Heating Process Research Articles

Coupled field modelling of thermomechanical response in materials using peridynamic heat transport model and non-ordinary state-based peridynamics

Predicting the mechanical response of materials subjected to transient heat processes is crucial in various engineering applications. This paper introduces a novel peridynamic (PD) coupled field model formulated within the framework of Non-Ordinary State-Based Peridynamics (NOSBPD). This model offers the capability to simulate the coupled thermo-mechanical behavior of materials by incorporating both thermal transport and mechanical deformation analyses. To verify the model’s accuracy, a benchmark problem involving a steel plate undergoing transient thermal expansion is investigated. This model presents a valuable tool for various engineering applications involving coupled thermo-mechanical processes.

Assessing the Performance of a Proton Exchange Membrane Green Hydrogen Generation System through Stack and Balance of Plant Modeling

The integration of Proton Exchange Membrane electrolyzers into hydrogen generation systems offers significant potential for sustainable energy solutions. Integrating hydrogen production with electricity, heat, and renewable energy sources enhances sustainability. PEM electrolyzers effectively address renewable energy intermittent by converting energy into hydrogen, leveraging their ramp rate and load-following capabilities. However, widespread commercialization hinges on cost reductions through new material development and a comprehensive understanding of the system's heat, mass, and electrochemical processes. This study presents a zero-dimension model developed using the Aspen Custom Modeler, detailing the electrochemical phenomena. A holistic PEM electrolysis model, including the stack and the Balance of Plant, is developed in Aspen Plus, demonstrating an overall system efficiency of 50%, with the BoP accounting for 8% of total electricity consumption. This research underscores the critical role of optimizing BoP subsystems and integrating grid-based backup solutions to enhance the economic viability and resilience of PEM electrolysis systems.

Assessing the Performance of a Proton Exchange Membrane Green Hydrogen Generation System through Stack and Balance of Plant Modeling

The integration of Proton Exchange Membrane electrolyzers into hydrogen generation systems offers significant potential for sustainable energy solutions. Integrating hydrogen production with electricity, heat, and renewable energy sources enhances sustainability. PEM electrolyzers effectively address renewable energy intermittent by converting energy into hydrogen, leveraging their ramp rate and load-following capabilities. However, widespread commercialization hinges on cost reductions through new material development and a comprehensive understanding of the system's heat, mass, and electrochemical processes. This study presents a zero-dimension model developed using the Aspen Custom Modeler, detailing the electrochemical phenomena. A holistic PEM electrolysis model, including the stack and the Balance of Plant, is developed in Aspen Plus, demonstrating an overall system efficiency of 50%, with the BoP accounting for 8% of total electricity consumption. This research underscores the critical role of optimizing BoP subsystems and integrating grid-based backup solutions to enhance the economic viability and resilience of PEM electrolysis systems.

Studying the influence of coolant speed on the processes of heat and mass transfer in technological equipment for processing disperse materials

Studying the influence of coolant speed on the processes of heat and mass transfer in technological equipment for processing disperse materials

Non-steady flow decomposition behaviors of heat and mass transfer on intrinsic kinetics for methane hydrate particles transported in pipelines

The differential equations governing the decomposition rate and activation energy, convective mass transfer, methane diffusion and fugacity, as well as heat conduction and enthalpy change were derived by integrating thermal convection, heat conduction, mass transfer and intrinsic kinetics. Mathematical models for decomposition kinetics and thermodynamics in a non-steady field were solved using a radial logarithmic grid for node division and discretization of the equations. The study elucidated the heat and mass transfer processes as well as decomposition kinetics in pipelines by analyzing the impacts of particle size, temperature, pressure, flow rate and activation energy on decomposition rate. The results indicated that compared with the isothermal decomposition of the intrinsic kinetic model and static experimental decomposition, the complex non-steady multiphase flow model offers a more accurately simulation of hydrate decomposition as well as associated heat and mass transfer processes. Hydrate decomposition is characterized as a non-isothermal dynamic ablation process with heat transfer rate and intrinsic kinetics dominating during the preliminary stage and the stable stage, respectively. An increasing in the slurry temperature, temperature fluctuation and flow rate accelerated the heat transfer rate capacity, enhanced convective heat transfer capacity and facilitated hydrate decomposition, with the mass transfer rate exhibiting lesser influence. The particle surface area and slurry temperature exhibited the most significant influence on hydrate decomposition, which was followed by flow rate. Upon increasing particle size from 1 mm to 5 mm and the temperature from 293 K to 313 K, the decomposition rate increased by 20.7 times and 13.5 times, respectively. Furthermore, enhancing temperature and flow rate while decreasing particle size and pressure decreased both the decomposition time and the duration required for the decomposition rate to reach its peak. Additionally, the decomposition rate and its constant vary with the activation energy.

