Numerical Heat Transfer Model Research Articles

A study of geothermal hydraulic fracture surface morphology and heat transfer characteristics

This study analyzed the morphological characteristics of heat-treated granite fracture surfaces subjected to cyclic hydraulic fracturing (CHF) and traditional hydraulic fracturing (THF). The differences in heat transfer characteristics between THF and CHF fracture surfaces were compared using a three-dimensional numerical heat transfer model. The heat transfer properties of CHF fracture surfaces were investigated under varying injection parameters, and corresponding mathematical models were constructed. It was found that the roughness of CHF fracture surfaces was greater than that of THF, and the heat transfer performance was superior. Specifically, the overall heat transfer coefficient (OHTC) for the C1-C3 fracture surfaces increased by 55.71, 63.40, and 75.91 W/m2/K, respectively, compared to the T1-T3 fracture surfaces. The average outlet temperature (Tout) of the CHF fracture surfaces increases with higher injection flow rates and decreases with higher injection temperatures. The OHTC and local heat transfer coefficient (LHTC) exhibit opposite trends. Specifically, injection flow rates have a quadratic polynomial relationship with the Tout and a logarithmic relationship with OHTC. Additionally, the Tout of the CHF fracture surface shows a linear positive correlation with injection temperature, while OHTC has a linear negative correlation.

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.

Characteristics of time series development and formation mechanism of icing interface strain under three-dimensional freezing conditions

In order to reveal the ice adhesion mechanism, this study proposes an ice/workpiece interface strain picking method and establishes a coupled numerical model of water phase change heat transfer and mechanics. The interfacial strain law of the workpiece surface with/without water during the water freezing process was investigated, and the time development characteristics of the water freezing interfacial strain were analysed. The results show that the water freezing interface strain goes through a rapid increase during the rapid cooling stage of water, a strain fluctuation stage under the mixed state of ice and water, and a stabilisation stage after the completion of the phase transformation. As the cooling temperature decreases, the strain generated by water in the subcooled state is gradually larger than the strain of the workpiece contracted at low temperature, the trend of water phase transformation and volume increase is more and more significant, and the maximum freezing interfacial strain on the surface of the workpiece increases gradually. The interfacial strains and deformations of different materials show similar trends, but there are differences in the frozen interfacial strains, which are related to the modulus of elasticity and coefficient of thermal expansion of the materials. The results of this study can help to understand the adhesion mechanism of ice on the material surface, and provide a reference for the engineering field in terms of anti-icing, de-icing and icing.

Analysis of the Heat Transfer Performance of a Buried Pipe in the Heating Season Based on Field Testing

Ground source heat pump (GSHP) systems have been widely used in the field of shallow geothermal heating and cooling because of their high thermal efficiency and environmental friendliness. A borehole heat exchanger (BHE) is the key part of a ground source heat pump system, and its performance and investment cost have a direct and significant impact on the performance and cost of the whole system. The ground temperature gradient, air temperature, seepage flow rate, and injection flow rate affect the heat exchange performance of BHEs, but most of the research on BHEs lacks field test verification. Therefore, this study relied on the results of a field thermal response test (TRT) based on a distributed optical fiber temperature sensor (DOFTS) and site hydrological, geological, and geothermal data to establish a corrected numerical model of buried pipe heat transfer and carry out the heat transfer performance analysis of a buried pipe in the heating season. The results showed that the ground temperature gradient of the test site was about 3.0 °C/100 m, and the temperature of the constant-temperature layer was about 9.17 °C. Increasing the air temperature could improve the heat transfer performance. The temperature of the surrounding rock and soil mass of the single pipe spread uniformly, and the closer it was to the buried pipe, the lower the temperature. When there is groundwater seepage, the seepage carries the cold energy generated by a buried pipe’s heat transfer through heat convection to form a plume zone, which can effectively alleviate the phenomenon of cold accumulation. With an increase in seepage velocity, the heat transfer of the buried pipe increases nonlinearly. The heat transfer performance can be improved by appropriately reducing the temperature and velocity of the injected fluid. Selecting a backfill material with higher thermal conductivity than the ground body can improve the heat transfer performance. These research results can provide support for the optimization of the heat transfer performance of a buried tube heat exchanger.

