Thermal Conductivity Model Research Articles

Dynamic Heat Transfer Modeling and Validation of Super-Long Flexible Thermosyphons for Shallow Geothermal Applications

In comparison to borehole heat exchangers that rely on forced convection, super-long thermosyphons offer a more efficient approach to extracting shallow geothermal energy. This work conducted field tests on a super-long flexible thermosyphon (SFTS) to evaluate its heat transfer characteristics. The tests investigated the effects of cooling water temperature and the inclination angle of the condenser on the start-up characteristics and steady-state heat transfer performance. Based on the field test results, the study proposed a dynamic heat transfer modeling method for SFTSs using the equivalent thermal conductivity (ETC) model. Furthermore, a full-scale 3D CFD model for geothermal extraction via SFTS was developed, taking into account weather conditions and groundwater advection. The modeling validation showed that the simulation results aligned well with the temperature and heat transfer power variations observed in the field tests when the empirical coefficient in the ETC model was specified as 2. This work offers a semi-empirical dynamic heat transfer modeling method for geothermal thermosyphons, which can be readily incorporated into the overall simulation of a geothermal system that integrates thermosyphons.

Numerical analysis of natural convective heat transfer with porous medium using JUPITER

ABSTRACT Japan Atomic Energy Agency (JAEA) has developed a numerical method with the JUPITER code with a porous medium model to calculate the thermal behavior in primary containment vessels (PCVs) of Fukushima Daiichi nuclear power stations of Tokyo Electric Power Company (1F). In this study, we performed an experiment and numerical simulation of the natural convective heat transfer with the porous medium and compared those results. In comparison of the temperature and velocity distributions between the experiment and simulation, the temperature distribution in the simulation was in good agreement with the distribution in the experiment except the temperature near the top and side surface of the porous medium. The velocity distribution also agreed qualitatively with the experimental result. In addition, we also performed the numerical simulations with various effective thermal conductivity models to discuss the effect of the conductivity based on the internal structure of porous media on the natural convective heat transfer. The result indicated that the temperature distribution in the porous medium and the velocity distribution of the natural convection were significantly different for each model, and the simulation result with the Kunii–Smith model was close to the experimental results.

Computational Model of the Effective Thermal Conductivity of a Bundle of Round Steel Bars.

During the heat treatment of round steel bars, a heated charge in the form of a cylindrically formed bundle is placed in a furnace. This type of charge is a porous granular medium in which a complex heat flow occurs during heating. The following heat transfer mechanisms occur simultaneously in this medium: conduction in bars, conduction within the gas, thermal radiation between the surfaces of the bars, and contact conduction across the joints between the adjacent bars. This complex heat transfer can be quantified in terms of effective thermal conductivity. This article presents the original model of the effective thermal conductivity of a bundle of round steel bars. This model is based on the thermo-electric analogy. Each heat transfer mechanism is assigned an appropriate thermal resistance. As a result of the calculations, the impact of the following parameters on the intensity of heat transfer in the bundle was examined: temperature, the thermal conductivity of the bars, the thermal conductivity of the gas, diameter, and emissivity of the bar, and bundle porosity. Calculations were performed for a temperature range of 25-800 °C, covering a wide spectrum of variables, including bar diameters, bundle porosity, and type of gas. The knowledge obtained thanks to the calculations performed will facilitate the optimization of heat treatment processes for the considered charge. The greatest scientific value of the presented research is the demonstration that, thanks to the developed computational model, it is possible to analyze a very complex heat transfer phenomenon using relatively simple mathematical relationships.

Spectral relaxation method to investigate novel ternary hybrid Carreau nanofluid model with permeable stenosed artery

AbstractThe exploration of blood‐based ternary nanofluid flow (Au, TiO₂, Ag) through a permeable stenosed artery with a spatially dependent heat sink source is pivotal for advancing biomedical and engineering innovations such as hyperthermia treatments, drug delivery systems, external cooling simulations, thermal ablation, and targeted therapies. This study focuses on the thermal and flow dynamics of a novel ternary nanofluid comprising Au, TiO₂, and Ag nanoparticles, modeled as Carreau fluid within the geometry of a permeable stenosed artery. The effects of magnetization and spatial heat sink sources are analyzed to investigate velocity and temperature profiles. A temperature‐dependent thermal conductivity model is employed to better understand heat transport in stenosed arteries. The spectral relaxation method (SRM) is utilized to derive numerical solutions, validated against the well‐established bvp4c numerical scheme. Among the nanoparticles studied, Au demonstrates the highest enhancement in heat transport due to its superior thermal conductivity. Notably, for increasing thermal radiation parameter values (0.72, 1.2, 1.5, 1.7), heat transport improves by 9%, 7%, 9%, and 6%, respectively.

