Distribution Of Heat Sources Research Articles

Bayesian Inference for Estimating Heat Sources through Temperature Assimilation

Abstract This paper utilizes a Bayesian inference framework to address the two-dimensional steady-state heat conduction problem, focusing on the estimation of unknown distributed heat sources in a thermally-conducting medium with uniform conductivity. The goal is to infer the locations, strength, and shape of heaters by assimilating temperature data in Euclidean space, employing a Fourier series to represent each heater's shape. The Markov Chain Monte Carlo method, incorporating the random-walk Metropolis-Hasting algorithm and parallel tempering, is utilized for posterior distribution exploration in both unbounded and wall-bounded domains. It is found that multiple solutions arise in cases where the number of temperature sensors is less than the number of unknown states. Moreover, smaller heaters introduce greater uncertainty in estimated strength. To address the challenge of estimating the heater's strength and shape simultaneously due to their strong correlation, our method incorporates sharp priors on one to ensure accurate and feasible solutions of the other. The diffusive nature of heat conduction smooths out any deformations in the temperature contours, especially in the presence of multiple heaters positioned near each other, impacting convergence. In wall-bounded domains with Neumann boundary conditions, the inference of heater parameters tends to be more accurate than in unbounded domains.

Simulation of indoor space thermal energy circulation in architectural environment design detail features based on visual object tracking algorithm

The heat circulation of interior space plays a crucial role in the design of the built environment, affecting energy efficiency and residential comfort. With the development of science and technology, visual target tracking algorithm provides a new possibility for optimizing thermal energy cycle. The purpose of this paper is to study the simulation method of indoor space thermal energy cycle based on visual target tracking algorithm to improve the efficiency of thermal energy management in building environment design and ensure indoor comfort. The research uses laboratory Settings, combined with high-performance cameras and advanced visual target tracking algorithms, to monitor indoor heat source distribution and personnel movement in real time. Through data acquisition and analysis, the indoor heat cycle model was constructed and simulated by computational fluid dynamics (CFD) software to evaluate the influence of different design parameters on the heat cycle. Through the optimization of the design scheme, the efficiency of indoor heat use is significantly improved, and the comfort score of residents is significantly improved. Therefore, the simulation of indoor space thermal energy cycle based on visual target tracking algorithm provides an effective tool for building environment design, which can realize efficient energy management and improve living comfort.

Numerical Simulation Analysis of Dock Bank Slopes’ Soil–Water Interface Recognition and Monitoring Device Models Based on Heat Transfer Principles

The erosion and sedimentation of bank slopes are important factors affecting the safety of wharf operations. The essence of bank slope monitoring is to identify the water–soil interface. This paper proposes a model for soil-and-water interface identification and monitoring equipment buried on the bank slope of the wharf, based on the difference in thermodynamic heat transfer between water and soil media, and presents the results of multi-condition numerical simulation. The comparison between numerical simulation results and indoor experimental results shows that the overall patterns are consistent, with an error of less than 11.4%, which is lower than the deviation between theoretical calculation results and indoor experiments. Based on the accuracy of the numerical calculation results, the temperature rise and propagation characteristics of linear heat sources made of iron and PVC in eight types of cohesive soils and six types of non-cohesive soils were studied. The results indicate that there are significant differences in the temperature distribution of linear heat sources made of iron and PVC in both water and soil media. The monitoring equipment model based on the difference in heat transfer between water and soil can be applied in practical engineering. This provides a foundation for the design and application of subsequent monitoring equipment.