An energy-environment coupled simulation framework for multi-scale and multi-facet evaluation of data center

This paper focuses on analyzing the thermal environment and optimizing energy consumption in data centers, which has largely omitted from previous studies. The thermal environmental of data centers is simulated and analyzed by utilizing the established “server-rack-room” multi-scale heat transfer numerical model. Based on this, the coupling simulation model of thermal environment and energy consumption in data centers is proposed to explore the relationship between them, and the corresponding optimization strategy is put forward. The energy consumption simulated by energy-environment coupled model and non-coupled model can reach a discrepancy of over 30 %, which indicates that the thermal environment impacts the power consumption of the data center significantly. Besides, the effect of several operational parameters of air conditioning system on the thermal environment and energy consumption of data center is analyzed. Through the particle swarm optimization algorithm, the optimal system parameters, which meet the requirements of thermal environment and lead to the lowest energy consumption, are found for typical cities in different climatic regions. The recommended settings include the supply air temperature of about 24 ∼ 26 ℃, the air supply volume of 8 m3/s, and the temperature difference of about 3.5 ℃ between the supply air temperature and the supply chilled water temperature. Under the optimized parameter setting, the highest temperature of server decreases to below 71 ℃, and the energy saving rate is more than 6 %.

An approach for thermal performance assessment and optimization design of energy diaphragm walls (EDWs) with seasonal thermal load via numerical modeling

The energy diaphragm wall (EDW) is a promising emerging technology for shallow geothermal energy utilization of existing buildings. However, analyzing the heat transfer characteristics of EDWs is a prerequisite and essential guarantee for rational heat transfer design and optimization. Generally, a single field or model test cannot fully consider and analyze the potential factors affecting the heat transfer characteristics. Therefore, this work uses numerical analysis methods to establish a 3D heat transfer numerical model of EDW suitable for the climatic and geological conditions and heat transfer requirements in Chongqing areas, China. The influencing parameters are divided into design, operating, and environmental aspects. A comprehensive analysis method has been developed that considers a range of indicators related to the temperature difference between the inlet and outlet, heat transfer efficiency, total heat transfer, and average daily heat transfer. The developed method also evaluates the significance of parameter effects based on transient and integrated heat transfer performance. The results show that the heat transfer fluid flow rate, operation mode, groundwater flow, excavation ratio and wall depth have the greatest impact on the thermal performance of the EDW, with a normalized influence degree NETotal of 1.0, 0.94, 0.80 and 0.77, respectively. Recommendations on the thermal conductivity of the concrete and pipe, pipe configuration, etc., and prospects for further research are also provided for the optimal design and thermal simulation optimization of energy diaphragm wall systems.

Longitudinal dispersivity estimation according to heat and mass groundwater transport model calibration for Baikalsk paper and mill site

The paper presents the results of the numerical three-dimensional model of groundwater heat and mass transfer in the territory of Baikalsk paper and mill site calibration based on the materials of groundwater composition and properties twenty-year monitoring, which showed that the longitudinal dispersion at heat transfer is an order of magnitude greater than at mass transfer.

Technical Note: Lifetime of evaporating droplets in a closed volume

The numerical modeling of heat and mass transfer of droplets within a closed volume containing gas heated in relation to the droplets was conducted. The droplet lifetime at variation of initial values of gas and droplet temperatures and droplet mass fraction has been determined. It was found that droplet lifetime exhibits a weak dependence on the initial droplet temperature and a pronounced dependence on the initial gas temperature. Moreover, it was demonstrated that the droplet lifetime in a closed volume is longer than in infinite space. This is due to the fact that the cooling of the surrounding gas by droplets results in a decrease in the evaporation rate of the droplets. A parameter is proposed which allows for the consideration of the effect of evaporating droplets on the thermal regime of the gas-drop mixture, and which enables the generalization of the results of numerical simulation to obtain an expression for the droplet lifetime in a closed volume. The error in the use of the obtained expression is estimated. It was determined that the margin of error for the calculation results is less than ten percent.

