Heat Transfer Model Research Articles

Research on temperature rise prediction model for circuit breaker based on numerical Laplace transform

Abstract The temperature rise in circuit breakers’ thermal paths is a critical indicator influencing their tripping characteristics, directly affecting response speed, reliability, and safety. Existing models for predicting circuit breaker temperature rise are often structurally limited, lack generality, and exhibit low predictive accuracy. Addressing this issue, this paper investigates an efficient, precise, and widely applicable theoretical model for predicting circuit breaker temperature rise. This model focuses on the thermal conduction mechanisms within small-scale circuit breakers, establishing a fundamental numerical heat transfer model based on Newton’s cooling formula and Fourier’s heat conduction law. By applying numerical Laplace transformation, the model is simplified into the complex frequency domain, and employing residue theorem for solving, it is transformed back into the time domain using Laplace inverse transformation to derive the predictive model. Experimental validation using a 32 A rated current circuit breaker demonstrates the model’s high predictive accuracy, suitability across various circuit breaker structures, with an average deviation below the permissible deviation in industry standards. This research holds significant implications for enhancing the thermal tripping characteristics of circuit breakers.

Physics-guided spatiotemporal approach for melt pool size prediction in laser powder bed fusion

ABSTRACT This study first proposes a physics-guided spatiotemporal graph. The melt pool temporal feature nodes and spatial feature nodes are extracted from melt pool images based on spatiotemporal correlations. These feature points are treated as graph nodes, and the edge weights in the graph are calculated based on an analytical heat transfer model. It supplements the physical information of accumulated heat. Based on this, the graph convolutional network (GCN) is used to extract spatiotemporal information of heat transfer, and the long short-term memory (LSTM) is used to capture the evolution patterns of the melt pool. Thus, a melt pool spatiotemporal feature extraction model is constructed for melt pool size prediction. The model achieves prediction errors within 12% for the melt pool area and 8.5% for the melt pool perimeter. Subsequently, interpretability analysis indicates that the physics-guided approach enhances the model's learning ability for the cumulative contribution of heat from neighboring tracks.

Modeling of Heat Transfer and Airflow Inside Evacuated Tube Collector With Heat Storage Media: Experimental Validation Powered by Artificial Neural Network

ABSTRACTSolar air heater (SAH) is a widely employed technology for harnessing solar thermal energy in numerous applications. Contemporary research optimizes designs within identical spatial constraints to maximize energy output. However, there is a recognized need to conduct analytical validation to stimulate the experimental setup and formulate an artificial neural network (ANN) model to govern and predict the operation system. This investigation involved developing and assessing an evacuated tube solar air heater (ETSAH) integrated with annulus‐filled heat storage media. Furthermore, this study introduced an ANN model and analytical solution to predict performance parameters, representing a noteworthy contribution. The proposed ANN model achieved its optimal validation performance with a mean square error of 5.4018 × 10−6 after 11 epochs within 31 of training. Also, correlation findings show that the optimal architecture of a feed‐forward backpropagation is achieved when the 5‐40‐40‐40‐2 model architecture is used. In this case, there are five neural nodes in the input layer that represent timing, temperature, radiation, and airflow rate. The power output of the ETSAH device shows a strong correlation with the flow rate, reaching its peak at 0.05 kg/s with a value of 2261 W and dropping to 368 W at 0.006 kg/s. Correspondingly, the greatest energy efficiency was measured at airflow rates of 0.05, 0.01, and 0.006 kg/s, accounting for 48.38%, 27.32%, and 19.65%, respectively.

Temperature Distribution in a Two-Scale Porous Structure of a Catalyst Made of Spherical Particles

The research deals with the determination of the temperature distribution in a two-stage porous catalytic medium when the heat flow passes through. The peculiarity of the proposed model of heat and mass transfer in a porous catalyst is to consider the change in the volume of the spherical particle that makes up the catalyst.A program for calculating the temperature distribution in a two-scale porous structure of a catalyst made of spherical particles that change in volume with time has been developed. It should be noted that the temperature gradient is rather high, and the temperature in the central region of the particle becomes high enough for the process of catalytic reaction initiation only after 3.25 s. The developed program together with analytical and empirical studies allow to find the range of temperature and time of heat treatment at which the given thermophysical characteristics of porous material will be observed.The work will be useful for engineers and scientists studying the problems of thermochemical reactors and heat transfer in catalytic fills.