A connectivity model for the effective thermal conductivity of a particle-filled system considering interfacial resistances

A connectivity model for the effective thermal conductivity of a particle-filled system considering interfacial resistances

Corrigendum to “A generalized thermal conductivity model of soil-rock mixture based on freezing characteristic curve” [Cold Regions Science and Technology 229 (2025) 104360].

Corrigendum to “A generalized thermal conductivity model of soil-rock mixture based on freezing characteristic curve” [Cold Regions Science and Technology 229 (2025) 104360].

Homogenization methods for thermal study of support structure in laser powder bed fusion (L-PBF) – application to process numerical modeling

PurposeThis paper aims to report on a homogenized model for the anisotropic thermal conductivity of support structures constructed by the laser powder bed fusion (L-PBF) process, and its application to the numerical simulation of the L-PBF process.Design/methodology/approachConsidering both analytical and numerical approaches, the model is developed across a temperature interval encompassing the entire L-PBF process. Subsequently, the homogenized material properties are incorporated into a thermal finite element model (FEM) of the L-PBF process to consider the effects of the support structures, taking into account their anisotropic properties.FindingsThe simulation results of the L-PBF process indicate that the support structures act as a thermal barrier, retaining more heat in part compared to direct printing on the substrate. The implementation of homogeneous thermal conductivity in the L-PBF process simulation demonstrates its efficiency and potential application to better control heat transfer during part construction.Originality/valueThe homogenized anisotropic thermal conductivity of a support structure has been characterized by both analytical and numerical approaches. Such homogenized anisotropic tensor was implemented in L-PBF numerical simulation. This showed a strong influence of the supports on the temperature distribution and evolution.

Tempered fractional thermal conduction model for magnetoelastic solids with spherical holes under time-dependent laser pulse heating

Tempered fractional thermal conduction model for magnetoelastic solids with spherical holes under time-dependent laser pulse heating

Modeling and optimization of thermal conductivity of synthesized MWCNT/water nanofluids using response surface methodology for heat transfer applications

Modeling and optimization of thermal conductivity of synthesized MWCNT/water nanofluids using response surface methodology for heat transfer applications

Evaluation of theoretical models for anisotropic effective thermal conductivity in continuous fiber-reinforced thermoplastic laminates

PurposeContinuous fiber-reinforced thermoplastic composites are a class of materials highly valuable for structural applications and modeling of heat transfer within them is critical to the design of their processing methods. However, the fiber reinforcement leads to highly anisotropic thermal conduction. Among a variety of methods to account for anisotropic thermal conductivity, continuum models with effective media approximation thermal conductivity are computationally efficient and require minimal data to begin modeling a specific composite material. The purpose of this study is to evalute the utility of these models.Design/methodology/approachIn this work, six potential effective media approximation models are evaluated against experimental heating data. Thick (>25 mm) glass fiber-reinforced polyethylene terephthalate glycol (PET-G) specimens with 40% fiber volume fraction were heated with embedded resistance heating to produce validation and testing data sets. A two-dimensional finite-difference solver was implemented using each of the six effective media approximation models. The accuracy of each model is compared.FindingsThe model developed by Cheng and Vachon was found to predict the experimental results most accurately. Fit statistics were similar in the testing and validation data sets. This model is recommended for simulation of transient heating in continuous fiber-reinforced thermoplastic composites with low-to-moderate fiber volume fractions.Originality/valueThere are a wide variety of mathematical models for effective media approximation thermal conductivity, though very few have been applied to continuous fiber-reinforced thermoplastic composites. This work shows that the simplest methods based on rules of mixtures are well outperformed by more modern and complex models, and should be incorporated for accurate prediction of heating during thermal processing of fiber-reinforced thermoplastic composites.