Model of the non-stationary thermal processes in the ground heat pump system

One of the main directions for improving heat supply systems is the tendency to switch to low-temperature heating systems by using heat pump units is the tendency of implementation the low-temperature heating systems based on the use of heat pump units. In the work, the main attention is focused on the improvement of thermal parameters and circuit design features of elements of the heat pump system of heat supply using soil energy. For this purpose, the toolkit of mathematical modelling of processes in ground heat pumps is applied, taking into account the climatic conditions of Ukraine. The paper proves the technical possibility of creating an autonomous system of alternative heat supply for energy-saving technologies with the possibility of using ground energy, taking into account environmental requirements. It is substantiated that the use of the proposed systems is a promising direction for Ukraine, which is experiencing a shortage of its own energy resources, because it provides an opportunity to increase the share of organic fuel substitution and reduce the volume of heat emissions into the environment. A mathematical model of heat processes in the elements of the heat exchange equipment of the heat pump system based on renewable energy (soil energy) and secondary energy (wastewater) was developed, taking into account environmental requirements (preventing hypothermia of the soil during the operation of soil pipes and damage to vegetation, respectively), which allows choosing a rational mode of operation of the system under seasonal climatic changes and technological conditions. Numerical modelling of heat processes in elements of the heat exchange equipment of the heat pump system using groundwater and waste water was performed, and the energy and environmental efficiency of the system under variable climatic and technological factors was determined. Analysis and generalization of the calculation results of the heat pump heat supply systems using alternative energy based on the proposed mathematical model, taking into account environmental requirements (preventing thermal relaxation of the soil) allows to take into account the change in the temperature gradient around the soil heat exchanger and more accurately determine the heat flow from each section of the heat exchanger. It has been established that for heat pumps with soil heat exchangers, the maximum substitution ratio of the traditional fuel is 75 %, and the economically feasible quantity of soil heat exchangers is 9 units. Heat pumps using waste water can completely replace traditional heat supply systems. For individual consumers, it is possible to recommend heat pump units with soil heat exchangers, at the same time, it is necessary to provide a backup source of energy to increase the reliability of heat supply.

Alpha-case promotes fatigue cracks initiation from the surface in heat treated Ti-6Al-4V fabricated by Laser Powder Bed Fusion

This research investigates the effect of the formation of an oxygen-stabilised titanium alpha layer – called alpha-case at the surface – on the fatigue properties of Ti-6Al-4V (Ti64) alloy components produced by Laser Powder Bed Fusion (L-PBF). Three post processing heat treatments with different controlled atmospheres were carried out on samples with as-built surfaces to evaluate how differences in alpha-case layer thickness and hardness affect the material’s susceptibility to surface embrittlement and its overall fatigue performance. The investigation includes bulk and subsurface microstructural analysis, surface characterisation by X-ray computed tomography (XCT), and fatigue testing. Key findings show that alpha-case layers can reduce the fatigue resistance of L-PBF fabricated Ti64. The presence of a 70±3 µm thick alpha-case layer was found to promote crack initiation. This is emphasised by a higher density of initiated cracks, thus leading to a reduction in fatigue life. Conversely, thinner alpha-case layers were found to have a reduced impact on the fatigue performance, highlighting the critical role of post processing heat treatments in modulating the fatigue resistance of the material. The use of XCT to characterise the surfaces of the specimens in 3D confirms that fatigue cracks primarily initiate at surface notches, highlighting the predominance of as-built surfaces over microstructure in determining the fatigue resistance of L-PBF Ti64 components.

How does heat generation affect the cut and chip wear of rubber?

