Three-dimensional Heat Transfer Model Research Articles

Performance of capillary box heat exchangers buried in seabed for seawater-source heat pumps

An innovative seawater-source heat pump system (SWHPs) was developed by employing capillary box heat exchangers (CBHEs) buried in the seabed as the front-end heat exchanger. Field experiments were firstly presented to test the efficiency of the SWHPs in a practical project. The experimental results show that even under extreme cold/hot climate conditions, the 24-hour COP/EER of the heat pump unit can reach respectively 2.96 and 5.39, which is superior to an alternative air source heat pump (ASHP). Furthermore, an unsteady state three-dimensional seepage and heat transfer model was established to study the thermal performance of CBHEs buried in the seabed using ANSYS FLUENT software. Based on the model, the influences of seawater seepage velocity, thermophysical characteristics of backfilled sand, and flow velocity in the capillary tube on the thermal characteristics of CBHEs were investigated. Moreover, considering the per area heat transfer rate of CBHEs as the evaluation target, the sensitivities of five representative factors including the flow velocity in capillary tubes, seawater seepage velocity, specific heat capacity, density and thermal conductivity of the backfilled sand were discussed using the single factor sensitivity analysis to detect the significant influence parameters.

Dynamic heat transfer characteristics of gravity heat pipe with heat storage

For the thermal performance enhancement of electronic components under intermittent high heat load, this paper proposes a gravity heat pipe with heat storage (GHPHS) that couples the advantages of GHPs and latent heat storage (LHS) units. A three-dimensional heat transfer model of GHPHS is developed and numerically studied, focusing on the comparison with traditional GHPs. Furthermore, the effects of the position and fin number of LHS units as well as the type and filling rate of phase change materials (PCMs) are investigated. The results indicate that the average heat source temperature reduces by 48.4 % and the maximum temperature duration shortens by 50 % with adding LHS units into GHPs, which can reduce the transient heat load shock and enhance the overall temperature uniformity. Moreover, the closer the LHS units is to heat sources, the better the temperature uniformity of GHPs is. When gallium is the PCM, the maximum heat source temperature reduces by 26 % when compared with the paraffin, and the increase in PCM fill rate facilitates a delay in the onset of maximum temperature and enhances the temperature uniformity. The fin number significantly affects the competition mechanisms between heat convection and conduction during the melting and solidification. As the fin number increases from 38 to 150, the maximum temperature of heat sources decreases by 29.7 % and the overall temperature uniformity of GHPs increases by 31.7 %. However, there is a limit to the influence of fin number on the thermal enhancement of GHPHSs.

Three-Dimensional Model of Soil Water and Heat Transfer in Orchard Root Zone under Water Storage Pit Irrigation

To reveal the water and heat transfer characteristics of the orchard soil under water storage pit irrigation and to regulate the distribution of soil water and heat for improving apple quality and increasing yield, a 3D soil water and heat transfer model of orchards under water storage pit irrigation was established. The model not only considered the influences of root water uptake, precipitation, evaporation, and irrigation, but also simulated the infiltration process of the variable water head in the pit according to the principle of mass conservation and introduced the pit coefficient to simulate the difference in radiation in the pit to describe the influence of the pit on the model. Verify and analyze the simulation results. Results showed that the variation trend of simulated soil moisture and heat was consistent with that of measured data. The mean absolute percentage error, root mean square error, and mean absolute deviation were 3.23%, 0.9460, and 0.6984 for soil temperature and 10.05%, 0.0269, and 0.0214 for water content after irrigation, respectively. The simulation results have high accuracy and show that the soil moisture content centers on the pit with an ellipsoid distribution and tends to be uniform over time. The soil temperature was higher in the 4–5 cm area near the soil surface and the wall of pit, and it remarkably changed with time. The intraday variation of soil temperature was mainly affected by atmospheric temperature, but a certain lag was observed compared with the change of atmospheric temperature. With the increase of the irrigation amount, the distribution range of soil moisture content and water high value area increased, while the average and maximum soil temperature decreased. With the increase of irrigation water temperature to 18–24 h after irrigation, the soil temperature in the ellipsoidal area around the pit remarkably increased. The model established in this paper can be used to simulate the hydrothermal status of the soil in the field under water storage pit irrigation. The results prove that the water storage pit irrigation can effectively improve the hydrothermal status of the middle-deep soil and promote the root system of fruit trees to absorb water.

