Temperature Difference Research Articles

Investigation on the Temperature and Stress Differences Between Sunny and Shady Surfaces of High-Altitude Concrete Bridge Piers

Investigation on the Temperature and Stress Differences Between Sunny and Shady Surfaces of High-Altitude Concrete Bridge Piers

Valence Band Modification and Enhanced Phonon‐Phonon Interactions for High Thermoelectric Performance in GeTe

AbstractThe strong coupling between carrier and phonon transport in thermoelectric (TE) materials severely limits improvements to the figure of merit (ZT). In this work, an approach is proposed to weaken electron‐phonon coupling, effectively enhancing the TE performance of GeTe. Alloying with Zn4Sb3 reduces excessive carrier concentration (nH), widens the bandgap, and promotes band convergence, synergistically improving charge carrier transport and ensuring a high power factor. Additional Pb doping further optimizes nH, boosting the power factor even more. Moreover, phonon transport is suppressed through Pb doping, as reflected in enhanced acoustic‐optical interactions due to the crossing of optical and acoustic modes, and a reduction in sound group velocity. This reinforced strong phonon scattering, combined with multi‐scale hierarchical nano/microstructures in the matrix, significantly reduces lattice thermal conductivity. As a result, a high ZT of 2.1 is achieved at 753 K in Ge0.9Pb0.1Te+0.9%Zn4Sb3. Alongside optimized mechanical performance, a high power density of 1.46 W cm−2 is realized at a temperature difference of 350 K in the fabricated 7‐pair TE module. The findings demonstrate the effectiveness of a stepwise optimization strategy for developing high‐performance TE materials.

Thermal Characteristics of the Extreme Cases of Tropopause Over the Tropics

ABSTRACTThe anomalous variability of extreme cases of the tropical tropopause provides insight into the stratosphere‐troposphere exchange process crucial for understanding climate change. The present study analyses the extreme variability of the tropopause and its thermal structure over the tropics using GPS radio occultation data over the period 2006–2019. The extremely cold and warm tropopauses and extremely high and low tropopauses are identified based on the cold point tropopause temperature and height, respectively, when their values exceed two standard deviations with respect to their climatological means. The analyses revealed frequent occurrence of extreme cases of tropopause over the Atlantic Ocean compared to the Western Pacific Ocean. Individually, extremely warm and low cases occur more frequently over the subtropics, while extremely cold and high cases occur frequently over the deep tropics. These extreme cases pose different thermal structures bounded within the extremely low and high tropopauses throughout the tropics. The height difference between the extremely high and low tropopause cases is wider over the Atlantic Ocean and adjoining areas compared to the western Pacific Ocean. The temperature difference between the extremely warm and cold tropopause cases is higher in the Atlantic, Central Pacific, and Indonesian regions compared to the American, Indian Ocean, and western Pacific Ocean regions. The relationship between the El Niño Southern Oscillation (ENSO) phases and extreme tropopause cases is also investigated which reveals a higher occurrence of extremely high tropopause cases during the El Niño phase while low tropopause cases during the La Niña phase. Our analysis also revealed the thermal patterns of the extreme cases characterising colder and sharper tropopause over the convective regions compared to subsidence regions.

Synthetic iterative scheme for thermal applications in hotspot systems with large temperature variance

A synthetic iterative scheme is developed for thermal applications in hotspot systems with large temperature variance. Different from previous work with linearized equilibrium state and small temperature difference assumption, the phonon equilibrium distribution shows a nonlinear relationship with temperature and mean free path changes with the spatial temperature when the temperature difference of system is large, so that the same phonon mode may suffer different transport processes in different geometric regions. In order to efficiently capture nonlinear and multiscale thermal behaviors, the Newton method is used and a macroscopic iteration is introduced for preprocessing based on the iterative solutions of the stationary phonon BTE. Macroscopic and mesoscopic physical evolution processes are connected by the heat flux, which is no longer calculated by classical Fourier’s law but obtained by taking the moment of phonon distribution function. These two processes exchange information from different scales, such that the present scheme could efficiently deal with heat conduction problems from ballistic to diffusive regime. Numerical tests show that the present scheme could efficiently capture the multiscale heat conduction in hotspot systems with large temperature variances. In addition, a comparison is made between the solutions of the present scheme and effective Fourier’s law by several heat dissipations problems under different sizes or selective phonon excitation. Numerical results show that compared to the classical Fourier’s law, the results of the effective Fourier’s law could be closer to the BTE solutions by adjusting effective coefficients. However, it is still difficult to capture some local nonlinear phenomena in complex geometries.

