Thermal Conductivity Model Research Articles

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.

Machine learning driven design of high-performance Al alloys

Aluminum (Al) alloys with both high strength and thermal conductivity (TC) are promising structural materials for wide application across different industries. Yet, design of such alloys is challenging, since strength and TC often share a trade-off. In this paper, we build prediction models for TC and ultimate tensile strength (UTS) of Al alloys using eXtreme gradient boosting (XGBoost) and support vector machine (SVM) algorithms, respectively. The models take physical descriptors from the alloy composition into account. Lasso and Gini Impurity algorithms were adopted for feature engineering. Guided by the models, an Al-2.64Si-0.43Mg-0.10Zn-0.03Cu alloy with TC over 190 W·m-1·K-1 and UTS over 220 MPa was designed. The alloy was fabricated and tested by experiment, and its UTS and TC are close to the model prediction. Microstructure characterization suggests that the fragmented and spherical Si phase, along with a few non-spherical Si phases, may be a key reason for the improved properties.

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

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

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.

Investigation of the Theoretical Model of Nano-Coolant Thermal Conductivity Suitable for Proton Exchange Membrane Fuel Cells.

The fuel cell vehicle is one of the essential directions for developing new energy vehicles. But heat dissipation is a critical technical difficulty that needs to be solved urgently. Nano-coolant is a promising coolant that can potentially replace the existing coolant of a fuel cell. However, its thermal conductivity has a significant impact on heat dissipation performance, which is closely related to nanoparticles' thermal conductivity, nanoparticles' volume fraction, and the nano-coolant temperature. Many scholars have created the thermal conductivity models for nano-coolants to explore the mechanism of nano-coolants' thermal conductivity. At present, there is no unified opinion on the mechanism of the micro thermal conductivity of the nano-coolant. Hence, this paper proposed a novel model to predict the thermal conductivity of ethylene glycol/deionized water-based nano-coolants. A corrected model was designed based on the Hamilton & Crosser model and nanolayer theory. Finally, a new theoretical model of nano-coolant thermal conductivity suitable for fuel cell vehicles was constructed based on the base fluid's experimental data.

Ultralow thermal conductivity in Si–Ge nanograin mixtures: A cost-effective granular material for thermoelectric applications

This paper presents a theoretical study of the thermal conductivity of Si–Ge nanograin mixtures using a multiscale computational methodology based on solving the Boltzmann transport equation for phonons with first-principles techniques. A size-dependent correction factor is developed to account for the spatial dependence of the phonon distribution function on nanograin size, with parameters derived from the phonon properties of infinite Si and Ge crystals. This approach makes it possible to accurately calculate the thermal conductivity within a single nanograin, using force constants obtained from first-principles calculations. Thermal energy transport by phonons across grain boundaries is modeled by accounting for phonon transmission by two-phonon processes, weighting specular, and diffuse transmission for each phonon mode as a function of the root-mean-square roughness of the boundary relative to the phonon wavelength. The boundary thermal conductance model, previously validated against experimental data, is implemented using first-principles techniques. This approach excludes specular transmission for phonon modes with specific symmetries while ensuring conservation of the total number of modes in each symmetry class. The study examines the influence of grain size, nanograin mixture composition, temperature, and boundary asperities on the thermal conductivity of nanograin mixtures.

Three-dimensional Darcy-forchheimer modelling of MHD hybrid nanofluid over rotating stretching/shrinking surface with Hamilton-Crosser and Yamada-Ota conductivity models

Instead of single nanoparticles, the combined effects of more than one solid nanoparticle have presented wide range of real-word application in several engineering as well as biomedical areas. The present analysis brings out a combined effect of Hamilton-Crosser and Yamada-Ota thermal conductivity models for the magnetohydrodynamic flow of hybridised fluid vi a rotating stretching/shrinking surface. The hybridised fluid comprised of silver and molybdenum tetrasulphide nanoparticle in association with the effect of Joule heating enriches the flow properties. Additionally, the Darcy-Forchheimer inertial drag with the impose of thermal radiation affecting the flow as well as heat transfer properties. The proposed mathematical model equipped with physical assumptions is transmuted into dimensionless form by utilizing similarity functions. Further, the traditional numerical technique is taken care of for the solution of the transmuted model equipped with diversified factors. The important characteristic of several factors are deployed graphically affecting various flow profiles. Finally, the outstanding features explored in the proposed investigation are stated as below; the comparative analysis reveals that, the heat transport properties became advanced in case of Hamilton-Crosser model rather than the Yamada-Ota conductivity model. However, the heat transportation rate is controlled by the increasing Eckert number but thermal radiation enhances it significantly.