A three-dimensional conjugate heat transfer model for methanol synthesis in a modular millireactor

In this work, a modular millireactor (MMR) is designed and modeled using the computational fluid dynamics (CFD) tool OpenFOAM. First, the method is validated against a conventional packed bed reactor (PBR) model (1D) with Aspen Plus. Next, the method is applied to study the effects of pressure (2–6 MPa) and temperature (483–533 K) on the performance of the MMR. Conjugate heat transfer (CHT) CFD results for the MMR are compared against a corresponding PBR at isothermal conditions. For the MMR, the methanol yield is shown to vary between 9–23 % within the studied parameter range. Overall, the MMR outperforms the PBR at conditions studied in this work. The maximum difference in methanol yield between MMR and the PBR is noted to be a factor of 1.71 at 533 K and 5 MPa. Such a large discrepancy advocates the usage of 3D CHT/CFD.

Laser scribing of fluorine-doped tin oxide coated on glass substrate in air and water

Fluorine-doped tin oxide (FTO) is one of the conductive layers used in the emerging perovskite solar cell technology, and the layer is typically scribed by a laser beam. However, thermal damage induced by laser deteriorates the scribe quality and in turn reduces the efficiency of the solar panel. This paper compares five different laser scribing techniques for isolating the FTO on the film and substrate sides both in air and water environments. The width and depth of laser-scribed channels, as well as burrs height, produced by using the different techniques were examined and compared. A clean and consistent scribe with negligible burrs was achievable by ablating the FTO film in the flowing water layer. Using this technique, its burr height index was found to reduce by 62.5% compared to the laser scribing of FTO film in air. A three-dimensional transient heat transfer model was also developed in this study to simulate the temperature field of workpiece subjected to the laser scribing in air and in flowing water environments. The thermal damage region was substantially small when the ablation was performed in the flowing water film. This could be a promising technique for the P1 scribing step in the manufacturing of emerging perovskite solar modules.

Study on heat storage performance of a novel vertical shell and multi-finned tube tank

High-efficient latent heat storage technology plays a crucial role in solar energy utilization. In this study, a shell-and-tube heat storage tank employing a novel fin structure has been proposed. A three-dimensional unsteady heat transfer model of the tank has been established. The effects of fin height, fin angle and fin number on liquid fraction, average temperature and heat storage rate have been investigated. The results show that the complete melting time of the phase change material in the novel finned tube is shortened by 66.4% compared with the finless structure. The melting time of the fins with heights of 34.20 mm, 42.75 mm, and 51.30 mm are shortened by 56.9%, 60.1% and 66.4%, respectively. When the fin height exceeds 51.30 mm, the melting rate remains almost unchanged. The fin angle is not the larger the better. Compared with the bending angles of 10°, 20° and 40°, the complete melting time of 30° is reduced by 14.0%, 11.6% and 6.4%, respectively. As the number of fins increases, the total heat storage time is shorter, but the total heat storage has also been reduced. The results can provide a good reference for design, operating, and energy-saving of latent heat storage systems.

Numerical evaluation of convective heat transfer properties of two-dimensional rotating PCM melt in the unilaterally heated rectangular container

This paper carried out numerical investigations on the flow and heat transfer characteristics of a phase change with two-dimensional rotation of the three-dimensional paraffin (RT -27)-filled rectangular encapsulated container (PCM-REC) in space. A three-dimensional transient numerical heat transfer model was established and the enthalpy method was used to simulate the solid-liquid phase transition process and the flow evolution at the PCM interface. In this paper, the solid-liquid interface distribution, temperature distribution and melting time of PCM in PCM-REC heated at a constant temperature on one side were compared when rotated at different angles (0°, arctan (0.4), 2arctan (0.4) and 90°) along the heating direction and vertical heating direction. Results demonstrated that the peak value of maximum natural convection velocity increased from 0.0072 m/s to 0.0184 m/s with increasing radial height when PCM-REC was rotated in vertical heating direction. When PCM-REC was rotated in two dimensions by the same angle, the melting time was fastest when γ was an obtuse angle, and with the increase of the obtuse angle, the melting time shortened from 17 min to 6 min; when γ was an acute angle, the melting time was slowest, and with the decrease of the acute angle, the melting time lengthened from 49 min to 288 min.