Developing computational and experimental models of heat transfer through multi-layered textile structures

Object signature management is a critical and urgent task that helps conceal and restrict the detection of contemporary optoelectronic systems. The design of thermal camouflage textiles and material solutions constitute a significant scientific area, however publications in this area are restricted because of military competitiveness and technological secrecy. Research on thermal camouflage materials has drawn interest both domestically and internationally for a variety of purposes, especially in military applications. Multi-layered Textile Structures (MTS) is a material with several advantages, such as its simple structure, capacity to combine many different materials with many different qualities, and great applicability. The article includes a model of computation and simulation of heat transfer through multi-layer textiles, as well as tests to assess the heat shielding effect and heat radiation energy of some samples of multi-layer textiles made of domestic materials. The initial computational and experimental results constitute an important foundation for further research and application of multi-layered textile structures.

Numerical Study on Composite Multilayer Insulation Material for Liquid Hydrogen Storage

This study investigated the heat transfer characteristics of composite multilayer insulation (MLI) materials used for the storage and transport of liquid hydrogen at cryogenic temperatures. This research focused on analyzing the effects of thermal boundary temperature, total layer count, and vacuum level on the heat flux through the insulation material. Based on the layer-by-layer model, a heat transfer model of composite MLI was constructed. This research introduces a novel method for analyzing the heat transfer properties of composite MLI in the liquid hydrogen temperature range. Results indicate that heat flux increases with higher thermal boundary temperatures, with the MLI layers near the cold boundary playing a critical role in overall insulation performance. Additionally, numerical analysis was conducted to examine the impact of different material combinations and variations in vacuum level on heat transfer characteristics. Findings reveal that adding spray-on foam insulation reduces heat flux by 20.76% compared to using MLI alone. Furthermore, increasing the total number of MLI layers effectively mitigates heat flux increase, achieving an optimal heat flux of 0.5377 W/m2 with a total of 50 layers.

Influence of heat pipe layout parameters on the cooling effect of spontaneous combustion coal gangue dumps

Existing research has found that the number, insertion depth and angle, filling rate, and working fluid of heat pipe (HP) can affect the distribution of temperature field inside coal gangue dumps. However, there is relatively little research on the optimal arrangement of heat pipes (HPs) in coal gangue dumps. In response to the above issues, based on the theoretical model of HP heat transfer, the influence of HPs layout on the temperature field of coal gangue dumps is analyzed through a combination of numerical simulation and experiments, and the optimal layout of HPs is obtained. The results show that the presence of HPs can change the heat conduction path in a coal gangue dump and help the coal gangue dumps to dissipate heat in time. As the insertion spacing of the HPs decreases and the insertion depth of the HPs increases, the area of the spontaneous combustion danger zone (SCDZ) decreases, the maximum temperature value (Tmax) decreases, and the better the cooling effect. The influence of the insertion spacing of HPs on the spontaneous combustion volume of coal gangue dumps is greater than the influence of the insertion depth of HPs. When the insertion spacing of HPs is 3 m and the insertion depth of HPs is 7 m, the spontaneous combustion volume and the highest temperature point respectively decrease by 11755m3 and 302.57 ℃, and the cooling effect of coal gangue dumps is the best. Consequently, this study provides a reference for the design and optimization of coal gangue fire fighting engineering with HP application in the future.

Single bischofite precursor droplet evaporation: Modeling and simulation covering the effects of decomposition reactions and environmental variables

Spray pyrolysis is an excellent method to realize high value utilizing industrial waste bischofite. Interacting droplet evaporation characteristics under the combined influence of ambient pressure, temperature, and decomposition reactions are a prerequisite for constructing spray pyrolysis devices. Therefore, this work established a comprehensive heat and mass transfer model during the multi-component droplet evaporation incorporating decomposition reaction. It also delved into the interplay between temperature and pressure, elucidating their combined influence on the decomposition process during evaporation. The results suggest that raising either temperature or pressure alone can speed up the decomposition process; raising both will more successfully increase the rate of decomposition conversion. In addition, a set of non-dimensionless parameters, mth/ml (mass transfer contribution rate) and Qth/Qd (heat transfer contribution rate), are proposed to characterize the contribution of the decomposition reaction to the evaporation process. Under the actual spray pyrolysis conditions, the mass transfer contribution rate, mth/ml, which is varied in a range of 2 %–70 %, indicating the important role of decomposition reaction during the mass transfer process. The maximum value of the heat transfer contribution rate Qth/Qd is less than 10 %, indicating the dominant role of evaporation in the heat transfer process. Based on the analysis, a theoretical direction for modeling may be provided.

