Analysis of the Temperature Characteristics of High-speed Train Bearings Based on a Dynamics Model and Thermal Network Method

High-speed trains often use temperature sensors to monitor the motion state of bearings.However,the temperature of bearings can be affected by factors such as weather and faults.Therefore,it is necessary to analyze in detail the relationship between the bearing temperature and influencing factors.In this study,a dynamics model of the axle box bearing of high-speed trains is established.The model can obtain the contact force between the rollers and raceway and its change law when the bearing contains outer-ring,inner-ring,and rolling-element faults.Based on the model,a thermal network method is introduced to study the temperature field distribution of the axle box bearings of high-speed trains.In this model,the heat generation,conduction,and dispersion of the isothermal nodes can be solved.The results show that the temperature of the contact point between the outer-ring raceway and rolling-elements is the highest.The relationships between the node temperature and the speed,fault type,and fault size are analyzed,finding that the higher the speed,the higher the node temperature.Under different fault types,the node temperature first increases and then decreases as the fault size increases.The effectiveness of the model is demonstrated using the actual temperature data of a high-speed train.This study proposes a thermal network model that can predict the temperature of each component of the bearings on a high-speed train under various speed and fault conditions.

Lumped-Parameter Thermal Network Model and Experimental Research of Interior PMSM for Electric Vehicle

A 25kW interior permanent magnet synchronous machine(IPMSM)applied to the electric vehicle is introduced in the paper.A lumped-parameter thermal network model is presented for IPMSM temperature rise calculation.Furthermore,a 3D liquid-solid coupling model considering the assembly clearance is compared with the 2D lumped-parameter thermal network model.Finally,a dynamometer platform for temperature rise measurement is established to verify the above-mentioned methods,which obtains the measured efficiency map at rated load case and overload case.At the same time,the measured no-load back electromotive Force(EMF),load line input voltage and load current are gathered.Thermocouple PTC100 is used to measure the temperature of the stator winding and iron core,and the FLUKE infrared thermal imager is applied to measure the surface temperature of PMSM and controller.Testing result shows that the lumped-parameter thermal network have a high accuracy to predict each part temperature.

Numerical Efficient Thermal Network for Calculating the Brake Disc Temperature

The simulation of the brake disc temperature is an important tool in the development of passenger cars.Nowadays thermal models of brake discs are real-time applications,running on electronic control units(ECUs)of cars to improve the vehicle safety in several ways.These models are often working with full empirical methods,leading to large deviations between calculation and measurement.To meet the requirements of automotive safety integrity levels(ASILs),these thermal models cannot rely on the state of the art ambient air temperature sensors,which causes unacceptable deviations.Focusing on numerical efficient thermal simulations,a new approach of a semi-analytical thermal network for simulating the brake disc temperature with minimal effort is proposed.The thermal network is based on lumped parameters,using two thermal capacity nodes and a constant ambient temperature.Using semi-analytical correlations,the model can be adapted to different geometries and car lines effortlessly.The empirical parameters of the model result only from two standardized tests.These parameters are used to evaluate the estimation accuracy in real driving situations.Additionally,the adaptability is tested for two different car lines and four brake disc dimensions.These tests are initially performed with unchanged parameters and afterwards with refitted parameters.The model shows a good estimation for the tested load cases.Compared to the state of the art,the proposed model is less accurate than complex finite element method(FEM)models and computational fluid dynamic(CFD)approaches,but shows a higher accuracy and better adaptability than other lumped parameter models with comparable numerical effort.Hence,possible applications can be dimensioning the brake system in the development process of new car lines or a real-time simulation on the latest ECU in the vehicle.