Thickness Distributions of Mold Flux Film and Air Gap in Billet Ultra-High Speed Continuous Casting Mold Through Multiphysics Modeling

The thicknesses of mold flux film and air gap are significant factors that affect the high-efficiency heat transfer, the strand lubrication and mold taper design of billet ultra-high speed continuous casting mold. Therefore, this paper established the three-dimensional fluid flow, heat transfer and solidification model, interfacial heat transfer model and two-dimensional stress-strain model to conduct multiphysics modeling. Thereby the thickness distributions of liquid slag, solid slag and air gap in the ultra-high speed billet continuous casting mold were obtained, and analyzing the effects of melting temperature of mold flux and mold taper. The results indicate that the thicknesses of liquid slag and solid slag increase and decrease respectively along the casting direction, and air gap mainly concentrates near the mold corner. The maximum thicknesses of liquid slag, air gap, and solid slag at the mold outlet are respectively 0.18 mm at the center of the strand surface (x = 0 mm), 0.28 mm at the strand corner (x = 80 mm) and 0.67 mm at x = 74 mm. The lower melting temperature of mold flux, the greater the liquid slag thicknesses and ascend from 0.14 to 0.18 mm, and conversely the maximum air gap thicknesses descend from 0.31 to 0.28 mm and existing ranges also get smaller, which is more favorable for the strand lubrication. To eliminate the air gap, the appropriate linear mold taper is 0.45% m−1 at the 6.5 m/min in casting speed.

Heat transfer performance of energy piles in seasonally frozen soil areas

Energy piles constitute a combination of ground source heat pump and building pile foundation technology. Energy piles can not only exchange heat with soil and extract geothermal energy but can also bear upper loads. However, due to the complex geological and climatic conditions in seasonally frozen soil areas, research on the heat transfer performance of energy piles in these areas is limited. According to the characteristics of the ground temperature distribution in seasonally frozen soil areas, the soil region can be divided into frozen and nonfrozen layers. First, a laboratory model test was carried out to investigate the heat transfer performance in these two layers. Then, a three-dimensional heat transfer model of an energy pile suitable for seasonally frozen soil areas was established. The actual working conditions of the real-scale model were simulated, and parametric analysis was then conducted. The results indicated that in annual energy pile operation, the energy pile maximum heat exchange amount per unit length can reach 125 W/m. In the performed parametric analysis, the pile length, concrete thermal conductivity, fluid volumetric flowrate and pipe type impose the greatest influence on the energy pile heat transfer performance, while the pile diameter and concrete cover thickness impose relatively little influence. Moreover, the influence of the pipe diameter should be further studied.

Coupled Fluid-Solid Heat Transfer of A Gas and Liquid Cooling PMSM Including Rotor Rotation

In order to study the problem of the high temperature reached by the end windings, caused by the high current in the armature windings of permanent magnet synchronous motors (PMSM), a 560 kW gas and liquid cooling PMSM used for a compressor is analyzed. The heat source is obtained by a two-dimensional numerical analysis of the electromagnetic field. A three-dimensional fluid-solid coupling heat transfer model is established. Under the action of the cooling medium, one-quarter of the PMSM structure is numerically simulated. The temperature distribution of the 560 kW PMSM is studied, including rotor rotation. The temperature distribution of the PMSM armature winding and the distribution of fluid around the winding under different inlet air flow speeds are analyzed. The calculated values of the end winding temperature at different currents are compared with the experimentally measured values. The rationality of the three-dimensional fluid-solid coupling heat transfer model and the correctness of the calculation method are verified. This paper provides both the analysis and the computation scheme of the fluid-solid heat transfer of the PMSM.