AbstractTire wear is a fracture process that has a decisive impact on tire life and on the environment. When a tire rolls, a heating process occurs due to friction caused by the viscoelastic rubber sliding over uneven road. This process occurs globally in the contact patch area and locally around the asperity tips, heating the tread and transferring heat to the surrounding material. On roads with a good quality pavement, the stress, and therefore the heat, is evenly distributed throughout the rubber material of the tire, which has a direct effect on fatigue wear. In contrast, unevenly distributed stress, and therefore heat, is generated in the tread when the tire rolls and slides over sharp asperities in rough terrain. This leads to very pronounced, unstable fracture processes that cause unevenly distributed wear, known as cut and chip (CC). The extent of heat generation or temperature evolution and its effect on CC wear have not yet been investigated and described in scientific publications. Therefore, this study firstly presents the detailed characterization of the influence of temperature development on the CC wear of a styrene–butadiene rubber, which commonly is used in treads of consumer tires. The investigations were carried out using the unique instrumented cut and chip technique in combination with a high-speed thermography.

COMSOL-Based Simulation of Microwave Heating of Al2O3/SiC Composites with Parameter Variations

The process of microwave heating involves the coupling of multiple physical phenomena, specifically including the distribution of the electromagnetic field in the resonant cavity. The electromagnetic effect generates heat and encourages the transfer of heat inside the material. In this numerical study, a 3D computer model of microwave heating of Al2O3/SiC composites using a multimode microwave heating chamber was established based on the simulation software COMSOL Multiphysics 5.6, and the symmetry treatment of the model was carried out, which effectively reduced the amount of model calculations and accurately analyzed the microwave heating characteristics of the samples. The analysis of the microwave heating characteristics of the sample was mainly preformed from the perspective of the electric field distribution in the resonant cavity, the sample heating rate and the sample heating uniformity, and then it was determined how the microwave source power and sample mold selection affect the temperature and electric field parameters of the sample. After experimental verification, the error between the simulation results and the temperature parameters obtained from the actual experiments is less than 2%. This study contributes to further understanding the heating behavior of Al2O3/SiC composites in complex multimode microwave heating environments and can be used to control the dynamic parameters during microwave heating in order to improve the heating rate and heating uniformity of samples.

Thermal Energy Resource Potentials of the Kara-Bogaz-Gol Gulf as a “Solar Pond”

Introduction. The use of environmentally-friendly engineering systems including solar energy technologies makes it possible to reduce energy costs and therefore to lower production costs and anthropogenic stress on the environment.Aim of the Study. The authors used innovative techniques to assess the thermal resource potential of solar radiation, to analyze the salt deposits of the Kara-Bogaz-Gol Gulf as thermal accumulators for the development, introduction and use of solar thermal technologies and to justify the technical and economic feasibility of their use in engineering systems in the Kara-Bogaz-Gol Gulf (Caspian region).Meterials and Methods. The study design is based on systematic theoretical calculations of the gross, technical, economic and ecological potentials of solar radiation taking into account environmental conditions. For calculating there were used the methods of mathematical modeling of heat and mass transfer processes in active solar energy systems when converting solar energy into thermal energy in the salty reservoir of the Kara-Bogaz-Gol Gulf as a “solar pond”.Results. There have been assessed the solar energy characteristics for the introduction of various engineering storage systems and technologies. There have been determined the results of energy storage on the reservoir salt surface during the day: in winter – 1 009.0 W/m2 per day, in summer – 1 574.7 W/m2 per day. It has been proven that the potential of solar energy conversion into thermal energy varies from 40 to 70% depending on the season. Aaccording to theoretical calculations, the solar pond efficiency in winter is 11.4% and in summer – 14.6%. In summer, there was measured the average temperature on the salt surface of the reservoir bottom, it ranges from 55.04 to 79.8 ºC, in winter from 20.0 to 25.6 ºC.Discussion and Conclusion. The results obtained can be used for strengthening energy security, developing energy systems and producing autonomous thermal power devices based on solar energy that will reduce the energy consumption of fossil fuels and improve the environmental situation in the region. The materials of the article can be used in preparing design estimates and feasibility study for developing various solar energy systems and technologies in the Caspian region.