Development of thermal conductivity model for alumina hybrid nanosuspensions using AI technique

Development of thermal conductivity model for alumina hybrid nanosuspensions using AI technique

Conditions for formation and preservation of andesite-hosted mafic enclaves during the 2018 Lower East Rift Zone eruption of Kīlauea

Andesites erupted at Kīlauea in 2018 in the Lower East Rift Zone for the first time in the known geological record. The evolved lavas erupted at Fissure 17 of the 2018 eruption, ranging from andesites to basaltic andesites, contain abundant mafic enclaves both in the lava flows and the ejecta, which are unusual at Kīlauea and in Hawai'i in general. Textural observations indicate that the enclaves originate from incomplete mixing of two magmas rather than the incorporation of cold basaltic wall rock. We suggest, on the basis of bulk and mineral compositions, that the source of the mafic enclaves is the early 2018 evolved basalt magma (phase 1b) that erupted concomitantly at adjacent fissures, which mixed with the andesite to produce the range of basaltic andesite compositions observed at Fissure 17. The coexistence of homogenized basaltic andesites and mafic enclaves within the same magma require a mixing mechanism resulting in both complete homogenization and preservation of enclaves. We propose that the range of mixing and mingling processes may be explained by spatial and temporal variability in the mixing percentages of the phase 1b basalt and the andesite within the andesite magma chamber. Field observations, chemical compositions, and 2D thermal conduction models suggest that enclaves are preserved where the basalt contribution to mixing is less than roughly 40 %, as a result of microlite crystallization leading to rigidification of the enclave magma. Above this threshold, the mixed magmas became largely homogenized. The scarcity of mafic enclaves at Kīlauea and in the Hawai'i igneous record is likely explained by mixing between magmas that lack sufficient compositional and rheological contrasts to preserve them.

Investigation on in-situ thermal behavior of tunnel surrounding rock based on the thermal probe test

Heat-transfer mechanism of energy tunnel is different from that of conventional borehole heat exchanger, where the thermal flux flows along perpendicular to the tunnel circumferential direction. However, the existing measurement methods cannot directly detect the in-situ thermal behavior and thermal conductivity of surrounding rock of tunnel circumferential direction. Hence, a thermal probe test (TPT) equipment was developed and the TPT was performed to investigate the in-situ thermal behavior of surrounding rock, the thermal conductivity measurement methods of tunnel surrounding rock was proposed and compared with laboratory measurement methods. The results showed that the developed TPT equipment achieved to directly detect the in-situ thermal behavior and thermal conductivity of circumferential surrounding rock. There was a significant variation in thermal response curves of different test areas due to the fact that joint development affected the transfer paths of the thermal flux, the temperature difference between test point 1 and test point 2 could reach up to 11.4 °C. The thermal conductivity tested by TPT was reliable and reflected the in-situ thermal behavior, the deviation was 6.99 % and 1.08 %, respectively, compared with laboratory measurement results. The joint development of the surrounding rock had a major impact on the thermal conductivity, where the thermal conductivity ranged from 0.66 to 2.91 W/m K in the 1# borehole and 1.96 to 3.66 W/m K in the 2# borehole. The local thermal conductivities were difficult to apply to an energy tunnel design, hence, the comprehensive thermal conductivity model of surrounding rock with joints was proposed based on series–parallel theory and was simplified according to the heat-transfer mechanism of energy tunnel. The comprehensive thermal conductivity model provided a new idea for obtaining the heterogeneity of thermal-physical properties of tunnel surrounding rock, which improved performance predictions and optimized design strategies for energy tunnel projects, enhancing their efficiency and reliability in various applications.

Numerical simulation and experimental analysis of thermal conduction and stress in laser cladding repair of thin-walled parts

To minimize the deformation of thin-walled parts during the laser cladding process and enhance the quality of the repaired parts, the Finite Element Abaqus software was used to develop a thermal conduction and 3D stress model, the heat source used in the experiments was a double ellipsoid heat source model. This model simulates the thermal process and the deformation resulting from residual stresses in the laser cladding process on a titanium alloy substrate with a thickness of 2 mm. Through the simulation, the temperature field of the substrate at the end of each pass was obtained, and the cladding sequence with the smallest temperature gradient during the multi-pass laser melting process was determined. By combining simulation and practice, the multilayer stacking pattern was optimized to achieve deformation control. Analog simulation experiments indicate that the optimized single-layer multi-pass laser cladding method results in less heat accumulation and thermal stress compared to the unidirectional sequential scanning method. The flatness test results show that the specimens have less deformation with the optimized multilayer stacking method. In addition, the metallographic organisation of the two cladding specimens is analysed in this paper, and the results show that the optimised specimens exhibit excellent microstructures and properties.