Prediction of Temperature Distribution in Concrete under Variable Environmental Factors through a Three-Dimensional Heat Transfer Model.

Temperature distribution in concrete is significant to the concrete structure’s macro properties and different factors affect the heat transfer in concrete, and therefore influence the temperature distribution. This work established a three-dimensional transient heat transfer model coupled with various environmental factors, using the finite element method for calculating the results and real-measured data for testing accuracy. In addition, a sensitivity evaluation of various factors was conducted. Due to various environmental factors, the results revealed that the prediction of temperature distribution in concrete by the three-dimensional model had great accuracy with an error of less than 4%. A particular hysteresis effect of temperature response in the concrete existed. Considering heat transfer in different spatial directions, the model can predict the temperature change of each spatial point instead of the spatial surface in different depths, proving the shortcomings of a one-dimensional heat transfer model. A greater solar radiation intensity caused a more significant temperature difference on the concrete surface: the surface temperature difference in July was twice as significant as that in December. Wind speed had a cooling effect on the concrete surface, and stronger wind speed accompanied with a stronger cooling effect made the surface temperature closer to the ambient temperature. Material properties had different effects on the temperature distribution of the surface part and internal part: the specific heat capacity determined the speed of the outer layer temperature change while the thermal conductivity determined the speed of the inner layer temperature change.

Experimental and Numerical Simulation of a Radiant Floor System: The Impact of Different Screed Mortars and Floor Finishings.

The radiant floor system market is growing rapidly because Europe is moving toward a low-carbon economy and increased awareness about environmental sustainability and energy efficiency, stimulated by the ambitious EU Energy Efficient Directive and nZEB challenge. The high growth rate of the market share is due to the involvement of homeowners in the specifications of their living commodities, so they are thus willing to invest more at the initial stage to obtain long-term benefits and lower energy exploration costs. We performed an experimental campaign over three slabs with a hydronic radiant floor system of equal dimensions, shape, and pipe pitch with different screed mortar formulations to assess their performance throughout a heating/cooling cycle. The temperature at different heights within the interior of the screed mortars and at the surface were monitored. The results revealed that an improved screed mortar has a relevant impact on the efficiency of the system. Moreover, a three-dimensional transient heat transfer model was validated using the experimental data. The model was used to evaluate the impact of different finishing materials, namely wood, cork, ceramic, and linoleum, on the floor surface temperatures. The results showed differences of 15% in the surface temperature when using different floor finishing solutions.

On the effect of thin-wall thickness on melt pool dimensions in laser powder-bed fusion of Hastelloy X: Numerical modeling and experimental validation

Laser Powder-bed Fusion (LPBF) is a common technique categorized as one of the Additive Manufacturing (AM) processes to efficiently fabricate complex geometries. The involvement of complex phenomena relating to laser and metal powder requires a thorough investigation to understand the complex multi-physics behind this process. Modeling and simulation tools shed light on predicting the temperature distribution and melt pool dimensions which have a significant impact on the quality of the final parts. In this study, a three-dimensional (3D) heat transfer model is developed to investigate the influence of the thickness of the printed thin-walls on melt pool dimensions and temperature distribution. The results indicate that the single-track simulation can predict the melt pool dimensions accurately and the calibrated model can be extended to the multi-track simulation for investigating the effect of thin-wall thicknesses on melt pool geometries. The simulation results demonstrate the evolution of melt pool geometries during the process. Due to the existence of heat accumulation during the process, decreasing the thicknesses of the thin-walls leads to enlarging the melt pool width significantly. Moreover, the simulation results show a higher temperature gradient during the LPBF process of thinner parts leading to a smaller grain size of the final microstructure. The validation of the simulation results showed the high capability of the model in predicting the transient temperature profile and melt pool geometries. The percentage difference between simulated and experimental melt pool width for thin-wall thicknesses 0.5 mm, 0.75 mm, and 1 mm are 7%, 7%, and 11%, respectively. Lastly, a process map has been provided to guide the selection of process parameters for printing thin-wall structures.