Accurate 3D Thermal Network Development for Direct-drive Outer-rotor Hybrid-PM Flux-switching Generator

Heat and thermal problems are major obstacles to achieving high power density in compact permanent magnet(PM)topologies.Consequently,a comprehensive,accurate,and rapid temperature rise estimation method is required for novel electric machines to ensure safe and reliable operations.A unique three-dimensional(3D)lumped parameter thermal network(LPTN)is presented for accurate thermal modeling of a newly developed outer-rotor hybrid-PM flux switching generator(OR-HPMFSG)for direct-drive applications.First,the losses of the OR-HPMFSG are calculated using 3D finite element analysis(FEA).Subsequently,all machine components considering the thermal contact resistance,anisotropic thermal conductivity of materials,and various heat flow paths are comprehensively modeled based on the thermal resistances.In the proposed 3-D LPTN,internal nodes are considered to predict the average temperature as well as the hot spots of all active and passive components.Experimental measurements are performed on a prototype OR-HPMFSG to validate the efficiency of the 3-D LPTN.A comparison of the results at various operating points between the developed 3-D LPTN,experimental test,and FEA indicates that the 3-D LPTN quickly approximates the hotspot and mean temperature of all components under both transient and steady states with high accuracy.

Leakage Proof,Flame-Retardant,and Electromagnetic Shield Wood Morphology Genetic Composite Phase Change Materials for Solar Thermal Energy Harvesting

Phase change materials(PCMs)offer a promising solution to address the challenges posed by intermittency and fluctuations in solar thermal utilization.However,for organic solid-liquid PCMs,issues such as leakage,low thermal conductivity,lack of efficient solar-thermal media,and flamma-bility have constrained their broad applications.Herein,we present an innova-tive class of versatile composite phase change materials(CPCMs)developed through a facile and environmentally friendly synthesis approach,leveraging the inherent anisotropy and unidirectional porosity of wood aerogel(nanowood)to support polyethylene glycol(PEG).The wood modification process involves the incorporation of phytic acid(PA)and MXene hybrid structure through an evaporation-induced assembly method,which could impart non-leaking PEG filling while concurrently facilitating thermal conduction,light absorption,and flame-retardant.Consequently,the as-prepared wood-based CPCMs showcase enhanced thermal conductivity(0.82 W m^(-1)K^(-1),about 4.6 times than PEG)as well as high latent heat of 135.5 kJ kg^(-1)(91.5%encapsula-tion)with thermal durability and stability throughout at least 200 heating and cooling cycles,featuring dramatic solar-thermal conversion efficiency up to 98.58%.In addition,with the synergistic effect of phytic acid and MXene,the flame-retardant performance of the CPCMs has been significantly enhanced,showing a self-extinguishing behavior.Moreover,the excellent electromagnetic shielding of 44.45 dB was endowed to the CPCMs,relieving contemporary health hazards associated with electromagnetic waves.Overall,we capitalize on the exquisite wood cell structure with unidirectional transport inherent in the development of multifunctional CPCMs,showcasing the operational principle through a proof-of-concept prototype system.

Regulatable Orthotropic 3D Hybrid Continuous Carbon Networks for Efficient Bi-Directional Thermal Conduction

Vertically oriented carbon structures constructed from low-dimen-sional carbon materials are ideal frameworks for high-performance thermal inter-face materials(TIMs).However,improving the interfacial heat-transfer efficiency of vertically oriented carbon structures is a challenging task.Herein,an orthotropic three-dimensional(3D)hybrid carbon network(VSCG)is fabricated by depositing vertically aligned carbon nanotubes(VACNTs)on the surface of a horizontally oriented graphene film(HOGF).The interfacial interaction between the VACNTs and HOGF is then optimized through an annealing strategy.After regulating the orientation structure of the VACNTs and filling the VSCG with polydimethylsi-loxane(PDMS),VSCG/PDMS composites with excellent 3D thermal conductive properties are obtained.The highest in-plane and through-plane thermal conduc-tivities of the composites are 113.61 and 24.37 W m^(-1)K^(-1),respectively.The high contact area of HOGF and good compressibility of VACNTs imbue the VSCG/PDMS composite with low thermal resistance.In addition,the interfacial heat-transfer efficiency of VSCG/PDMS composite in the TIM performance was improved by 71.3%compared to that of a state-of-the-art thermal pad.This new structural design can potentially realize high-performance TIMs that meet the need for high thermal conductivity and low contact thermal resistance in interfacial heat-transfer processes.