Evolution Mechanism of Blast Furnace Cooling Plate Slag‐Hanging Behavior with Different Cooling System Structure

Based on the 3D heat transfer numerical simulation model, the evolution mechanism of blast furnace cooling plate slag‐hanging behavior with different cooling system structures is analyzed. Cooling plate reduced by 20 mm will not affect its slag‐hanging behavior. Copper cooling plate is best suited for high heat load areas. The vertical spacing of cooling plate is extended by 200 mm, the uniformity of the slag layer decreases by 5%, and the temperature of cooling plate and refractory material increases by 11 and 50 °C. Cooling plate vertical spacing of 510 mm or less can ensure stable slag hanging in the blast furnace. When using a single refractory material, the average uniformity of the slag layer is 95%, 86%, and 79% for graphite brick, semigraphite brick, and sialon‐SiC brick, respectively. Si3N4‐SiC brick cannot operate properly in high heat load areas. The factory can consider setting 125 mm sialon‐SiC brick in the furnace; graphite brick is used outside the furnace lining. The slag layer is well distributed, and the average value of uniformity is about 90%. Even if the slag layer is fully dislodged, the hot surface temperature of the furnace lining is 785 °C, and it can be quickly reslag hanging.

Numerical simulation and multi-objective optimization design of conjugate heat transfer in novel double shell-passes multi-layer helically coiled tubes heat exchangers

A novel double shell-passes multi-layer helically coiled tubes heat exchanger (DSMHCTHE) is proposed to improve the flow and heat transfer performance of the shell side. It was studied by using conjugate heat transfer numerical model. By changing coil diameter and pitch, the influence of coil torsion on the performance of the heat exchangers was investigated in the range of 0.0637–0.3183, and compared with the conventional multi-layer helically coiled tubes heat exchangers (MHCTHE). Two kinds of heat exchangers were optimized by using multi-objective optimization differential evolution algorithm. The results indicate that the coil pitch has a greater effect on the overall heat transfer coefficient, and the effects of coil pitch variations in the inner and outer helically coiled tubes follow different patterns. Compared with MHCTHE, the heat transfer rate of DSMHCTHE are increased by 13.9 %–19.1 %, the comprehensive performance is increased by 13.0 %–18.0 %, and the heat transfer entropy generation number and friction entropy generation number are lower. It shows that DSMHCTHE have better application potential as heat exchangers.

Heat transfer performance of energy pile and borehole heat exchanger: A comparative study

Geothermal structures are widely utilized to satisfy the heating and cooling demands of buildings, providing a promising alternative to the escalating scarcity of energy. As two types of geothermal heat exchangers, energy piles and borehole heat exchangers exhibit different efficiencies in extracting geothermal energy. This paper examines the thermal performance of an energy pile and a borehole heat exchanger under heating and cooling conditions through field tests, introducing the heat exchange rate per unit pipe length (q0) as a metric. Furthermore, a three-dimensional heat transfer numerical model was developed and validated. The parametric analysis was subsequently conducted to investigate the sensitivity of heat exchange efficiency to five parameters, including flow rate, inlet temperature, pipe diameter, soil thermal conductivity, and soil temperature. The results showed that the heat transfer efficiency of the borehole heat exchanger was 42.2 % and 48.7 % lower than that of the energy pile under the heating and cooling conditions, respectively. Moreover, the heat transfer efficiency of the energy pile and borehole heat exchanger is most sensitive to inlet temperature, with the latter showing greater sensitivity to pipe diameter. This study provides valuable insights into optimizing the design and operation of energy piles and borehole heat exchangers to meet the growing energy demands of buildings.