Study on the heating process, high temperature mechanical properties and fatigue properties of a low-carbon microalloyed steel

The dynamic continuous cooling transformation (CCT) experiments of a low-carbon microalloyed building structure steel were conducted on a Gleeble-3500 thermal simulation test machine, and the corresponding dynamic CCT curve was drawn. According to the dynamic CCT curves, different austenitization temperatures were designed to clarify the influence of austenitization temperature on the transformation and microstructure of the tested steel. The results showed that when the austenitization temperatures were set as 1050, 1150 and 1250 °C, respectively, the microstructure mainly consisted of ferrite and granular bainite. With the increase of austenitization temperature, the starting temperature of ferrite transformation gradually decreased, but the starting and ending temperatures of bainite transformation gradually increased, leading to the increase of the volume fraction of granular bainite. In addition, the tensile properties of the tested steel at different temperatures were determined. The tensile strength gradually decreased with the increase of the tensile temperature, and the highest tensile strength was 502 MPa for the room-temperature sample, while the elongation showed different trends. It was the largest elongation (57.8%) at the tensile temperature of 500 °C, while the smallest value of 19.2%–23.2% was obtained in the 200–300 °C tensile samples. Finally, the fatigue property of the experimental steel was detected by plotting the corresponding fatigue curves. The fatigue limit strength under 1 million cycles was about 376.2 MPa. Results provide a theoretical reference for the setting of heating process in the real industrial production and the application of the low-carbon microalloyed building structured steel.

Boosted gas separation performances of polyimide and thermally rearranged membranes by Fe-doping

Herein, p-ferrocenylaniline (CPFEA) is first synthesized from p-nitroaniline and ferrocene as raw materials. Then, a series of Fe-doped rearrangeable polyimide (PI) membranes are prepared by polymerizing 4,4′-(hexafluoroisopropylidene)dithiocarboxylic anhydride (6FDA) and 2,2′-bis(3-amino-4-hydroxyphenyl)hexafluoropropane (6FAP), with CPFEA as an end-capper, followed by thermal imidization and thermal rearrangement (TR) treatment. During the heating process, Fe2+ undergoes a valence state transition, ultimately leading to the coexistence of Fe2+ and Fe3+. The experimental results show that as the CPFEA content increases, the mechanical properties of the Fe-doped PI membranes gradually decrease, but the glass transition temperatures significantly increase due to the chelation of iron ions. In addition, owing to the synergistic effect of Fe2+/Fe3+ on thermal rearrangement reactions and intermolecular interactions, the gas permeabilities and selectivities of the TR composite membranes are greatly improved. Among them, the TR-1.0 %CPFEA sample exhibits the gas permeabilities of 2727, 2442, 407, 107, and 118 Barrer for CO2, H2, O2, N2, and CH4, and the separation performance of CO2/N2 is close to the 2008 Robeson upper limit, the CO2/CH4 exceeds the 2008 Robeson upper limit. When the thermal treatment temperature reaches 500 °C, the gas permeabilities to CO2, H2, O2, N2, and CH4 are respectively boosted to 30591, 13146, 5958, 1714, and 1882 Barrer, and the CO2/CH4 separation performance exceeds the 2019 upper limit. Therefore, this work proposes a feasible method to boost the gas separation performance by end-capping PI backbones with CPFEA, and the Fe-doped TR composite membranes are expected to play a certain role in the environmental and industrial fields.

Stretchable Composite Films Are Prepared by Using Cellulose Pulp with Differential Substitution of Carboxymethyl Cellulose and Thymol with an Infrared Heating Process for Packaging Application.

Herein, cellulose pulp (CP), carboxymethyl cellulose (CMC), and thymol-based eco-friendly, transparent, and flexible composite films are prepared. These materials dissolved well in an environment-friendly process in N-methyl morpholine N-oxide (NMMO) ionic liquids using infrared heating. Fourier-transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), and scanning electron microscopy (SEM) analyses are used to study the structure, microstructure, and morphology of the composite films. The thermal properties of the CP/CMC/thymol composites are thoroughly studied by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The thermal stability of the composites (T 5%-57.8-91.2 °C and T 10%-216.6-284.1 °C) significantly improves following the CMC addition. In each case, all the composite film exhibits unique T g (140.5-143.1 °C) values, as confirmed by DSC. The tensile strength of the cellulose pulp is 66.5 MPa, increasing to 78.4 MPa for the CP/CMC-1:0.5 composites and steadily increasing to 93.8 MPa with increasing CMC content. Similarly, CMC increases the EB of cellulose pulp from 9.3 to 7.4%. The water vapor permeability and swelling ratio values of the CP/CMC/thymol composites are in the range of 1.9-2.11 × 10-9 g/(m2·Pa·s) and 52.5-50.8° respectively. The CP, CMC, and thymol-based composite do not exhibit cytotoxicity to the aneuploid immortal keratinocyte cell line and demonstrate excellent antioxidant properties, for promising packaging and biomedical applications.