Multifunctional Integrated Organic-Inorganic-Metal Hybrid Aerogel for Excellent Thermal Insulation and Electromagnetic Shielding Performance

Vehicles operating in space need to withstand extreme thermal and electromagnetic environments in light of the burgeoning of space science and technology.It is imperatively desired to high insulation materials with lightweight and extensive mechanical properties.Herein,a boron-silica-tantalum ternary hybrid phenolic aerogel(BSiTa-PA)with exceptional thermal stability,extensive mechanical strength,low thermal conductivity(49.6 mW m^(-1)K^(-1)),and heightened ablative resistance is prepared by an expeditious method.After extremely thermal erosion,the obtained carbon aerogel demonstrates noteworthy electromagnetic interference(EMI)shielding performance with an efficiency of 31.6 dB,accompanied by notable loading property with specific modulus of 272.8 kN·m kg^(-1).This novel design concept has laid the foundation for the development of insulation materials in more complex extreme environments.

Efficient Electromagnetic Wave Absorption and Thermal Infrared Stealth in PVTMS@MWCNT Nano‑Aerogel via Abundant Nano‑Sized Cavities and Attenuation Interfaces

Pre-polymerized vinyl trimethoxy silane(PVTMS)@MWCNT nano-aerogel system was constructed via radical polymerization,sol-gel transition and supercritical CO_(2)drying.The fabricated organic-inorganic hybrid PVTMS@MWCNT aerogel structure shows nano-pore size(30-40 nm),high specific surface area(559 m^(2)g^(−1)),high void fraction(91.7%)and enhanced mechanical property:(1)the nano-pore size is beneficial for efficiently blocking thermal conduction and thermal convection via Knudsen effect(beneficial for infrared(IR)stealth);(2)the heterogeneous interface was beneficial for IR reflection(beneficial for IR stealth)and MWCNT polarization loss(beneficial for electromagnetic wave(EMW)attenuation);(3)the high void fraction was beneficial for enhancing thermal insulation(beneficial for IR stealth)and EMW impedance match(beneficial for EMW attenuation).Guided by the above theoretical design strategy,PVTMS@MWCNT nano-aerogel shows superior EMW absorption property(cover all Ku-band)and thermal IR stealth property(ΔT reached 60.7℃).Followed by a facial combination of the above nano-aerogel with graphene film of high electrical conductivity,an extremely high electromagnetic interference shielding material(66.5 dB,2.06 mm thickness)with superior absorption performance of an average absorption-to-reflection(A/R)coefficient ratio of 25.4 and a low reflection bandwidth of 4.1 GHz(A/R ratio more than 10)was experimentally obtained in this work.

Self‑Assembly of Binderless MXene Aerogel for Multiple‑Scenario and Responsive Phase Change Composites with Ultrahigh Thermal Energy Storage Density and Exceptional Electromagnetic Interference Shielding

The severe dependence of traditional phase change materials(PCMs)on the temperature-response and lattice deficiencies in versatility cannot satisfy demand for using such materials in complex application scenarios.Here,we introduced metal ions to induce the self-assembly of MXene nanosheets and achieve their ordered arrangement by combining suction filtration and rapid freezing.Subsequently,a series of MXene/K^(+)/paraffin wax(PW)phase change composites(PCCs)were obtained via vacuum impregnation in molten PW.The prepared MXene-based PCCs showed versatile applications from macroscale technologies,successfully transforming solar,electric,and magnetic energy into thermal energy stored as latent heat in the PCCs.Moreover,due to the absence of binder in the MXene-based aerogel,MK3@PW exhibits a prime solar-thermal conversion efficiency(98.4%).Notably,MK3@PW can further convert the collected heat energy into electric energy through thermoelectric equipment and realize favorable solar-thermal-electric conversion(producing 206 mV of voltage with light radiation intensity of 200 mw cm^(−2)).An excellent Joule heat performance(reaching 105℃with an input voltage of 2.5 V)and responsive magnetic-thermal conversion behavior(a charging time of 11.8 s can achieve a thermal insulation effect of 285 s)for contactless thermotherapy were also demonstrated by the MK3@PW.Specifically,as a result of the ordered arrangement of MXene nanosheet self-assembly induced by potassium ions,MK3@PW PCC exhibits a higher electromagnetic shielding efficiency value(57.7 dB)than pure MXene aerogel/PW PCC(29.8 dB)with the same MXene mass.This work presents an opportunity for the multi-scene response and practical application of PCMs that satisfy demand of next-generation multifunctional PCCs.