Analysis of temperature changes in living tissue using the modified fractional thermal conduction model under laser heat flux on the skin surface

Analysis of temperature changes in living tissue using the modified fractional thermal conduction model under laser heat flux on the skin surface

Spurious radiated power signal following massive material injections in JET and the effect of neutral gas pressure on resistive bolometers.

Massive material injections in the JET tokamak have been observed to substantially affect resistive bolometer measurements, resulting in a spurious radiated power signal proportional to the quantity injected and reaching up to 8MW. These bolometers are calibrated and designed to operate in near vacuum but certain scenarios requiring large gas injections can push the neutral pressure past nominal values. This study demonstrates that the bolometry measurement can be affected at neutral pressures above 0.1Pa following injections with standard gas valves, shattered pellet injections, and particularly massive gas injections. The power measurement of resistive bolometers is based on the temperature difference between a measurement sensor exposed to radiation and a shielded reference sensor. We employ a thermal conductivity model to demonstrate that the conduction through the gas and the distinct geometries between the sensors can affect their cooling efficiency. This additional cooling pathway, coupled with the Joule heating from the applied voltage causes the equilibrium temperatures of the sensors to diverge. Being the very basis of the measure, this temperature difference induces a signal that is erroneously interpreted as radiated power. Experiments show large discrepancies in the response to neutral pressure among bolometer channels, attributed to variations in channel physical parameters. Nonetheless, the modeled total radiated power reproduces the experimental measurements within an order of magnitude, affirming the sensitivity of resistive bolometers to neutral pressure and gas species.

Optimizing Backfill Materials for Ground Heat Exchangers: A Study on Recycled Concrete Aggregate and Fly Ash for Enhanced Thermal Conductivity.

This study investigates the potential use of recycled concrete aggregate (RCA), fly ash (FA), and their mixture (RCA+FA) as backfill materials for shallow vertical ground heat exchangers (GHEs). Granulometric, aerometric, and Proctor compaction tests were conducted to determine soil gradation, the void ratio, and the optimal moisture content (OMC) for maximum dry density. RCA demonstrated efficient compaction at lower moisture levels, while FA required higher moisture to reach maximum density. A 10% FA addition was optimized to fill voids in the RCA soil skeleton without compromising structural stability. Thermal conductivity tests were performed using a TP08 probe in both dry and wet states. The results showed that the RCA+FA mix exhibited a notable increase in thermal conductivity at around 6% moisture content due to the formation of water bridges between particle contacts. FA, in contrast, displayed a more linear relationship between conductivity and moisture. The RCA+FA mix achieved higher thermal conductivity than either material alone, particularly near full saturation, making it a promising option for efficient heat exchange. Thermal conductivity modeling, based on the Woodside and Messmer model, confirmed the RCA+FA mix's high conductivity and estimated full saturation conductivity values with a small error. The Kersten number (Ke) was employed to predict conductivity across varying moisture levels, with results showing a strong correlation with saturation ratio (Sr).

Polyethylene glycol modified polysiloxane and silver decorated expanded graphite composites with high thermal conductivity, EMI shielding, and leakage-free performance

Phase change thermal interface materials (PCTIMs) have attracted significant attention due to their dual capability in temperature control and thermal buffering. However, the widespread application of PCTIMs in electronic devices is hindered by critical drawbacks such as low thermal conductivity (к), absence of electromagnetic interference shielding effectiveness (EMI SE), poor flexibility, and susceptibility to leakage. In this study, leakage-free PCTIMs were successfully fabricated with ultra-high thermal conductivity (к∥ = 23.4 W m−1 K−1, к⊥ = 8.1 W m−1 K−1), outstanding phase change functionality, exceptional EMI SE (73.2 dB), and excellent flexibility. A polyethylene glycol-modified polydimethylsiloxane (pPDMS) was synthesized through chemical grafting, demonstrating its significant potential as substrates for PCTIMs. Moreover, a designed material called silver nanoparticles-decorated expanded graphite (Ag-EG), was prepared to facilitate multidimensional material collaboration and incorporated into the pPDMS matrix to obtain Ag-EG@pPDMS composites. This integration resulted in a three-dimensional (3D) multi-layer orientation structure that enabled superior thermal conductivity in both in-plane and through-plane directions. To investigate the influence of 3D multi-layer orientation structure on Ag-EG@pPDMS, theoretical analysis was conducted using Effective Medium Theory (EMT) and Foygel thermal conduction models, which were further simulated by finite element analysis confirming substantial enhancement in material properties attributed to the 3D multi-layer orientation structure. Thermal management and electromagnetic interference (EMI) shielding applications were conducted using computers, wireless bluetooth earphones, and other electronic devices, indicating the superior thermal conductivity and EMI shielding of Ag-EG@pPDMS composites.