A Simulation-Based Digital Design Methodology for Studying Conjugate Heat Transfer in Tundish

The successful design of refractory lining for a tundish is critical due to the demand of superheat control, improvement of steel cleanliness and reduction in material cost during continuous casting. A design of experiment analysis, namely, the Taguchi method, was employed to analyze two-dimensional heat transfer through refractory linings of a single-strand tundish, with the consideration of the thickness and the thermal conductivity of lining materials. In addition, a three-dimensional conjugate heat transfer model was applied in the tundish, taking in account the molten steel flow and heat conduction in the linings. A special focus of this study was to demonstrate the analysis methodology of combining Taguchi and CFD modelling to explore lining design in terms of thickness and thermal conductivity for the given process conditions during tundish operations.

Numerical study on the air-cooled thermal management of Lithium-ion battery pack for electrical vehicles

A Lithium-ion battery is one of the most common batteries being widely used as the power source in Electric Vehicle (EV) due to its high energy density, power density, long life span and environment friendly. Due to the high power requirement of EV, thousands of cylindrical Lithium-ion battery cells are typically connected in parallel and/or series forming a battery pack. This significantly generates enormous heat through the internal resistance effect and exothermic reactions inside the battery during the charge or discharge process. If the fetal heat cannot be dissipated sufficiently, the battery cells may encounter capacity fade, thermal runaway and instability issues. Thus, efficient thermal management of the Lithium-ion battery pack is essential to restrain high temperature and non-uniformity of temperature in the battery pack. This issue remains a challenge, although much research has been conducted on this topic. In this work, the air cooling thermal management system is numerically investigated due to lower manufacturing cost, simple layout requirements and higher reliability of the system. A transient three-dimensional heat transfer model of the cylindrical Lithium-ion battery pack is developed to study the effect of the inlet velocity, discharge rate and cell arrangement structure on the cooling performance. The proposed system is designed to minimize the maximum cell temperature and the cell temperature uniformity. The simulated results can be further applied as a reference in designing the structures of the battery pack and planning the cooling strategies.

Numerical Investigation of the Effects of the Beam Scanning Pattern and Overlap on the Temperature Distribution during the Laser Dopant Activation Anneal Process

Laser thermal annealing (LTA) has played an important role in the fabrication of scaled semiconductor devices by reducing the heat budget of the dopant activation process. During the laser annealing of entire wafer areas, the beam scanning pattern and overlap ratio have significant effects on uniform heating during the process. In this study, a numerical simulation of the LTA process was carried out using a three-dimensional transient heat transfer model. The temperature distribution produced by different laser scan paths and beam overlap ratios was analyzed. Additionally, the behavior of the dopant (phosphorus) diffusion induced under the multipath and beam overlapping conditions was numerically investigated. According to the simulation result, a zig-zag pattern generated hot spots around the corner areas of the beam path due to the greater heat accumulation per unit area; however, a bidirectional pattern induced cold spots due to the absence of laser heating around the corner areas. It was also found that the maximum temperature reachable in the beam overlapped region was much lower than that obtained along the beam scanning path, and the most uniform heating could be obtained when the zig-zag pattern and a 50% overlap ratio were used. According to the dopant diffusion and concentration distribution predicted for the case of the zig-zag pattern and 50% overlap ratio, the difference in the dopant diffusion length was approximately thirty times within the scanned area.

Numerical study on effect of natural wind and piston wind on anti-freezing length of tunnels with high geo-temperature in cold region

Taking Zilashan Tunnel as an example, a three-dimensional unsteady heat transfer model of surrounding rock, tunnel lining and wind flow was established. The reliability of the temperature calculation model was verified by a 1:30 model test and field test. The influences of natural wind speed, natural wind temperature, train speed and traffic volume on the anti-freezing length of tunnels in cold regions were studied. In particular, this paper focuses on the influence of piston wind direction on the anti-freezing length of the tunnel during 50 years of operation. The results show that the maximum anti-freezing length is positively correlated with the velocity of the natural wind, and the maximum anti-freezing length increases by 787 m on average when the velocity of the natural wind increases by 1 m/s. The maximum anti-freezing length is 2352 m when only the influence of natural wind is considered. When the average temperature of the natural wind is greater than 5 °C, the anti-freezing length of Zilashan Tunnel is 0 m. The maximum anti-freezing length increases with the increase of train speed. The anti-freezing length is the longest when the natural wind is in the same direction as the piston wind, and the minimum anti-freezing length is more than 1200 m under different train speeds. When the traffic volume is 20 trains/day, the anti-freezing length increases with the increase of train speed regardless of the direction of piston wind. Under most working conditions, the surrounding rock near the tunnel entrance will freeze; when the traffic volume is greater than 20 trains/day, the surrounding rock near the tunnel exit will freeze with the natural wind speed and train speed at 1.5 m/s and 200 km/h respectively.