Enhanced framework for solving general energy equations based on metropolis-hasting Markov chain Monte Carlo

Due to the widespread presence of heat and mass transfer phenomena in industrial applications, numerous studies have been devoted to the accurate solution of energy equations, providing a foundation for the analysis of heat and mass transfer processes in practical applications. In this study, a Green's Function Markov Superposition Monte Carlo (GMSMC) for solving general energy equations has been developed based on probability and statistical principles owing to its advantageous features of insensitivity towards dimension and geometric complexity as well as the capability to handle multiple integrals in complex domains. The energy equation is first decomposed, and corresponding probability models are established for each component, considering their interrelationships. Subsequently, a solution framework for solving the general energy equation is constructed by integrating these probability models based on a Markov chain structure. The mathematical principles and formulae of the proposed method are derived in detail. The performance of the proposed method is validated by several heat transfer systems with different combinations of boundary conditions and features, which mainly include the distribution of the internal heat source and whether the convection or transient term is included. Results of the validation show that the temperatures obtained by the proposed method are in good agreement with the FEM based on a fine grid, no matter whether the calculation is for a single point or a distribution.

Research on multi-heat source arrangement optimization based on equivalent heat source method and reconstructed variational autoencoder

The variational autoencoder (VAE) architecture has significant advantages in predictive image generation. This study proposes a novel RFCNN-βVAE model, which combines residual-connected fully connected neural networks with VAE to handle multi-heat source arrangements. By integrating analytical solutions, polynomial fitting, and temperature field superposition, we accurately simulated the temperature rise distribution of a single heat source. We further explored the use of multiple equivalent heat sources to replace adiabatic boundary conditions. This enables the analytical method to effectively solve the two-dimensional conjugate convective heat transfer problem, providing a reliable alternative to traditional numerical solutions. Our results show that the model achieved high predictive accuracy. By adjusting the β parameter, we balanced reconstruction accuracy and latent space generalization. During the stable phase of the multi-heat source optimization iteration, 73.4% of the results outperformed the dense dataset benchmark, indicating that the model successfully optimized heat source coordinates and minimized peak temperature rise. This validates the feasibility and effectiveness of deep learning in thermal management system design. This research lays the groundwork for optimizing complex thermal environments and contributes valuable perspectives on the effective design of systems with multiple thermal sources or for applications like multi-beam lighting equalization.

Synergistic effects of multi-segmented magnetic fields, wavy-segmented cooling, and distributed heating on hybrid nanofluid convective flow in tilted porous enclosures

This study investigates the complex thermal-fluid behavior within a tilted porous enclosure filled with a Cu−Al2O3-water hybrid nanofluid, subject to segmented magnetic fields, wavy cooling segments, and distributed heat sources. The research explores the intricate interplay between geometric factors and thermal-magnetic forces to enhance heat transfer in industrial applications. The finite volume method (FVM), coupled with the SIMPLE algorithm and a TDMA solver, is employed to solve the governing transport equations. A comprehensive parametric analysis examines the effects of key dimensionless parameters: Darcy-Rayleigh number (10–104), Darcy number (10-4–10-1), Hartmann number (0–70), magnetic field angle (0°-180°), nanoparticle volume fraction (0–2 %), porosity (0.1–1.0), wavy cooler undulation height (0–0.3), magnetic segment width (0–1), number of segmental magnetic fields (0–4), and enclosure tilting angle (0°–180°). The study elucidates the physical mechanisms underlying the transition from uniform to segmented heating scenarios. Results reveal a remarkable enhancement of up to 38 % in heat transfer performance when transitioning from a conventional square enclosure to the proposed configuration with partial waviness on opposing walls. This improvement stems from increased surface area and disrupted thermal boundary layers, promoting better fluid mixing. The application of a segmented magnetic field with strategic orientation resulted in up to 26 % enhancement by modulating flow patterns and creating localized convection cells. The segmented heating generates thermal plumes that interact with the magnetic field-induced Lorentz forces, further improving thermal transport. The findings provide valuable insights into the design and optimization of efficient heat transfer systems in various industries, including electronics cooling, solar thermal collectors, and nuclear reactors, demonstrating significant potential for energy savings and improved thermal management through the strategic integration of hybrid nanofluids, magnetic fields, and geometric modifications in porous media applications.

