distribution estimation in LIBs. First, an extreme learning machine (ELM)-based offline spatiotemporal model is constructed to approximate the thermal dynamics of LIB. Second, an adaptive reduced order observer is designed based on the offline model developed in the previous step. The offline model is then updated with the estimation results of the observer. As the performance of the estimator is highly related to the placement of sensors, a genetic algorithm (GA)-based integrated optimization strategy is also developed to determine the optimal sensor location for online estimation. Finally, the whole temperature distribution is estimated in real time using the observer, the measured voltage, current and the limited available temperature data. Two experiments on different batteries with different input currents verify the effectiveness of this developed model.

Determination of Temperature Distribution of Rohri, Sindh using Artificial Neural Network and Regression Analysis

As time passes, the world is facing the problem of global warming, which results in a rise in average daily temperature. Proper knowledge of temperature distribution and future prediction may help to cope with the situation in the near future. Climate forecasting has gone through various faces; in the early days’ people used to predict the behavior qualitatively. Now environmental scientists have developed a quantitative method for forest climate behavior with certain uncertainties. Empirical models have been developed based on regression analysis to estimate temperature distribution. Two models, linear and non linear, use dew point temperature and relative humidity as independent variables. In addition to regression analysis, Artificial Neural Network (ANN) has been utilized to predict the average daily temperatures of Rohri Sindh, a city in Pakistan in the Sindh province. Both empirical models and ANN estimates are in good agreement with the known values of average daily temperatures.

Heat flow data and thermal structure in northeastern Japan

New heat flow data corrected for climate change over Northeastern Japan were obtained using the temperature profile of the borehole of the High Sensitivity Seismograph Network (Hi-net). The obtained spatial distribution of heat flow shows low heat flow on the forearc side, high heat flow along the Ou Backbone Range, and low heat flow in the plains on the back-arc side. However, the distribution is not clearly divided into high and low heat flow along the VF front; for example, the low heat flow extends from near the northern Kitakami Mountains on the forearc side to the Ou Backbone Range crossing the VF, while the high heat flow extends to the central Kitakami Mountains and Sendai plain on the forearc side. In addition, a crustal temperature structure model was developed that considers into account the presence of sedimentary layers, the temperature dependence of thermal conductivity, and differences in heat generation due to lithology. There is a good correlation between this temperature structure and the lower limit of the seismogenic layer, which is between 400 and 450 °C. Compared to previous studies, the crustal thermal structure calculation method assumed is a model whose estimated temperature distribution is sensitive to structural differences; however, a more accurate estimation of the temperature structure is possible if detailed structural information is available. On the other hand, it seems necessary to treat fluid behavior in more detail in areas of high heat flow. However, the estimation of crustal temperature structure, especially in regions with thick sedimentary layers, is considered an improvement over the previous study.Graphical

Temperature distribution prediction in control cooling process with recurrent neural network for variable-velocity hot rolling strips

Control cooling is an essential method for microstructure and mechanical property control in hot rolling strip making. Therefore, it is vital to realize high-precision temperature distribution prediction and control in cooling process to ensure the industrial production. In this paper, a traditional mechanism model based on finite-difference method combined with online cycle velocity calculation strategy was introduced as one of the baseline methods estimating temperature distribution. However, considering calculation time, variable-velocity rolling makes it difficult to rapidly realize temperature and modifying water distribution of all segments in cooling zone. Herein, a temperature distribution prediction method based on recurrent neural network was proposed, by fully considering the variable-velocity rolling dynamic characteristics. And the temperature distribution prediction performance of the model with different recurrent cell and time steps was evaluated. The results indicated that the proposed model could realize temperature distribution prediction, and the model based on bi-LSTM and 48 timesteps has the highest determination coefficient value of 0.976, the lowest root mean square error of 8.03, and a mean absolute error of 5.7. Furthermore, compared with baseline model, the proposed model retained lower computational cost, making it applicable in industrial application by providing real-time temperature distribution prediction.

Efficient temperature estimation for thermally stratified storage tanks with buoyancy and mixing effects

Estimating the state thermal storage devices is key to use them efficiently to reduce the uncertainty of renewable sources. Although stratified storage tanks are one of the most efficient and cost-effective storage systems, they lack accurate state estimation methods. In this paper, we propose a general methodology for estimating the state of thermally stratified storage tanks of different topologies and capacity. The method is based on a simple moving horizon estimation technique and a 1-D smooth model that can integrate buoyancy effects into a smooth equation. The novelty of the proposed approach is that it is the first state estimation approach that considers both buoyancy and mixing effects. This distinction is paramount to an adequate estimation of the temperature distribution in the storage tank which can then be used for different aims, namely as a basis for model predictive controls. Besides the novel state estimation approach, the paper has three more contributions: (i) it shows how a model for seasonal storage devices can be further extended to smaller stratified tanks with different topologies; (ii) it modifies such a model so that the model equations can be integrated into a single dynamical equation; (iii) it proposes the most complete case study to date for modeling and estimating temperature distribution inside small stratified storage tanks. The analysis of the proposed approach is done in several stages. First, to validate the applicability of the model to small tanks and multiple topologies, we perform a model identification and parameter estimation for three different stratified tanks. Second, we test the accuracy of the proposed state estimation approach in those three stratified tanks employing the estimated parameters in the first experimental study and the models also previously defined. Finally, to further validate the models, we perform a simulation for each of the three tanks and we compare the accuracy of the simulation against real data. As we show, both the state estimation approach and the model are satisfactorily accurate as they display average mean errors below 2 °C.

Finite Difference Method Simulation on Effect of Blood Perfusion on Temperature Distribution of Female Human Skin

&lt;p&gt;&lt;span lang="EN-US"&gt;Bioheat&lt;/span&gt;&lt;span lang="EN-US"&gt; transfer is a combination of heat transfer and biology process comprising of transfer of heat from human living tissue to the environment. This study aims to estimate the temperature distribution of female human’s skin. In this study, effect of varied blood perfusions of 1.5, 2.0, 2.5 and 3.0 kg/s.m&lt;sup&gt;3 &lt;/sup&gt;on bioheat transfer of female human skin, which was modeled into four layers, was simulated. To address this issue, one-dimensional unsteady state finite difference method was applied in this study. Result of this study informed that the finite difference method can be used to solve the bioheat transfer equation and to estimate temperature distribution of different skin layers of female human. In this study, blood perfusion affects temperature distribution in the four layers of unstable women's skin. The highest blood perfusion of 3 kg/s.m&lt;sup&gt;3&lt;/sup&gt; resulted in more homogeny temperature distribution of different skin layers. This circumstance occurred since higher blood perfusion increases heat transfer between blood and skin layers.&lt;/span&gt;&lt;/p&gt;