Thermal conductivity measurements of liquid ethane and ethane + propane binary mixtures

Based on the transient hot-wire apparatus, the thermal conductivity of ethane was measured in the temperature range of 146–247 K and pressure < 14 MPa in the liquid phase. The thermal conductivity of ethane + propane binary mixture was measured in the temperature range of 156–288 K and pressure < 25 MPa in the liquid phase. The mole fractions of ethane in binary systems are 0.198, 0.525, and 0.736. The deviation between experimental results and REFPROP calculation falls within 3 % of ethane and mixture. Subsequently, the previous established thermal conductivity model, derived from dimensional analysis, was employed to predict the thermal conductivity of n-alkanes mixture. The mixture critical parameters were obtained first by the mixing rules, and the thermal conductivity of the mixture were calculated. Comparisons were made between the experimental data of ethane and the previously constructed n-alkane model, resulting in an average absolute relative deviation (AARD) of 4.42 %. Similarly, the experimental data of the ethane + propane mixture was compared with the mixture prediction model proposed in this study, yielding an AARD of 1.92 %. The relative deviation between experimental data and model calculations demonstrates good consistency.

Prediction of thermal conductivity of frozen soils from basic soil properties using ensemble learning methods

Thermal conductivity is one of the important properties required for understanding the frozen soils behavior. There are several models available in the literature for the prediction of thermal conductivity of frozen soils based on the proportions of unfrozen water, ice, gas, and soil particles. In this study, two ensemble learning methods-based models; namely, the Random Forest (RF) model and the Least Squares Boosting (LSB) model, are extended to estimate the thermal conductivity of frozen soils. These models utilize basic soil properties as input parameters that include water content, dry density, temperature, and fractions of gravel, sand, silt, and clay, can be measured easily, or determined. Additionally, seven widely used thermal conductivity models, referred to as the traditional models for frozen soils, were evaluated. Both the RF and LSB models, as well as the traditional models, were assessed using data of 823 tests derived from 43 soils with different textures that were gathered from the literature. The results highlight that the traditional models have their strengths and limitations in terms of their use for different types of soils. In contrast, the proposed ensemble learning methods-based models provide higher prediction accuracy compared to the traditional models and can be applied to all soil types and temperature ranges. Furthermore, estimation from the ensemble learning methods-based models can be used to provide probability of multi-dimensional analysis of frozen soils.

Cross-scale study of heat transfer performance in metal rubber with complex topological structures

Metal Rubber (MR), characterized by its porous topology and metal-based entangled structure, is commonly utilized in high-temperature environments. The intricate nature of MR's structure complicates the accurate experimental investigation of its thermophysical properties, thereby restricting its broader applications. Therefore, based on numerical simulation, the three-dimensional reconstruction of the spatial topology of MR is achieved. Additionally, MATLAB-LS/DYNA-ABAQUS is coupled to replicate the heat transfer process of MR at macro-microscopic scales. Our findings elucidate the relationship between MR's density, number of contact points, and thermal conductivity, revealing a stepwise decrease in thermal conductivity along the forming direction and a spatially varying anisotropic heat transfer mechanism that involves energy feedback on non-forming surfaces. Specifically, at the material level of investigation, a molecular dynamics model for heat transfer in microscopic metal wire contacts was generated. This model enables the simulation and dynamic tracking of atomic group thermal behavior under temperature effects. Finally, equivalent thermal conductivity (ETC) tests were conducted concurrently. By integrating the thermoelectric analogy method, we introduced for the first time a hybrid series-parallel mode and the tortuosity of discontinuous materials. This approach comprehensively considers critical factors such as porosity, temperature, and interlayer thermal resistance, culminating in the development of a predictive numerical model for thermal conductivity in porous metal-based materials. In this study, a bottom-up multiscale research approach is proposed to deeply explore the spatially multidirectional heat transfer mechanisms of microporous metal-based tangled materials, from the material level to the complex topological structural level. Simultaneously, new dimensions are opened for the study of such materials with unique discontinuous structural characteristics.