Improving heat transfer in an air-cooled engine by redesigning the fins

Heat transfer modelling and simulation were carried out in a single-cylinder, four-stroke, air-cooled engine to evaluate the heat transfer rate of the engine block. The modelling studies of cylinders with different numbers of fins and different geometry were performed using the SolidWorks computer platform. The tested components were made of 6063-T6 aluminium alloy castings. The simulation concerned different numbers of fins as well as changing the geometry of fins with circular and rectangular perforations. The results of the studies showed the possibility of improving the power to mass ratio for cylinder efficiency and heat transfer rate. It was shown that a large number of fins leads to an increased heat transfer rate, but it affects the overall engine efficiency due to the increase in the total engine mass. Circular perforation is a better design solution than rectangular perforated fins with the same cross-section. Circular perforation provides a lower engine cylinder mass and gives more than 4 % better heat transfer rate. The perforation size was tested using circular perforations with a diameter of 7.14 mm, 8.5 mm and 10 mm. With a 7.14 mm diameter perforation the heat transfer rate increases slightly compared to the other tested ones, while a 10 mm diameter perforation provides the best mass reduction.

Analytical generalized thermal resistance model for conductive heat transfer in pebble beds based on heat flux weighted temperature difference

A novel model for inter-particle contact thermal resistance based on analytical solutions is proposed. By applying the concept of heat flux weighted temperature difference in thermal resistance modeling for the first time, this model offers greater physical significance than traditional thermal resistance models. It effectively describes the dissipation in the heat transfer process and the influence of particle radius on thermal resistance, making it a generalized thermal resistance model suitable for multi-dimensional systems. The impact of applying different levels of uniform heat flux boundary conditions on thermal resistance is analyzed from the perspective of energy dissipation, revealing that a more uniform heat flux input results in lower thermal resistance. The effects of contact radius and particle size on the dimensionless generalized thermal resistance of inter-particle contact were studied, showing that the dimensionless resistance increases with larger particle contact radius and smaller particle size. Using the thermal discrete element method, the thermal resistance model with uniform heat flux density boundary conditions was applied to calculate the effective thermal conductivity of the pebble bed. Considering the distribution of contact radius, differences in effective thermal conductivity at various heights of the pebble bed due to different contact radii were examined and compared with the traditional fixed-coefficient contact resistance model. It was found that the difference between the two models decreases as the contact radius decreases. Finally, multiple sets of fixed contact radii were established under three different particle sizes, revealing that as the contact radius increases, the deviation between the new generalized resistance model and the traditional fixed-coefficient model rises from 8.18 % to 14.64 % for different particle radii.

Qualitative Analysis of the Heat Transfer in a Package of Square Steel Sections

During the heat treatment of square or rectangular steel sections, a heated charge, arranged in regular packages, is placed inside a furnace. This type of charge forms a porous medium through which a complex heat flow occurs during heating. Several heat transfer mechanisms act simultaneously within this medium: conduction through the section walls, conduction and natural convection within the gas, thermal radiation between the section walls, and complex heat transfer (mainly contact conduction) at the joints between the adjacent sections. This article presents a qualitative analysis of heat transfer, aiming to determine the contribution of individual heat transfer mechanisms to the overall process. For this purpose, an analytical model of complex heat transfer within the package was employed, based on the thermo-electric analogy. The results from experimental studies were used to calculate the natural convection and heat transfer at the joints. It was assumed that the material of the sections was low-carbon steel, and the gas was air. Calculations were performed for the temperature range of 25 °C to 700 °C, considering three different geometrical configurations of the sections. It was shown that the effective thermal conductivity (ETC) of the package for the considered geometrical cases varies between 2.2 and 10.6 W/(m·K), which is an order of magnitude lower than the thermal conductivity of the individual sections. This parameter increased dynamically with the temperature. Moreover, the heat transfer intensity within the package of sections was nearly an order of magnitude lower than the heat conduction observed in a solid steel charge. Additionally, it was shown that the primary heat transfer mechanisms governing the heating process were thermal conduction (in the lower temperature range—up to approximately 350 °C) and thermal radiation (in the higher temperature range—above 350 °C). The gas convection inside the sections had a minimal impact on the heating process of the package. The primary parameters influencing the quality of the results were the joint resistance between the adjacent sections and the emissivity of the sections. The presented model can be used for the optimization of heat treatment processes for the considered charge.