Metal–Organic Gel Leading to Customized Magnetic‑Coupling Engineering in Carbon Aerogels for Excellent Radar Stealth and Thermal Insulation Performances

Metal–organic gel(MOG)derived composites are promising multi-functional materials due to their alterable composition,identifiable chemical homogeneity,tunable shape,and porous structure.Herein,stable metal–organic hydrogels are prepared by regulating the complexation effect,solution polarity and curing speed.Meanwhile,collagen peptide is used to facilitate the fabrication of a porous aerogel with excellent physical properties as well as the homogeneous dispersion of magnetic particles during calcination.Subsequently,two kinds of heterometallic magnetic coupling systems are obtained through the application of Kirkendall effect.FeCo/nitrogen-doped carbon(NC)aerogel demonstrates an ultra-strong microwave absorption of−85 dB at an ultra-low loading of 5%.After reducing the time taken by atom shifting,a FeCo/Fe3O4/NC aerogel containing virus-shaped particles is obtained,which achieves an ultra-broad absorption of 7.44 GHz at an ultra-thin thickness of 1.59 mm due to the coupling effect offered by dual-soft-magnetic particles.Furthermore,both aerogels show excellent thermal insulation property,and their outstanding radar stealth performances in J-20 aircraft are confirmed by computer simulation technology.The formation mechanism of MOG is also discussed along with the thermal insulation and electromagnetic wave absorption mechanism of the aerogels,which will enable the development and application of novel and lightweight stealth coatings.

MXene@c-MWCNT Adhesive Silica Nanofiber Membranes Enhancing Electromagnetic Interference Shielding and Thermal Insulation Performance in Extreme Environments

A lightweight flexible thermally stable composite is fabricated by com-bining silica nanofiber membranes(SNM)with MXene@c-MWCNT hybrid film.The flexible SNM with outstanding thermal insulation are prepared from tetraethyl orthosilicate hydrolysis and condensation by electrospinning and high-temperature calcination;the MXene@c-MWCNT_(x:y)films are prepared by vacuum filtration tech-nology.In particular,the SNM and MXene@c-MWCNT_(6:4)as one unit layer(SMC_(1))are bonded together with 5 wt%polyvinyl alcohol(PVA)solution,which exhibits low thermal conductivity(0.066 W m^(-1)K^(-1))and good electromagnetic interference(EMI)shielding performance(average EMI SE_(T),37.8 dB).With the increase in func-tional unit layer,the overall thermal insulation performance of the whole composite film(SMC_(x))remains stable,and EMI shielding performance is greatly improved,especially for SMC_(3)with three unit layers,the average EMI SET is as high as 55.4 dB.In addition,the organic combination of rigid SNM and tough MXene@c-MWCNT_(6:4)makes SMC_(x)exhibit good mechanical tensile strength.Importantly,SMC_(x)exhibit stable EMI shielding and excellent thermal insulation even in extreme heat and cold environment.Therefore,this work provides a novel design idea and important reference value for EMI shielding and thermal insulation components used in extreme environmental protection equipment in the future.

A graph neural network approach to the inverse design for thermal transparency with periodic interparticle system

Recent years have witnessed significant advances in utilizing machine learning-based techniques for thermal metamaterial-based structures and devices to attain favorable thermal transport behaviors.Among the various thermal transport behaviors,achieving thermal transparency stands out as particularly desirable and intriguing.Our earlier work demonstrated the use of a thermal metamaterial-based periodic interparticle system as the underlying structure for manipulating thermal transport behavior and achieving thermal transparency.In this paper,we introduce an approach based on graph neural network to address the complex inverse design problem of determining the design parameters for a thermal metamaterial-based periodic interparticle system with the desired thermal transport behavior.Our work demonstrates that combining graph neural network modeling and inference is an effective approach for solving inverse design problems associated with attaining desirable thermal transport behaviors using thermal metamaterials.