Experimental and analytical investigation of intensive cooling of local distributed heat sources by means of forced flow of liquid

In this work a two-phase forced flow in channels of small geometric dimensions is analyzed. The Navier-Stokes equation was used to create a theoretical model describing the phenomenon of a evaporation of a flowing vapor and the Maxwell equation was used to describe the flow of a thin liquid layer. Both equations are coupled and overall create an original theoretical model describing the phenomenon of the evaporation of a liquid layer. This model of a liquid forced convection cooling the flat element with distributed internal heat sources is theoretically and experimentally analyzed. A flow of the cooling and evaporating liquid is forced by a suction of the vacuum pump. The cooling process is investigated theoretically for two specific cases with both, a constant and a cyclic heat emission. The impact of the liquid layer thickness on the cooling intensity is analyzed for both cases.

Noninvasive reconstruction of internal heat source in biological tissue using adaptive simulated annealing algorithm

The heat distribution information of human lesions is of great value for disease analysis, diagnosis, and treatment. It is a typical inverse problem of heat conduction that deriving the distribution of internal heat sources from the temperature distribution on the body surface. This paper transforms such an inverse problem of bio-heat transfer into a direct one, thereby avoiding complex boundary conditions and regularization processes. To noninvasively reconstruct the internal heat source and its corresponding 3D temperature field in biological tissue, the adaptive simulated annealing (ASA) algorithm is used in the simulation module, where the position P(x, y, z) of point heat source in biological tissue and its corresponding temperature T are set as the optimization variables. Under a certain optimized sample, one can obtain the simulated temperature distributing on the surface of the module, then subtract the simulated temperature from the measured temperature of the same surface which was measured using a thermal infrared imager. If the sum of absolute values of the difference is smaller, it indicates that the current sample is closer to the true location and temperature of the heat source. When the values of optimization variables are determined, the corresponding 3D temperature field is also confirmed. The simulation results show the simulated position and temperature of the heat source are very approximate with those of the real experimental module. The method presented in this paper has enormous potential and promising prospects in clinical research and application, such as tumor hyperthermia, disease thermal diagnosis technology, etc.

Modeling and simulation of temperature field in high-shear and low-pressure grinding with liquid-body-armor-like grinding wheel

High-shear and low-pressure grinding using liquid-body-armor-like grinding wheel is a new grinding process. It has a great potential in the field of precision and ultra-precision machining. To clarify the unclear grinding heat characteristics, heat generation mechanism, and heat source distribution of the liquid-body-armor-like grinding wheel, a temperature field model was developed for high-shear and low-pressure grinding with ABAQUS. The thermal characteristics of the new grinding wheel were investigated by studying the heat flux and convective loads under different grinding parameters. The effectiveness of the heat model was validated through high-shear and low-pressure grinding experiments. The simulation results closely matched with the experimental results, with an average error of 5.84 % and a minimum error of 0.94 %. The grinding temperature decreased gradually from the centre of the heat source towards the edge of the workpiece in both horizontal and vertical directions. The temperature raised with the increase of the grinding velocity, ranging from 39.66 °C at 4 m/s to 77.82 °C at 14 m/s. It decreased with the workpiece feed rate, dropping from 39.66 °C at 500 mm/min to 32.00 °C at 3000 mm/min. As the normal grinding force increased, it gradually increases from 30.80 °C to 39.66 °C. The grinding temperature of the liquid-body-armor-like grinding wheel was lower than that of the traditional grinding wheel.