Construction of a numerical model for cigarette smoking and combustion and simulation of combustion cone shape

Abstract Understanding the thermal conditions inside a burning cigarette is a top priority for controlling chemical emissions and cigarette design. Since experimental methods are difficult to observe in depth, this paper starts from the perspective of numerical simulation and models the structure of the tobacco distribution of the cigarette, integrating the end surface ignition model, puffing model, chemical reaction model, heat and mass transfer and diffusion model have established a three-dimensional comprehensive model that can represent the changes in combustion cone morphology during cigarette combustion. The model covers chemical reaction and mass transfer as well as generation, flow and reaction mechanism. The simulation results show that the model can better predict the temperature distribution, component distribution and combustion cone morphology changes during cigarette smoking and combustion. It provides an effective means for in-depth research on cigarette combustion.

Estimating the effective char depth in structural timber elements exposed to natural fires, considering the heating and cooling phase

This research study investigates the effect of different heating and cooling regimes on the effective cross-section of timber elements exposed to natural fires. An advanced calculation method based on a 1D finite-difference heat transfer model and effective thermo-physical properties is adopted to analyse the heat penetration and the consequent reduction in mechanical properties. In particular, the research focuses on the evolution and penetration speed of the char depth (300 °C isotherm) and zero-strength layer (determined through in-depth temperatures and reduced mechanical properties). Results reveal how the char depth mainly develops during the heating phase, with non-negligible contributions from the cooling phase. In contrast, the zero-strength layer increases throughout the whole fire exposure, particularly during cooling and, possibly, after the end of the cooling phase. In general, the heating phase contributes about 2/3 to the total effective char depth, while the cooling phase about 1/3. The most challenging conditions were found for the fires of the longest durations (heating and overall), corresponding to low ventilation and high fuel load density conditions. The study emphasises the necessity of incorporating the cooling phase in performance-based methodologies for fire-safe timber structures to avoid under-estimating heat penetration effects.

Analytical Model for Heat Transfer Around Energy Piles in Layered Soil With Interfacial Thermal Resistance by Integral Transform Method

ABSTRACTEnergy piles are commonly deployed in vertically layered geological conditions due to the geological structure and pile foundation backfill. The imperfect contact between adjacent soil layers results in resistance to heat transfer at the interface, known as the interfacial thermal resistance effect. In this paper, the energy pile was simplified as a finite‐length solid cylindrical heat source, and an analytical model was established for layered heat transfer of energy piles considering the interfacial thermal resistance effect. The Laplace‐domain solutions to the temperatures in the layered ground were derived by using the finite Hankel and Laplace transforms. The Crump method was subsequently employed to numerically invert Laplace‐domain solutions to the time‐domain solutions. The proposed model was validated by comparing with an analytical solution of a homogeneous model and COMSOL numerical solution. These solutions were used to analyze the temperature response around energy piles considering interfacial thermal resistance. Finally, a parametric study was performed to explore the effects of interfacial thermal resistance and other thermal properties of the soil layer on the layered heat transfer of energy piles.

Enhanced Efficiency of Latent Heat Energy Storage by Inclination

Latent heat storage (LHS) has emerged as a promising solution for addressing the challenges of large-scale and long-term energy storage, offering a clean and reusable system. Being in the developmental stage, and with only limited theoretical predictions being available, there is a need to enhance the efficiency of LHS systems. In this study, we use numerical simulations to study the melting process of a phase-change material (PCM) in a rectangular domain. A significant enhancement in the melt rate of the PCM is found by a simple inclination of the domain, with a 60% increase in melt rate compared to a standard square unit without inclination through enhanced heat transfer. We establish a theoretical relation for the optimal PCM melt rate, based on the inclination angle and the domain aspect ratio, outlining the optimal conditions for the PCM melt rate, which is solely dependent on the domain geometry. We further propose a heat-transfer model that predicts the optimal aspect ratio for achieving the maximum melt rate as a function of the Rayleigh and Prandtl numbers. Published by the American Physical Society 2024

Heat transfer characteristics of petroleum coke particle packed bed: An experimental and CFD simulation study