Performance analysis of heat pipe micro-reactor with Stirling engine based on full-scope multi-physics coupled simulation

Heat pipe micro-reactors (HPMRs) with Stirling engines for power conversion are emerging as a promising surface power technology. We developed a comprehensive multi-physics solver using the open-source finite-volume code OpenFOAM to perform high-fidelity analysis of HPMR systems’ steady-state and dynamic performance. The solver couples a 3D coarse-mesh multi-group neutron diffusion model with a 3D fine-mesh thermal conduction model using a mapping approach to accurately simulate multi-physics phenomena in the reactor core. Additionally, it integrates a 2D high-temperature heat pipe model as boundary conditions for heat transfer in the core, a 1D Stirling engine model for energy conversion, and a lumped parameter radiator model for heat dissipation. Applied to the HOMER-15 reactor system, the solver aided to identify the optimal working point of the system, achieving 3 kW of electric power with a conversion efficiency of 25.2 % under 20-Hz Stirling engine frequency and 3.34-MPa pressure. The transient full-scope simulation with the solver shows that the load-follow strategy based on gas charging and venting in Stirling engines is capable to accommodate 35 % step increase of external load. When the unexpected reactivity insertion is within 0.1$, the peak temperature in the reactor core is below the allowable limit temperature. Analysis of single failure of Stirling engines indicates that the system safety and reliability can be enhanced by either incorporating an appropriate number of engines or enhancing heat transfer between Stirling engine channels.

Features of hydrocarbon liquid-based nanofluid under augmentation of parametric ranges in non-Darcy media

Transport properties of hydrocarbon liquid-based nanofluids in non-Darcy media have key significance in chemical, thermal and mechanical engineering. Therefore, the key focus of this research is to investigate the transport mechanism in nanofluid using Koo–Kleinstreuer–Li (KKL) thermal conductivity model in non-Darcy media under squeezing and permeable effects. The functional fluid is a homogenous mixture of Cu and kerosene. The problem formation is carried out via nanofluid-enhanced properties and similarity rules. Then numerical scheme was endorsed for the results analysis under increasing physical ranges. It is observed that the velocity [Formula: see text] increased when the values of [Formula: see text] vary from 1.0 to 4.0. However, quick particles movement is noticed for [Formula: see text] for 1.0–4.0 and [Formula: see text]1.0 to [Formula: see text]4.0. Further, the thermal process in Cu/kerosene depreciates for [Formula: see text], 1.0, 1.5, 2.0, [Formula: see text], 4, 6, 8 and [Formula: see text], [Formula: see text]4.0, [Formula: see text]6.0, [Formula: see text]8.0, respectively. The stronger permeability of the lower plate highly reduced the fluid movement and depreciation in the movement can be optimized when the fluid sucks from the channel through the lower plate.

Phonon engineering enabled reduction in thermal conductivity of SnS/Cu2Se composites: An experimental and numerical insights

SnS is a promising chalcogenide-based material that shows great potential for thermoelectric applications. Lattice thermal conductivity is the only independent parameter that can be modified without disrupting the complex relationship of parameters such as electrical conductivity and the Seebeck coefficient. Herein, Cu2Se x wt% (x = 1%, 3%, 5%, 7%) composited with SnS were synthesized by hydrothermal method. The addition of Cu2Se in SnS has resulted in a suppression of the intrinsic thermal conductivity from 0.891 W/mK to 0.447 W/mK for Cu2Se 5 wt% composited SnS at 753 K. Increasing Cu2Se% in the SnS matrix has led to decrease in crystallite size from 33 nm - 29 nm, while the dislocation density and microstrain showed an increasing trend. The different physical and microstructural factors were analysed to understand the influence on thermal conductivity using numerical techniques. Physical parameters like Cu2Se distribution, pelletizing temperature, pressure, volume fraction, and intrinsic material qualities are studied using effective thermal conductivity models and Maxwell Eurecken 2 shows the best fit. The Hasselman-Johnson model analyses interfacial thermal conductivity and shows an increasing trend from 0.31 × 10–6 to 6.2 10–6 m2K/W. In addition, the microstructural variables such as dislocations, stacking faults, and point defects are present in the samples. The phonon relaxation time for each mode of vibration determined using Raman spectroscopy also points towards the decrease in contribution from optical phonons by 30% from 7.71 × 10–13 to 5.31 × 10–13 s. The temperature-dependent and power-dependent Raman spectroscopy indicated lattice softening and anharmonic coupling leading to a red shift in the spectrum. A combination of optical and acoustic phonon contributions helped to reduce the thermal conductivity by about 50% for Cu2Se-composited SnS.