Research on the heat transfer characteristics of through-hole transpiration cooling based on ceramic matrix composites

Ceramic matrix composites (CMCs) are one of the primary materials used for transpiration cooling in aircraft due to their lightweight and high-temperature durability characteristics. However, there is relatively little research on the transpiration cooling of through-holes in CMCs at high temperatures. This paper establishes a numerical model for flow and heat transfer of through-holes transpiration cooling in the combustion chamber environment of a scramjet engine, analyzing the effects of blowing ratio, hole arrangement, hole size, and material thermal conductivity on the effectiveness of transpiration cooling, revealing potential strategies for optimizing hole arrangement using Response Surface Methodology (RSM). The calculation results show that increasing the blowing ratio can effectively enhance transpiration cooling performance. However, a higher blowing ratio increases the pressure gradient within the through-holes, leading to non-uniform coolant distribution and an increased temperature gradient. The plum hole arrangement provides better cooling performance than the parallel hole arrangement. Under the same blowing ratio, cooling efficiency improves by 8%, and uniformity increases by 50%. Increasing the size of the leading-edge holes can effectively reduce the pressure gradient within the through-holes. After optimization, the temperature gradient and average temperature improve by 8.824% and 4.290%, respectively. Additionally, enhancing the thermal conductivity in the direction of heat flow increases cooling efficiency more significantly compared to other directions.

Modeling the thermal behavior of multifunctional syntactic foams containing phase change materials for heat management applications

AbstractSyntactic foams are lightweight porous composites obtained by the addition of hollow glass microspheres (HGMs) to a polymer matrix. This work experimentally and numerically investigates the thermal behavior of epoxy‐based syntactic foams with enhanced multifunctionality produced by incorporating microencapsulated phase change materials (PCMs) as functional fillers, providing thermal energy storage and temperature stabilization due to its large latent heat of melting. Foams are fabricated using varying ratios of HGMs (0–40 vol%) and PCM (0–40 vol%) to achieve tuned densities and thermal properties with a total filler content of up to 40 vol%. A one‐dimensional numerical heat transfer model based on the enthalpy method is presented to simulate the thermal behavior of these materials. The model accurately incorporates the specific heat and thermal conductivity of the foam components, as well as the latent heat absorption during PCM melting (up to 68 J/g). The model is experimentally validated by demonstrating good agreement with the measurements of transient temperature profiles during heating tests on the foam samples. The validated tool is then leveraged to model the thermal response of the foams under a sinusoidally varying heat source, similar to the possible real applicative scenarios. These results can help optimize foam compositions balancing energy storage density, heat transfer properties, and structural support for lightweight energy storage systems. Potential applications include high‐efficiency thermal management in battery packs, electronic cooling, solar energy storage, and sustainable temperature‐controlled buildings.Highlights Foams with 0–40 vol% PCM and 0–40 vol% HGM show up to 68 J/g latent heat. 1D numerical model accurately captures thermal conductivity and PCM phase change. Validated model simulates thermal response under sinusoidal heat, optimizing foam composition. Foams act as thermal reservoirs, maintaining up to 5°C lower surface temperatures than epoxy.

Analysis of Longitudinal Cracking and Mold Flux Optimization in High-Speed Continuous Casting of Hyper-Peritectic Steel Thin Slabs

Longitudinal crack defects are a frequent occurrence on the surface of thin slabs during the high-speed continuous casting process. Therefore, this study undertakes a detailed analysis of the solidification characteristics of hyper-peritectic steel thin slabs. By establishing a three-dimensional heat transfer numerical model of the thin slab, the formation mechanism of longitudinal cracks caused by uneven growth of the initial shell is determined. Based on the mechanism of longitudinal crack formation, by adjusting the performance parameters of the mold flux, the contradiction between the heat transfer control and lubrication improvement of the mold flux is fully coordinated, further reducing the incidence of longitudinal cracks on the surface of the casting thin slab. The results show that, using the optimized mold flux, the basicity increases from 1.60 to 1.68, the F- mass fraction increases from 10.67% to 11.22%, the Na2O mass fraction increases from 4.35% to 5.28%, the Li2O mass fraction increases from 0.68% to 0.75%, and the carbon mass fraction reduces from 10.86% to 10.47%. The crystallization performance and rheological properties of the mold flux significantly improve, reducing the heat transfer performance while ensuring the lubrication ability of the molten slag. After optimizing the mold flux, a surface detection system was used to statistically analyze the longitudinal cracks on the surface of the casting thin slab. The proportion of longitudinal cracks (crack length/steel coil length, where each coil produced is about 32 m long) on the surface of the thin slab decreases from 0.056% to 0.031%, and the surface quality of the thin slab significantly improves.