Analysis and Experiment of Thermal Field Distribution and Thermal Deformation of Nut Rotary Ball Screw Transmission Mechanism

This study designs a differential dual-drive micro-feed mechanism, superposing the two “macro feed motions” (“motor drive screw” and “motor drive nut”) using the same transmission of “the nut rotary ball screw pair” structure. These two motions are almost equal in terms of speed and turning direction, thus the “micro feed” can be obtained. (1) Background: Thermal deformation is the primary factor that can restrict the high-precision micro-feed mechanism and the distribution of heat sources differs from that of the conventional screw single-drive system owing to the structure and motion features of the transmission components. (2) Discussion: This study explores the thermal field distribution and thermal deformation of the differentially driven micro-feed mechanism when two driving motors are combined at different speeds. (3) Methods: Based on the theory of heat transfer, the differential dual-drive system can be used as the research object. The thermal equilibrium equations of the micro-feed transmission system are established using the thermal resistance network method, and a thermal field distribution model is obtained. (4) Results: Combined with the mechanism of thermal deformation theory, the established thermal field model is used to predict the axial thermal deformation of the differential dual-drive ball screw. (5) Conclusions: Under the dual-drive condition, the steady-state thermal error of the nut-rotating ball screw transmission mechanism increases with the increase in nut speed and composite speed and is greater than the steady-state thermal error under the single screw drive condition. After reaching the thermal steady state, the measured thermal elongation at the end of the screw in the experiment is approximately 10.5 μm and the simulation result is 11.98 μm. The experimental measurement result demonstrates the accuracy of the theoretical analysis model for thermal error at the end of the screw.

Annual dynamics of global remote industrial heat sources dataset from 2012 to 2021

The spatiotemporal distribution of industrial heat sources (IHS) is an important indicator for assessing levels of energy consumption and air pollution. Continuous, comprehensive, dynamic monitoring and publicly available datasets of global IHS (GIHS) are lacking and urgently needed. In this study, we built the first long-term (2012–2021) GIHS dataset based on the density-based spatiotemporal clustering method using multi-sources remote sensing data. A total of 25,544 IHS objects with 19 characteristics are identified and validated individually using high-resolution remote sensing images and point of interest (POI) data. The results show that the user’s accuracy of the GIHS dataset ranges from 90.95% to 93.46%, surpassing other global IHS products in terms of accuracy, omission rates, and granularity. This long-term GIHS dataset serves as a valuable resource for understanding global environmental changes and making informed policy decisions. Its availability contributes to filling the gap in GIHS data and enhances our knowledge of global-scale industrial heat sources.

Thermal Design of Tile Type Active Phased Array Radar Antenna

Abstract Based on the structure and heat source distribution characteristics of the tile-type active phased array radar antenna, forced air cooling is adopted for its heat dissipation design. The heat dissipation path and fins of the main heating module of the antenna were designed and calculated, and the reliability of the thermal design was verified through software simulation and thermal testing.

A modified Green-Naghdi fractional order model for analyzing thermoelectric MHD

PurposeWhereas, the classical Green-Naghdi Type II (GN-II) model struggles to accurately represent the thermo-mechanical behavior of thermoelectric MHD due to its inability to account for the memory effect. A new mathematical model of the GN-II theory incorporates a fractional order of heat transport to address this issue.Design/methodology/approachThe employment of the matrix exponential method, which forms the basis of the state-space approach in contemporary theory, is central to this strategy. The resulting formulation, together with the Laplace transform techniques, is applied to a variety of problems. Solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also, a problem with the distribution of heat sources is considered. The numerical technique is used to achieve the Laplace transform inversion.FindingsAccording to the numerical results and its graphs, the influences of the fractional order parameters, figure-of-merit factor, thermoelectric power and Peltier coefficient on the behavior of the field quantities are investigated in the new theory.Originality/valueThe new modeling of thermoelectric MHD has advanced significantly as a result of this work, providing a more thorough and precise tool for forecasting the behavior of these materials under a range of thermal and magnetic conditions.