A generalized thermal conductivity model of soil-rock mixture based on freezing characteristic curve

Soil-rock mixtures, served as important geotechnical materials for road construction and embankment dams, are widely distributed in cold regions. Thermal conductivity is a significant parameter in qualitatively assessing the heat transfer properties and determining the temperature field in cold regions geotechnical engineering. This study experimentally investigated the influence of rock content and temperature variations on the thermal conductivity of soil-rock mixtures, and a generalized thermal conductivity model based on the freezing characteristic curve was established. The results showed that both rock content and water-ice phase transitions affect the heat flux within soil-rock mixtures. The heat flux exhibited distinct variation trends during the freezing-thawing processes. Notably, hysteresis in heat flux was observed during the early stages of freeze-thaw cycles, disappearing after 8, 6, and 4 freeze-thaw cycles for soil-rock mixtures with rock contents of 10 %, 25 %, and 40 %, respectively. Additionally, the rock content seldom influenced the freezing temperature, while it significantly affected the thermal conductivity of soil-rock mixture. Furthermore, a generalized thermal conductivity model based on the freezing characteristic curve was established and verified, the proportion of thermal conductivity associated with the water-ice phase increased for the modified parallel model, while the modified series thermal conductivity model exhibited reversed results as the temperature decreased. Moreover, all the thermal conductivity models could obviously reflect the water-ice phase transition on the thermal conductivity of soil-rock mixture. However, the modified effective thermal conductivity model agreed best with the experimented results.

Investigation of magnetite water nanofluid flow through a stretching sheet using the Hamilton and Crosser model for nanoparticle shape factor and effective thermal conductivity

The main objective of this current investigation is to study the heat and mass transfer of the convective MHD Fe3O4−H2O nanofluid through an expanding sheet in the presence of thermal radiation. The Hamilton and Crosser model describes the shape and effective thermal conductivity. The fluid flow governing PDEs has been transformed into a system of ODEs by utilizing appropriate similarity transformation. We used SQLM or Spectral Quasilinearization method to solve them numerically and draw the graphical conclusion using MATLAB software. The skin friction, the Nusselt number and the Sherwood number have been determined numerically and portrayed graphically for the pertinent parameter. It has been observed that for the increment of the volume fraction of Fe3O4 nanoparticles, the fluid velocity tends to reduce while the thermal profile is enhanced. We also observed that for the increment of the buoyancy parameter, the mass transfer is enhanced. Additionally, for the enhancement of the Schmidt number from 0.1 to 1.2, the rate of mass transfer coefficient increases very rapidly. The outcome of the current study has been compared with previously published data, and there is a satisfactory agreement.

Discussion of “Thermal conductivity of porous building materials: An exploration of new challenges in fractal modelling solutions”

In November 2023 this journal published “Thermal conductivity of porous building ma­terials: An exploration of new challenges in fractal modelling solutions”. That paper gauges four fractal building materials’ thermal conductivity models, concluding that fractal-geometry-based approa­ches appear “a promising method” as they “demonstra­te high reliability in repro­ducing experimental data”. This discussion of the pa­per aims to shine a different light on the potential of fractal thermal conductivity models. It shows that good agreement with experimental data usually ori­ginates from calibration of various “physical” factors comprised in these models, with the fitted numbers commonly deviating from physical rea­lity. Moreover, exemplary instances reveal that good agreement with experimental data is obtained des­pite misinterpretation of measured outcomes or critical defects in model development, or, exceptio­nally, due to fabrication of validation information. This discussion does hence not share the pa­per’s positive opinion on the prospects of fractal-geometry-ba­sed ther­­mal conductivity models, and advises caution instead.