Thermal performance of phase-change wall of a hotel building under hot-summer and cold-winter climate

ABSTRACT In China, the energy consumption in the building sector has increased tremendously in the past decades. It is important to investigate advanced passive energy-saving technologies for buildings. By applying phase-change materials in walls, the peak cooling/heating load can be significantly reduced. In the present study, a numerical model of one-dimensional heat transfer within a phase-change wall was developed and solved by Matlab, which was successfully validated with published data. Subsequently, the model was used to simulate the thermal performance of a phase-change wall in a hotel building in Shanghai, China. Simulation results demonstrate that the performance of the phase-change wall is optimized when the phase-change material is applied to both sides of the wall. Year-round heat transfer is minimized using layers of paraffin (C16-C28) and capric acid (2 cm), with phase-change temperatures of 43℃ and 16.3℃, respectively. The PCM wall reduces inwardthe inward heat transfer by 26.9% compared with a common wall without phase-change material. The outward heat loss is also reduced by 15.7% during the heating season. This study demonstrates that the PCM wall can effectively reduce indoor heat gain in summerin the summer and heat loss in winterin the winter. The numerical model has proven to be feasible for optimizing construction design.

Experimental and Numerical Study of Newly Assembled Lightweight Radiant Floor Heating System

In this study, the heating capacity of a new prefabricated assembled hot water radiant modular heating system made from a recycled waste building masonry structure is investigated through experimental and numerical simulation methods. The heating capacity of the system in different working conditions (a water supply temperature of 48 °C, 51 °C, 56 °C, and 61 °C; a flow rate of 0.49 m3/h, 0.35 m3/h, and 0.21 m3/h) is analyzed and verified. A three-dimensional steady-state heat transfer numerical model of the floor heat transfer of the module is established, and the accuracy of the model is verified through the measured results to investigate the heating capacity of this system under different water supply temperatures, flow rates and coil spacings. The results show that the new prefabricated hot water radiant module heating system has a 0.9 °C higher air temperature and 2.1 °C higher average floor surface temperature than the traditional wet floor radiant heating system under the same experimental conditions, and the response time is 44% shorter. The water supply temperature can significantly change the heating capacity of the system, while the water supply flow rate has little effect on the system. The established three-dimensional steady-state numerical model can be in good agreement with the measured results. This study can provide an experimental and theoretical basis for the design and application of such systems.

Simulation Study of Thermal Performance on the Inner and Outer Surfaces of Semi-Transparent Photovoltaic (STPV) Glass with Different Transparency

This paper used the experimentally verified one-dimensional steady-state heat transfer numerical model of the semi-transparent photovoltaic (STPV) glass to simulate the influence of wind speed, ambient temperature and air gap thickness on the surface temperature of PV modules, and analyzed the thermal performance of the inner and outer surfaces of STPV glazing with different transparency. Results shows that for every 1m/s increase in wind speed, the outer surface temperatures of SL-STPV glass with transparency of 10%, DL-STPV glass with transparency of 20% and 40% decreased by 3 °C, 3.02 °C and 2.22 °C, respectively. For every 10 °C increase in ambient temperature, the outer surface temperatures of SL-STPV glass with transparency of 10%, DL-STPV glass with transparency of 20% and 40% increase by 8.45 °C, 7.6 °C, and 7.79 °C, respectively. For the DL-STPV glass with transparency of 20% and 40%, for every 2 mm increase in the thickness of the air gap, the outer surface temperature increases by 0.13 °C and 0.12 °C, respectively. The heat transfer between the inner surface of the glass and the indoor environment increases the heat gain through the glass into the room in summer, which will lead to an increase in refrigeration energy consumption. However, in winter, the heat exchange between the inner surface and the in-door air to heat the indoor air reduces the heating energy consumption to a certain extent, and achieves the effect of building energy conservation to a certain extent.