Three-phase lag model for thermal conductivity of a thermo-viscoelastic porous medium

This paper investigates the propagation of waves and the thermal behavior in a thermo-viscoelastic porous medium using the three-phase-lag (TPL) model which accounts for phase lags in the heat flux vector, temperature gradient and thermal displacement gradient. The study aims to capture the interactions between thermal, mechanical, and structural properties of the thermo-viscoelastic porous, isotropic, homogeneous medium. The governing equations, incorporating the TPL heat conduction law and constitutive relations for the viscoelastic porous material, are derived and analyzed. The impact of relaxation times, porosity, and viscoelastic parameters on heat propagation is investigated through analytical solutions by normal modal analysis. Analytical representations of various physical quantities (stresses components, displacements, temperature,…) in the material's domain are derived. These expressions are then assessed numerically for a specific material, with the outcomes depicted graphically. A comparison is made between the predictions of the three-phase-lag (TPL), the dual-phase-lag (DPL) and Lord–Shulman (L–S) theories in the absence and presence of voids.

Temperature-Dependent Thermal Conductivity Identification by Bayesian Inference

The identification of temperature-dependent thermal conductivity in aerogel material, which is commonly used as insulation in thermal protection structures of high-speed aircraft, faces the challenge of selecting the appropriate model in engineering practice. Considering the uncertainties in the selection process of an appropriate functional model, a novel Bayesian probability method computational framework based on response data is established to improve the accuracy of thermal conductivity identification. Three implementation steps are presented: 1) the database of candidate models is established; 2) the reconstructed signals can be calculated by a heat transfer analysis model; and 3) the posterior probability of each candidate model is estimated to obtain the optimal thermal conductivity model and determine the characteristic coefficients. Numerical simulations of a theoretical one-dimensional heat transfer model and a curved thermal protection structure are performed to verify the proposed method. Then, a heating experimental investigation of the curved thermal protection structure is conducted to identify the temperature-dependent thermal conductivity of aerogel material. The results indicate that the temperature-varying thermal conductivity can be accurately identified by the proposed method, which can be applied to the heat transfer analysis and design of aerogel materials in high-speed aircraft.

Аналіз розподілу температури у двошаровій композитній циліндричній оболонці зумовленої конвективним теплообміном на її зовнішній поверхні

A non-stationary thermal conductivity problem for a two-layer cylindrical shell is formulated. The materials of the constituent layers of the shell are assumed to be homogeneous and isotropic. This shell is convectively heated by the external environment. The system of linear two-dimensional equations for the integral temperature characteristics summed over the component layers of the shell was used as the initial system of equations of the problem under consideration. When obtaining this system, the hypothesis of a linear distribution of temperature along the thickness of the entire shell was applied. On the basis of the developed two-dimensional mathematical model of thermal conductivity for layered cylindrical shells, a general solution to the thermal conductivity problem for a two-layered cylindrical shell was obtained. A temperature distribution was found for such a shell, which is locally convectively heated by the external environment in a rectangular region on the outer surface. For the numerical analysis, a metal-ceramic cylindrical shell was considered, the inner layer of which is made of tungsten, and the outer layer is made of ceramics. Under such a structure and conditions of heat exchange with the external environment for the considered shell, the effect of its geometric parameters and thermophysical characteristics of the materials of its component layers on the temperature field on the outer surface of the shell was investigated. The revealed new qualitative and quantitative regularities can be used to estimate temperature fields in composite elements of layered structures and in structures with one-sided coatings. The dependences of temperature distributions on geometric parameters and thermophysical characteristics obtained in this work are the basis of the theoretical basis for the analysis of temperature regimes of metal-ceramic cylindrical shells. In particular, metal-ceramic dental crowns to predict their temperature regimes are modeled by the two-layer metal-ceramic cylindrical shells described above, which are locally convectively heated by the external environment

Cascaded lattice Boltzmann simulation of Newtonian and non-Newtonian mixture nanofluids with variable thermophysical properties in a cavity with vertical heat radiator