Thermal analysis of sinusoidal doubly salient Electro-Magnetic Machine with distributed magnetomotive forces considering complex heat distribution and material thermal characteristics

Sinusoidal doubly salient electro-magnetic machine with distributed magnetomotive forces has DC excitation and AC armature windings in the same stator slot, which leads to the complicated distribution of heat sources and thermal resistances. One of the keys to design this motor is to estimate the temperature rise accurately. In this paper, the thermal performance of the motor materials at different temperatures was tested. According to the complex structure characteristics, the layered and sub-regional equivalent model of the stator slot is proposed. The model not only uses the material thermal data obtained from experiments, but also considers the complex thermal resistances and AC/DC losses distribution in the slots, as well as the influence of winding and insulation processes on the temperature rise of the motor, which is conducive to obtaining the highest point of the motor temperature and ensuring the calculation accuracy. The 3-D global steady-state temperature distribution of sinusoidal doubly salient electro-magnetic machine with distributed magnetomotive forces is studied, and the temperature rise of each part under different current densities is also analyzed. Finally, the temperature experiment of the prototype is carried out. The experiments show that the accurate loss calculation and thermal parameters make the maximum error between the simulation model and the actual measurement is 3.8 °C. The results not only guide the selection of reasonable armature and excitation winding current density of sinusoidal doubly salient electro-magnetic machine with distributed magnetomotive forces, but also provide data and experience support for temperature estimation of motors with complex winding distribution.

Modeling of laser-assisted micro-milling Inconel718

Nickel-based superalloy Inconel718 is a typical difficult-to-machine material with the characteristic of high strength and hardness. Demands for micro parts of nickel-based superalloy Inconel718 are growing in aerospace, biomedical and other fields. Laser-assisted micro-milling (LAMM) can realize precision machining of the workpiece because of its lower cutting force. However, the machining mechanism and the change law of cutting force during LAMM of nickel-based superalloy Inconel718 are still unclear. There is a crucial need for modeling of LAMM Inconel718. This paper explores LAMM of nickel-based superalloy Inconel718 and realizes the simulation of LAMM process. A three-dimensional transient heat transfer finite element (FE) model is established to predict the temperature distribution of a Gaussian heat source in LAMM. Multiple sets of simulations of laser pre-heating with various laser power are conducted to analyze the temperature fields of workpiece and determine the appropriate laser parameters. A novel 3D model of the full machining process of LAMM Inconel 718 is constructed by ABAQUS with multi-subroutine, a fully coupled thermal-mechanical process is achieved. A modified Johnson-Cook constitutive model is used to reflect the size effect and flow stress of LAMM Inconel 718. Finally, the validity of the models is verified by experiments. Based on the verified model, the appropriate laser pre-heating parameters are obtained, and the prediction of cutting forces of LAMM Inconel718 is achieved.

On some computational aspects for electromagnetic-thermal dosimetry of mm waves

This work is on the use of a state-of-the-art hybrid boundary element method/finite element method (BEM/FEM) for electromagnetic (EM) dosimetry and the coupled thermal dosimetry model based on the Pennes’ heat transfer equation (PHE) for biological tissue solved by means of FEM. The distribution of the induced electric field obtained in both homogeneous and non-homogeneous human head models using EM model is used as a distributed heat source in the piecewise homogeneous human head thermal dosimetry model. As the penetration depth is inversely proportional to the frequency of incident EM wave, we consider the heating depth in several human head models, to illuminate whether homogeneous models in the EM part of the model are pertinent in the thermal dosimetry part. If confirmed, the results could be found useful in standardisation efforts related to the assessment of human exposure to EM fields in the high frequency range.

Reconstruction of internal heat source in biological tissue using parallel particle swarm optimization