Thermal Maturity Map Based on Vitrinite Reflectance of Yamama Formation in Basrah Oil Fields, South of Iraq

This study aims to create a detailed thermal maturity map based on vitrinite reflectance in the Basrah oil fields in southern Iraq. The specific objective was to determine areas with the highest thermal maturity within the Yamama Formation. The selected fields for analysis were WQ-60, Lu-12, Zb-42, Nr-12, Mj-12, and Ru-72, which belong to the West Qurna, Luhas, Zubair, Nahr Umar, Majnoon, and Rumaila oilfields, respectively. The Petromod 1D software was used for basin modeling and thermal history reconstruction. By inputting geological and geophysical data, the software enabled the construction of a comprehensive thermal basin history. The primary focus was on evaluating vitrinite reflectance values, which serve as a proxy for thermal maturity. The results of the study revealed significant variations in thermal maturity within the Yamama Formation across the selected fields. The Nahr Umar field (Nr-12) exhibited the highest thermal maturity, characterized by elevated vitrinite reflectance values. This indicates that organic matter within the Yamama Formation has undergone significant heating and maturation processes in this particular field. On the other hand, the Zubair field (Zb-12) displayed the lowest vitrinite reflectance values, suggesting a lower level of thermal maturity. This could be attributed to different burial histories, variations in the thermal gradient, or other tectonic movements in the area.

Convective diffusive thermal flow over an inclined surface with viscous dissipation and aligned magnetic field applications

This investigation incorporating the fluctuation in heat and mass transfer associated to the mixed convection magnetized flow of viscous fluid due to inclined surface with porous media. The contribution of Soret effects and viscous dissipation appliances is addressed. Furthermore, the heat transfer improvement is also assessed by thermal radiation, heat source and joule heating effects. The chemical reaction enrollment is also studied for concentration phenomenon. The convection of problem into non-dimensional framework is based on implication of new variables. The perturbation technique is followed to tracking the analytical outcomes. Physical visualization and interpretation of results under the influence of perturbed parameters have been studied. It is observed that heat and mass transfer enhances due to Soret number. Presence of chemical reaction leads to decrement of concentration profile. Claimed results presents applications in heat and mass transfer processes, chemical reaction, manufacturing systems, chemical engineering, extrusion processes etc.

Humic substances and inorganic ions synergistically precipitate at the gas–liquid interface in a simulation experiment of direct-contact heat and mass transfer processes

Direct-contact heat and mass transfer processes are widely employed in saline wastewater treatment. However, these processes are accompanied by serious ultrafine particle emission, a phenomenon associated with the solute’s transition across the gas–liquid interface. A thorough comprehension of the solute’s behavior at this gas–liquid interface is vital for clarifying the crossing process and guiding particle control strategies. Here, solutions containing saturated inorganic ions and humic substances were evaporated to analyze their behaviors at the gas–liquid interface in an experimental simulation of direct-contact heat and mass transfer processes. It was found that these substances co-precipitated at this interface. Humic substances can bind with inorganic ions via chemical bonds, monovalent ions through cation-π interactions, and divalent ions through electrostatic and chelation interactions. Moreover, humic substances can act as nucleation sites for precipitating inorganic crystals. These distinctive binding mechanisms caused a synergistic relationship between humic substances and inorganic ions during precipitation. Amidst precipitation, humic substances with high humification degrees and large molecular weights were predominantly enriched. Inorganic ions, comprising over 93% of the total precipitate mass, constituted the principal constituents. Among these, Na+, with an enrichment factor of 2.10, precipitated more readily at the gas–liquid interface compared to divalent ions. These conclusions concerning the binding mechanisms of humic substances and inorganic ions, along with their precipitation characteristics, were validated in the submerged combustion evaporation process of membrane-concentrated leachate.