The central moments-based cascaded lattice Boltzmann method (CLBM) for then Newtonian and non-Newtonian Buongiorno’s model mixture nanofluids (CuO, ZnO, Al2O3-water) has been implemented and applied in a square chamber with a vertical heat radiator using accelerated graphics processing unit (GPU) computing through compute unified device architecture (CUDA) C/C++ platform. Due to the higher numerical stability, the CLBM is a superior numerical tool to the raw moments-based MRT-LBM (multiple-relaxation-time lattice Boltzmann method). Three different models for the viscosity and thermal conductivity of the nanofluids: (i) the Binkmann model for the constant viscosity and the Maxwell model for the constant thermal conductivity (ii) Binkmann and Maxwell model with temperature dependent Brownian motion and (iii) Corcione model with non-Newtonian fluid where the temperature and strain rate determine the nanofluid effective thermal conductivity and viscosity, have been used. The enclosure’s upper and bottom walls are thermally adiabatic, but the left and right walls are uniformly cold. A vertical heater is immersed in the middle position of the cavity. The benchmark results for non-Newtonian, Newtonian, and nanofluids for the various computational domains are used to validate the current code adequately. The Bingham number (Bn), the Rayleigh number (Ra), and The volume fraction of the nanoparticles (ϕ) are the three key parameters that are varied in this investigation to demonstrate the effects of natural convection on the isotherms, streamlines, isolines of nanoparticle volume fractionation, yielded and unyeilded zone, and average Nusselt number (Nu¯). The Brownian motion effects of the nanoparticles augmented the average rate of heat transfer and the use of the Bingham nanofluids reduced the heat transfer enhancement. For the CuO-water nanofluid, the augmentation of the rate of heat transfer is 15.42% from ϕ=0 to 4% while Ra=106 and the corresponding heat transfer enhancement for the ZnO-water nanofluid is 11.11%. For the Bingham fluid, the rate of heat transfer increases 7% from Ra=105 to Ra=106 while ϕ=2% and Bn=0.3. The findings can be applied to optimize automotive radiator systems, which are crucial for maintaining engine temperature.

Statistical and numerical analysis of magnetic field effects on laminar natural convection heat transfer of nanofluid in a hexagonal cavity

This paper presents a statistical and numerical investigation that examines the optimization and sensitivity analysis of the unsteady laminar natural convective heat transfer flow of Fe3O4-water nanofluid in a hexagonal cavity considering the impacts of a sloping magnetic field in one-component nanofluid model. The inclined walls of the cavity are maintained at a constantly low temperature, while the bottom wall is uniformly heated. The upper wall, however, is regarded as adiabatic. The nanofluid thermal conductivity model incorporates the impact of Brownian motion. The Galerkin weighted residual finite element method has been employed to solve the governing dimensionless equations. The results are provided regarding the average Nu, streamlines, and isotherms. The study uses response surface methodology to analyze the sensitivity of parameters such as the Ha, Ra, and nanoparticle volume percentage. Using a response surface policy allows for optimizing the process and identifying the most favorable circumstances to achieve the maximum thermal transfer rate. The flow pattern of the nanofluid is significantly affected by the magnetic field and its alignment. The numerical results indicate a significant rise in the average Nu as the nanoparticle volume percentage, magnetic field inclination angle, nanoparticle type factor, and Ra increase. Conversely, the Hartmann number and the nanoparticle's diameter have contrasting effects. When considering Brownian motion, the average Nu grows by 225.89 % for Ra = 106 with ϕ = 0.03 and 25.28 % for the other case. The optimal condition for heat transfer occurs when Ra = 106, Ha = 4, and ϕ =0.03 while keeping the other parameters constant.

Influence of degree of saturation on the thermal conductivity of soils: Experimental and comparative model analysis

The thermal conductivity can characterize thermal behaviour of soils in different engineering studies: environmental, geothermal, geotechnical and buildings construction. However, accurately measuring and predicting this parameter poses a challenging task. Measuring this parameter can be very complex, considering several factors, such as soil heterogeneity and external climatic conditions. In addition, predictions models may not capture all the nuances of real-world soil conditions, leading to less accurate predictions of ?. The objectives of this paper encompassed two primary aspects: (i) Evaluation of laboratory tests of thermal conductivity of unsaturated soil. (ii) Assessment of five highly recommended soil thermal conductivity models to determine their validity and strengthen their trustworthiness. The studied material consisted of calcareous tufa locally available in Beni-Saf region (Algeria). The tested samples were compacted to the Standard and Modified Proctor Optimum (SPO, MPO) followed by drying periods under laboratory conditions. The thermal conductivity of samples was evaluated using transient method. The models’ predictive results of the thermal conductivity were assessed with different criteria such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Coefficient of Determination R². Furthermore, this work also attempts to deliver an in-depth discussion of the effect of degree of saturation Sr on the thermal conductivity of soils.