With the rapid development of engineering thermophysics, researches on human biological heat transfer phenomena has gradually shifted from qualitative to quantitative. The heat distribution information of human lesions is of great value for disease analysis, diagnosis, and treatment. It is a typical inverse problem of heat conduction that deriving the distribution of internal heat sources from the temperature distribution on the body surface. Differing from traditional numerical methods for solving heat conduction, this paper transforms such an inverse problem of bio-heat transfer into a direct one, thereby avoiding complex boundary conditions and regularization processes. To noninvasively reconstruct the internal heat source and its corresponding 3D temperature field in biological tissue, the parallel particle swarm optimization (PPSO) is used in the simulation module, where the position P(x, y, z) of point heat source in biological tissue and its corresponding temperature T are set as the optimization variables. Under a certain optimized sample, one can obtain the simulated temperature distributing on the surface of the module, then subtract the simulated temperature from the measured temperature of the same surface which was measured using a thermal infrared imager. If the absolute value of the difference is smaller, it indicates that the current sample is closer to the true location and temperature of the heat source. When the values of optimization variables are determined, the corresponding 3D temperature field is also confirmed. The simulation results show the simulated position and temperature of the heat source are very approximate with those of the real experimental module. The method presented in this paper has enormous potential and promising prospects in clinical research and application, such as tumor hyperthermia, disease thermal diagnosis technology, etc.

Simulation of Natural Convection with Sinusoidal Temperature Distribution of Heat Source at the Bottom of an Enclosed Square Cavity.

The lattice Boltzmann method is employed in the current study to simulate the heat transfer characteristics of sinusoidal-temperature-distributed heat sources at the bottom of a square cavity under various conditions, including different amplitudes, phase angles, initial positions, and angular velocities. Additionally, a machine learning-based model is developed to accurately predict the Nusselt number in such a sinusoidal temperature distribution of heat source at the bottom of a square cavity. The results indicate that (1) in the phase angle range from 0 to π, Nu basically shows a decreasing trend with an increase in phase angle. The decline in Nu at an accelerated rate is consistently observed when the phase angle reaches 4π/16. The corresponding Nu decreases as the amplitude increases at the same phase angle. (2) The initial position of the sinusoidal-temperature-distributed heat source Lc significantly impacts the convective heat transfer in the cavity. Moreover, the decline in Nu was further exacerbated when Lc reached 7/16. (3) The optimal overall heat transfer effect was achieved when the angular velocity of the non-uniform heat source reached π. As the angular velocity increases, the local Nu in the square cavity exhibits a gradual and oscillatory decline. Notably, it is observed that Nu at odd multiples of π surpasses that at even multiples of π. Furthermore, the current work integrates LBM with machine learning, enabling the development of a precise and efficient prediction model for simulating Nu under specific operational conditions. This research provides valuable insights into the application of machine learning in the field of heat transfer.

A two-dimensional semi-analytic thermal model for global temperature distribution predicting and hot spot monitoring in interior permanent magnet synchronous motor

A two-dimensional semi-analytical thermal model (SATM) is presented, aiming to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring for interior permanent magnet synchronous motor (IPMSM). Thereby, it provides a reliable analysis tool for thermal behavior evaluation and prevents undesired consequences induced by excessive temperature rise, which is of great worth and significance in promoting the flourishing of IPMSM. SATM combines the analytical method, lumped parameter thermal network, and finite element analysis to obtain an analytical solution for thermal behavior through mathematical derivation by considering the complicated configuration, heat source distribution, heat dissipation condition, and material thermal dependence. Through SATM, it is possible to observe the global temperature distribution as well as the location and size of hot spots in each element. The temperature distribution gradient on the static is more pronounced than that on the dynamic; secondly, the area with the most severe heating is mainly found on the winding; furthermore, the hot spot on the winding is mainly located a little bit inside the center. Moreover, the thermal behavior of IPMSM at rated load is investigated by numerical analysis and experiments. A comprehensive comparison with SATM is done. The computational deviations between SATM and numerical analysis regarding the hot spot, minimum, and average temperatures on each element are all within 4.06 %. However, SATM consumes only 20.92 % of the time and 68.29 % of the storage of the numerical analysis. The measured data also fully prove the reliability and validity of the comparison. It is certain that SATM can well break through the limitation of the existing non-numerical technique to quickly and accurately achieve global temperature distribution predicting and hot spot monitoring of IPMSM. It provides researchers and engineers engaged in thermal behavior evaluation with good analysis means, design guidance, and optimization direction.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.