Synthesis, crystal structure, and thermal properties of energetic complex Cu(II) and Ag(I) based on 3-amino-4-(4,5-diamino-1,2,4-triazole-3yl)-furazan

High nitrogen compounds have received much attention due to their great potential as high energy density materials, and the selection of high nitrogen heterocyclic rings as ligands for energetic coordination compounds (ECCs) play a leading role in regulating the energy properties of ECCs. Furazan is rarely used as a building block for the development of high-energy metal ligands. In this study, a new type of high nitrogen ligand 3-amino-4-(4,5-diamino-1,2,4-triazole-3yl)-furazan (ATF) was selected and four kinds of high energy coordination polymers [Cu(II)(ATF)2·4H2O](NO3)2·2H2O (1), [Cu(II)(ATF)2·4H2O](ClO4)2·2H2O (2), [Ag(I)(ATF)2]ClO4·H2O (3) and [Ag(I)(ATF)2NO3] (4) were prepared by water solvent volatilization method and characterized for the first time. The single crystal XRD confirmed that there were abundant hydrogen bond interactions in the four complexes, resulting in dense aggregation with densities of 1.680 ∼ 2.089 g·cm−3. Meanwhile, theoretical calculations show that the detonation velocities of the four ECCs, 7578 ∼ 8192 m·s−1. In terms of thermal stability, the decomposition temperatures of the four ECCs (Td: 253 ∼ 288 °C) showed higher thermal stability during the rapid heating process than the reported ECCs (Cu(PZCA)2(ClO4)2, [Ag+(daf)NO3−]n and CHHP). Both shock and friction sensitivities are greater than 20 J and 300 N. This new structural motif is a promising high-energy material. Moreover, they can promote the combustion decomposition of ammonium perchlorate (AP) well, and the promotion effect of 1 and 2 is better than that of 3 and 4. In the field of explosives and propellants, four ECCs can be attractive candidates.

Cold crystallization behavior of poly(lactic acid) induced by poly(ethylene glycol)-grafted graphene oxide: Crystallization kinetics and polymorphism

Cold crystallization between the glass transition and melt temperature is of particular significance for crystalline regulation due to the slow crystallization rate of poly(lactic acid) (PLA). Incorporation of nucleation agents can promote PLA crystallization by reducing the nucleation activation energy and offering nucleation sites. Herein, we investigated the cold crystallization behavior of PLA induced by poly(ethylene glycol)-grafted graphene oxide (PEGgGO) which was synthesized and identified as a powerful nucleation agent for melt crystallization. The obtained results showed that PEGgGO not only accelerated the cold crystallization kinetics of PLA, but also promoted the polymorphic transition kinetics during the heating process. The half crystallization time of PLA induced by PEGgGO was shortened by 51 % and the final crystallinity increased by 57 % compared to that induced by GO alone at the same loading of 0.5 wt%. In addition, relative to GO, PEGgGO enabled the α′-to-α phase transition kinetics of PLA by a reduced transition temperature range of 26 % due to its excellent nucleation ability even at cold crystallization. The flexible PEG chains on GO facilitated crystalline regulation of PLA owing to the improved chain mobility. This work provides a broader framework for fashioning semicrystalline PLA products with enhanced crystallinity and refined crystal structure towards prospective applications.

Influence of 1,1′-Azobis(cyclohexanezonitrile) on the thermo-oxidative aging performance of diolefin elastomers

Abstract Diolefin elastomers play an important role in production and life, but their unsaturated structure leads to extreme vulnerability to heat and oxygen attack, so research into the aging of diolefin elastomers has been a hot spot in the industry. To overcome this limitation, a strategy based on the thermal decomposition of 1,1′-Azobis(cyclohexanezonitrile) (Azo) is devised, which forms stabilized compounds with imine groups during the heat process and captures radical. The diolefin elastomer was combined with azo, and isoprene rubber (IR) is chosen as a model material. Azo was added to IR to prepare the composite material (IR-Azo), and the thermo-oxidative resistance of the composite was significantly improved. Such as, after being exposed to thermo-oxidative conditions for 24 h, IR-Azo showed a tensile strength of 14.96 MPa with a retention rate of 68.25% which exceeded that of many traditional antioxidants. This study provides new insights into the development of elastomers with excellent thermo-oxidative resistance.

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.