Study on thermal decomposition kinetics of azobenzene-4,4′-dicarboxylic acid by using compensation parameter method and nonlinear fitting evaluation

Recently,azobenzene-4,4'-dicarboxylic acid(ADCA)has been produced gradually for use as an organic synthesis or pharmaceutical intermediate due to its eminent performance.With large quantities put into application in the future,the thermal stability of this substance during storage,transportation,and use will become quite important.Thus,in this work,the thermal decomposition behavior,thermal decomposition kinetics,and thermal hazard of ADCA were investigated.Experiments were conducted by using a SENSYS evo DSC device.A combination of differential iso-conversion method,compensation parameter method,and nonlinear fitting evaluation were also used to analyze thermal kinetics and mechanism of ADCA decomposition.The results show that when conversion rate α increases,the activation energies of ADCA's first and main decomposition peaks fall.The amount of heat released during decomposition varies between 182.46 and 231.16 J·g^(-1).The proposed kinetic equation is based on the Avrami-Erofeev model,which is consistent with the decomposition progress.Applying the Frank-Kamenetskii model,a calculated self-accelerating decomposition temperature of 287.0℃is obtained.

Design,progress and challenges of 3D carbon-based thermally conductive networks

The advent of the 5G era has stimulated the rapid development of high power electronics with dense integration.Three-dimensional(3D)thermally conductive networks,possessing high thermal and electrical conductivities and many different structures,are regarded as key materials to improve the performance of electronic devices.We provide a critical overview of carbonbased 3D thermally conductive networks,emphasizing their preparation-structure-property relationships and their applications in different scenarios.A detailed discussion of the microscopic principles of thermal conductivity is provided,which is crucial for increasing it.This is followed by an in-depth account of the construction of 3D networks using different carbon materials,such as graphene,carbon foam,and carbon nanotubes.Techniques for the assembly of two-dimensional graphene into 3D networks and their effects on thermal conductivity are emphasized.Finally,the existing challenges and future prospects for 3D carbon-based thermally conductive networks are discussed.

Flexible,thermal processable,self-healing,and fully bio-based starch plastics by constructing dynamic imine network

The serious environmental threat caused by petroleum-based plastics has spurred more researches in developing substitutes from renewable sources.Starch is desirable for fabricating bioplastic due to its abundance and renewable nature.However,limitations such as brittleness,hydrophilicity,and thermal properties restrict its widespread application.To overcome these issues,covalent adaptable network was constructed to fabricate a fully bio-based starch plastic with multiple advantages via Schiff base reactions.This strategy endowed starch plastic with excellent thermal processability,as evidenced by a low glass transition temperature(T_(g)=20.15℃).Through introducing Priamine with long carbon chains,the starch plastic demonstrated superior flexibility(elongation at break=45.2%)and waterproof capability(water contact angle=109.2°).Besides,it possessed a good thermal stability and self-adaptability,as well as solvent resistance and chemical degradability.This work provides a promising method to fabricate fully bio-based plastics as alternative to petroleum-based plastics.

Increasing both the electromagnetic shielding and thermal conductive properties of three-dimensional graphene-CNT-SiC hybrid materials

During the operation of electronic devices,a considerable amount of heat and electromagnetic radiation is emitted.Therefore,the investigation of materials with electromagnetic shielding and thermal management abilities has significant importance.Hybrid materials of three-dimensional graphene networks containing both carbon nanotubes(CNTs)and SiC whiskers(3D graphene-CNT-SiC)were synthesized.Using an aqueous-phase reduction method for the self-assembly of the graphene oxide,a three-dimen-sional porous graphene structure was fabricated.SiC whiskers,inserted between the graphene layers,formed a framework for longit-udinal thermal conduction,while CNTs attached to the SiC surface,created a dendritic structure that increased the bonding between the SiC whiskers and graphene,improving dielectric loss and thermal conductivity.It was found that the thermal conductivity of the hybrid material reached 123 W·m^(-1)·K^(-1),with a shielding effectiveness of 29.3 dB when the SiC addition was 2%.This result indic-ates that 3D graphene-CNT-SiC has excellent thermal conductivity and electromagnetic shielding performance.