Three-dimensional finite discrete element-based contact heat transfer model considering thermal cracking in continuous–discontinuous media

This paper proposes a three-dimensional heat transfer model that considers contact heat transfer and thermal cracking in continuous–discontinuous media. The 3D heat transfer model comprises the heat conduction model inside the continuum and the contact heat transfer model between discrete blocks. The model is combined with the 3D Finite Discrete Element (FDEM) for coupled thermo-mechanical calculation, which includes the following three parts: the temperature distribution of the system is obtained by the 3D heat transfer model considering contact heat transfer; then, the thermal stress caused by the temperature is applied to the system equation to perform the mechanical fracture calculation; finally, the heat exchange coefficient of the newly generated broken joint element is updated for heat transfer calculation at the next time. Some examples are given to verify the 3D contact heat transfer model with analytical solutions. Moreover, the influence of the heat exchange coefficient of the joint element and the contact heat transfer coefficient is discussed. Finally, examples of contact heat conduction in 3D granular assemblage, and thermal cracking caused by contact heat transfer are demonstrated. These examples demonstrated excellent capacity of the model in simulating contact heat transfer and thermal cracking in continuous–discontinuous media.

Analytical estimation of fusion zone dimensions and cooling rates in part scale laser powder bed fusion

The laser powder bed fusion process is increasingly used for the building of metallic parts by melting and solidification of alloy powders under a fast-moving finely focussed laser beam. A quick estimation of the resulting temperature field, fusion zone dimensions, and cooling rates is needed to ensure the manufacture of dimensionally accurate parts with minimum defects. A novel three-dimensional analytical heat transfer model with a volumetric heat source that can simulate the laser powder bed fusion process in part scale quickly and reliably is proposed here. The volumetric heat source term is constructed to analytically simulate the evolution of melt pools with a fair range of depth to width ratio. The proposed analytical model can simulate the building of multiple tracks and layers in part scale dimensions significantly faster than all the numerical models reported in the literature. The computed results of fusion zone shapes and sizes and cooling rates are found to be in good agreement with the experimentally reported results in builds of three commonly used alloys with diverse materials properties, SS316L, Ti6Al4V, and AlSi10Mg. Based on the analytically computed results, a set of easy-to-use process maps is presented to estimate multiple process conditions to obtain a set of target fusion zone dimensions without trial-and-error testing.

Heat Insulation Performance of Lattice Thermal Protection Structure with Reinforced Plate

A lightweight lattice structure is proposed, which can be applied to the thermal protection system of high speed aircraft. The structure uses carbon fiber reinforced silicon carbide ceramic matrix composite as the framework, and the inner cavity can be filled with heat insulation materials with small thermal conductivity. In order to study the heat insulation performance of the structure, the three-dimensional finite element heat transfer model of the lattice structure with and without heat insulation material was established. Abaqus software was used to calculate the temperature distribution and change of the lattice structure under different temperature boundary conditions. The equivalent thermal conductivity of the lattice structures under different temperature boundary conditions is defined and calculated. The results show that the heat insulation effect of the lattice structure is improved obviously with the addition of heat insulation materials, but the time required to reach the stable state is increased. Without heat insulation materials, the strength of cavity radiation is greatly affected by the temperature boundary conditions on the top surface and positively correlated. Increasing heat insulation materials can effectively block the generation of cavity radiation, thus enhancing the heat insulation effect. The conclusion provides a foundation for further application of the lattice structure in thermal protection system of high speed aircraft.