AbstractDue to the complexity of the internal pore structure of petroleum coke loose particle‐packed beds, measuring their thermal conductivity has always been a challenging problem. This work independently developed an experimental apparatus for testing the thermal conductivity of petroleum coke particle‐packed beds and constructed a forward calculation model for the heat transfer process, which was based on one‐dimensional unsteady heat transfer. Using the Sparse Nonlinear OPTimizer (SNOPT) algorithm, a mathematical relationship between the thermal conductivity λ of the coke bed, temperature T, and equivalent particle diameter dp was established through inverse modeling. Concurrently, a digital model of the petroleum coke particle packed bed was derived utilizing three‐dimensional computed tomography (CT) scanning technology, and a pore‐scale gas–solid radiation heat transfer model was formulated based on CFD simulation technology, thereby further elucidating the heat transfer mechanism within the petroleum coke particle packed bed. The research results indicate that the temperature predicted by the established thermal conductivity model aligns well with experimental data. Further CFD simulation studies demonstrate that a smaller particle size leads to a larger temperature difference between the wall and the center of the packed bed, while a higher gas velocity results in a smaller temperature difference, with a linear correlation observed between these two factors. At high temperatures, thermal radiation between particles in the porous petroleum coke‐packed bed plays a dominant role. The research outcomes can offer significant theoretical support for a profound analysis of the heat transfer behavior of petroleum coke‐packed beds within a vertical shaft calciner.

Crystallization modeling of two semi-crystalline polyamides during material extrusion additive manufacturing

In this work, a heat transfer model is developed for thermally-driven material extrusion additive manufacturing of semicrystalline polymers that considers the heat generated during crystallization by coupling crystallization kinetics with heat transfer. The materials used in this work are Technomelt PA 6910, a semicrystalline hot melt adhesive with sub-ambient glass transition temperature (Tg) and slow crystallization, and PA 6/66, a traditional semicrystalline polyamide with a higher Tg and fast crystallization. The coupled model shows that the released heat during crystallization depends on material selection, with Technomelt PA 6910 and PA 6/66’s temperatures increased by less than 1 °C and up to 6.3 °C, respectively, due to enthalpy of crystallization. Increasing the layer time decreases the layer temperature as well as the initial crystallinity. However, its effect on final crystallinity in Technomelt PA 6910 is negligible due to continued crystallization of the material after printing. Experimental validation shows good agreement for Technomelt PA 6910, but consistently underpredicts PA 6/66 crystallinity. Increasing modeled environmental temperature leads to better agreement with experimental results for PA 6/66, suggesting that higher temperatures may have been experienced. Shear-induced crystallization may also be contributing to crystallinity in this material. The results from this model highlight the importance of and interrelationships between material and processing parameter selection and can aid in achieving quality prints from semicrystalline thermoplastics.

DEM analysis of heat generation and transfer during granular flow in a rotating drum

In many granular material handling processes, heat generation, and subsequent temperature rise, due to contacts between particles and surfaces is common. Aiming to explore this phenomenon, friction-induced heat generation and heat transfer models are developed and implemented into a Discrete Element Method (DEM) in this paper. The DEM models are validated qualitatively for the temperature distribution pattern and quantitatively for the evolution of particle temperature rise using data obtained experimentally. Moreover, the temperature distribution of the drum end plates obtained in the simulations shows the same annulus pattern observed in experiments. It is also found that increasing the rotation speed of the drum leads to an increase in the annular heated region of drum and in the net heat that particles obtain. In addition, a higher rotation speed leads to higher absolute fluctuations and lower relative variability of particle temperature.

Modelling of heat and mass transfer in a two-phase closed thermosyphon

Modelling of heat and mass transfer in a two-phase closed thermosyphon

Modeling and analysis of fluid-solid coupling heat transfer and fluid flow in transonic nozzle

Solid rocket motors (SRMs) are the power units of modern aerospace transportation, and it is of great significance to predict their flow and heat transfer characteristics by numerical simulation. This numerical study is based on a self-developed code framework MHT (Multi-X Heat Transfer, where X represents the region, scale, physical field, and other aspects) and presents an effective method of analyzing fluid–solid coupling heat transfer problem in an axisymmetric supersonic nozzle. For the nozzle wall heat conduction and nozzle-in fluid flow there are two kinds of solution methods, the detached (solved separately in solid and fluid region and them coupling at the interface) and the whole field method (solve the conduction and convection simultaneously). The whole field method is more efficient but few scholars use it to solve the nozzle coupled problem. This paper introduces the numerical details of the whole field solution method, and provides a new idea for the coupling solution of the nozzle. In addition, a mixed grid system is proposed around the interface region of fluid and solid, in which the quadrilateral structured mesh is used at the fluid side, and the triangular unstructured mesh is used for the outer fluid region and the whole solid region to ensure the accuracy of the 1st-oder normal derivatives calculation. The self-developed code is validated by comparison with well-known commercial soft-ware. Transient results of temperature and velocity are presented for the instants of 1st 20 and 40 s of a practical nozzle.