Numerical analysis of heat and mass transfer in separated ventilation of deeply buried long air intake tunnels

Using earth air tunnel heat exchangers (EATHE) to pre-treat air entering underground space is an effective measure for energy-saving. This paper addresses the scarcity of numerical model for heat and mass transfer in long, separated air intake tunnels by establishing a three-dimensional model that considering condensation, specifically analyzing the heat transfer process in tunnels with separated ventilation earth air tunnel heat exchanger (SV-EATHE). The accuracy of the model was verified by engineering measured data. The heat transfer performance of EATHE and SV-EATHE is compared and analyzed by using the model. The results indicate that the annual heat exchange of SV-EATHE is approximately 80 % of that of EATHE, with the latent heat exchange from March to September accounting for 77.2 % of EATHE's. SV-EATHE significantly reduces condensation in traffic tunnels. Increasing ventilation will correspondingly increase the heat exchange and reduce dehumidification, but the rate of change will gradually decrease. The change in partition wall thickness has an approximately linear relationship with the amount of heat exchange. For every 0.1 m increase in diaphragm wall thickness, the heat exchange in the intake duct in August is reduced by approximately 1500 kWh and the dehumidification is reduced by approximately 0.6 kg/h.

Thermal performance simulation and numerical analysis of a fuel cell waste heat utilization system for automotive application

To recover the waste heat generated by proton exchange membrane fuel cells, an onboard fuel cell waste heat utilization system used for cockpit heating was constructed in this study. The heat transfer numerical model of the system was established, and experimental data validated the feasibility of the model. Additionally, the thermal performance of the onboard fuel cell waste heat utilization system was analyzed under various operational conditions. The results indicate that the air temperature and heat transfer coefficient of the heat exchanger are positively correlated with the thermal performance of the cockpit heating, while the radiator inlet air velocity and pump speed show a negative correlation with the system’s performance. Under other steady conditions, the stabilized temperature of the cockpit is increased by 150 % when the air temperature increases from 0 °C to 40 °C, and the cockpit temperature is reduced by 20 % when the water pump speed accelerates from 100 to 300 r/min. Furthermore, under 20 °C ambient temperatures and with an inlet air velocity of 3 m/s, water pump speed of 500 r/min, and a heat exchange coefficient of 5,000 W·m−2·K−1, the fuel cell waste heat utilization system achieves an optimal waste heat utilization efficiency of 50.8 % underrated working conditions. In summary, this study offers theoretical guidance for designing and numerically evaluating a vehicular waste heat utilization system using fuel cells.

Evaluation of Heat Transfer and Fluid Dynamics across a Backward Facing Step for Mobile Cooling Applications Utilizing CNT Nanofluid in Laminar Conditions

In a variety of engineering applications, the efficacy of heat dissipation in mobile cooling systems is greatly influenced by the Backward Facing Step. Its significance in optimizing cooling solutions for mobile devices is highlighted by the fact that its design and fluid dynamics are crucial in minimizing skin friction and improving passive heat transfer. In this paper, we present a verification of an advanced numerical model for heat transfer and fluid flow through a Backward Facing Step, used in mobile cooling. The objective of this study is to explore fluid separation, a method enhancing passive heat transfer and reducing skin friction. ANSYS/FLUENT software has been used to solve the backward facing step in a horizontal duct filled with pure water. Carbon nanotube (CNT) dispresed into the base fluid at different volume fractions of 0.2%, 0.65%, and 1%. This study focused on laminar flow conditions ranging from Reynolds numbers 200 to 900. In order to reduce the computation time and ensuring the accuracy and reliability of numerical simulations, a grid independence study has been conducted. The findings revealed a substantial rise in the average Nusselt number and heat transfer coefficient with increased Reynolds number and volume fraction of nanoparticles. Specifically, the nanofluid (CNT/water) exhibited the highest average Nusselt number and heat transfer coefficient with volume fractions 1%. Furthermore, the research showed a decrease in the skin friction factor as both Reynolds number increased and nanoparticles’ volume fraction decreased. The increments of nanoparticles' concentrations lead to increase viscosity, promotes agglomeration, alters flow behaviour by inducing turbulence, and enhances heat transfer. These factors collectively contribute to higher skin friction due to increased resistance to fluid flow and disrupted streamline patterns