Formation of Natural Melanin/TiO_(2) Nanostructure Hybrids with Enhanced Optical,Thermal and Magnetic Properties as a Soft Material

The natural Melanin/TiO_(2) was synthesized by the use of ultrasonication under UV radiation.The influence of natural melanin on the structural,optical and thermal properties of TiO_(2) nanoparticles was investigated by using Fourier transform infrared spectroscopy,thermogravimetric analysis and UV-Vis spectroscopy.It was observed that incorporating natural melanin on TiO_(2) nanoparticles(TiO_(2)-Mel)occurred at 2.01 eV with a low value of Urbach energy around 100 meV indicating improvement in the crystalline structure.Magnetic measurement at room temperature showed diamagnetic behavior.Furthermore,thermal results showed that TiO_(2)-Mel is stable even at temperatures up to 400℃.According to the results obtained by the thermal stability of melanin with titanium dioxide,it can be a good candidate in many applications such as solar cells and optoelectronics.

Genetic source,migration and accumulation of helium under deep thermal fluid activities:A case study of Ledong diapir area in Yinggehai Basin,South China Sea

Based on the geochemical parameters and analytical data,the heat conservation equation,mass balance law,Rayleigh fractionation model and other methods were used to quantify the in-situ yield and external flux of crust-derived helium,and the initial He concentration and thermal driving mechanism of mantle-derived helium,in the Ledong Diapir area,the Yinggehai Basin,in order to understand the genetic source,migration and accumulation mechanisms of helium under deep thermal fluid activities.The average content of mantle-derived He is only 0.0014%,the ^(3)He/^(4)He value is(0.002–2.190)×10^(−6),and the R/Ra value ranges from 0.01 to 1.52,indicating the contribution of mantle-derived He is 0.09%–19.84%,while the proportion of crust-derived helium can reach over 80%.Quantitative analysis indicates that the crust-derived helium is dominated by external input,followed by in-situ production,in the Ledong diapir area.The crust-derived helium exhibits an in-situ 4 He yield rate of(7.66–7.95)×10^(−13)cm^(3)/(a·g),an in-situ 4 He yield of(4.10–4.25)×10^(−4)cm^(3)/g,and an external 4 He influx of(5.84–9.06)×10^(−2)cm^(3)/g.These results may be related to atmospheric recharge into formation fluid and deep rock-water interactions.The ratio of initial mole volume of 3 He to enthalpy(W)is(0.004–0.018)×10^(−11) cm^(3)/J,and the heat contribution from the deep mantle(X_(M))accounts for 7.63%–36.18%,indicating that deep hot fluid activities drive the migration of mantle-derived 3 He.The primary helium migration depends on advection,while the secondary migration is controlled by hydrothermal degassing and gas-liquid separation.From deep to shallow layers,the CO_(2/3) He value rises from 1.34×10^(9)to 486×10^(9),indicating large amount of CO_(2)has escaped.Under the influence of deep thermal fluid,helium migration and accumulation mechanisms include:deep heat driven diffusion,advection release,vertical hydrothermal degassing,shallow lateral migration,accumulation in traps far from faults,partial pressure balance and sealing capability.

Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition:application of the clique polynomial method and physics-informed neural networks

The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled,and then are nondimensionalized by suitable dimensionless terms.Further,the obtained nondimensional equations are solved by the clique polynomial method(CPM).The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations.Additionally,the current study implements deep neural structures to solve physics-governed coupled equations,and the best-suited hyperparameters are attained by comparison with various network combinations.The results of the CPM and physicsinformed neural network(PINN)exhibit good agreement,signifying that both methods effectively solve the thermal modeling problem.