Numerical study on the hydrothermal characteristics of a wire-wrapped rod bundle with nonuniform wire pitches

In this study, thermal hydraulic behaviors in a 19-pin bundle fuel assembly with nonuniform wire pitches is investigated by combing CFD with the Kriging method. To optimize the design, two geometric variables—the ratio of inner pitch to reference pitch (Pi/P) and the ratio of outer pitch to reference pitch (Po/P)—are selected, and the design space is sampled using Latin Hypercube Sampling (LHS). The sampled points are then subjected to CFD analysis. Convergence is considered achieved when the residuals of all variables are below 1e-5. The optimization problem aims to minimize the objective function, which is a linear combination of the cross-sectional temperature difference and friction factor. Sequential Quadratic Programming (SQP) is employed to search for the optimal point using a constructed meta-model. When compared to the reference shape, the optimal shape exhibits higher axial velocity in the inner channel, higher average temperature, smaller temperature difference at the outlet section, and reduced pressure drop in the fuel assembly. The Kriging model accurately predicts the cross-sectional temperature difference and friction coefficient for the optimal shape, consistent with the CFD calculation results. This confirms the accuracy and feasibility of the Kriging model in fuel assembly optimization.

A solar thermoelectric system by temperature difference for efficient removal of chromium (VI) in water and soil

In this work, we designed and developed a facile solar thermoelectric generator (STEG)-based system and a new electrokinetic remediation (EKR) system, which consists of main electrodes and unenergized auxiliary electrodes. The prepared nanocomposite was investigated for the effectiveness of the STEG+PANI-CNT/GF system in remediating Cr-contaminated. Photothermal performance test were applied in order to examine this STEG could export a power density of 365.56 mW/dm2 and output potential of 801 mV at the temperature difference of 50 ℃. Thus the STEG could be used as the power to construct a Cr(VI) removal system using polyaniline (PANI) film/carbon nanotubes (CNT) modified graphite felt (GF) electrode (PANI-CNT/GF) as cathode and graphite rod as anode. The as-prepared STEG+PANI-CNT/GF system exhibited a significant Cr(VI) removal efficiency (96.2 % in water) through electromigration, electro-adsorption and electroreduction. Moreover, a multi auxiliary electrodes (AEs) system (STEG+PANI-CNT/GF+AEs) with six PANI-CNT/GF auxiliary electrodes was constructed in remediating Cr(VI)-contaminated soil, showing Cr(VI) removal efficiency of 16.7–60.1 % higher than that of STEG+PANI-CNT/GF. The PANI-CNT/GF auxiliary electrodes could bind Cr(VI) and adjust electric field distribution, contributing to adsorption and reduction of Cr(VI). Consequently, this work provides a promoting approach for heavy metals removal in future application.

Assessing the impact of ecological, climatic, and socioeconomic factors on age-specific malaria incidence in India: a mixed-model approach using the Global Burden of Disease Study (2010–2019)

BackgroundMalaria continues to be a critical public health concern in India, predominantly driven by complex interplays of ecological, climatic, and socioeconomic factors.MethodsThis study aimed to assess the association between climatic variables (temperature and precipitation) and malaria incidence across India from 2010 to 2019, utilizing data from the Global Historical Weather and Climate Data for climate metrics and the Global Burden of Disease Study for malaria incidence rates. Generalized Linear Mixed Models (GLMMs) with a Poisson distribution were employed to analyze the data, adjusting for socio-economic status, as indexed by the Human Development Index (HDI).ResultsThe results indicated a declining trend in both the number of malaria cases and age-specific incidence rates (ASIR) over the study period. In 2010, India reported approximately 20.7 million cases with an ASIR of 1688.86 per 100,000 population, which significantly reduced to 9.8 million cases and an ASIR of 700.80 by 2019. High malaria incidence was consistently observed in the states of Jharkhand and Odisha, whereas Sikkim reported the lowest numbers. Statistical analysis identified significant associations between malaria incidence and both temperature deviations and precipitation levels, with variations also linked to HDI, suggesting better detection and reporting capabilities in more developed areas.ConclusionThe study underscores the critical interactions between climatic variables and socio-economic factors in shaping the trends of malaria incidence across India. These findings highlight the necessity for adaptive, localized public health strategies that integrate environmental monitoring with socio-economic data to efficiently predict and manage malaria outbreaks.

Optimal design of a high-performance heat exchanger for modular thermoelectric generator towards low-grade thermal energy recovery

Thermoelectric generator (TEG) has been identified as a promising method for low-grade thermal energy recovery owing to its lack of moving parts, scalability, and compatibility with other devices generating waste heat. Heat exchanger, as one of the most important components of the modular TEG, plays a crucial role in improving the overall performance of the TEG. Nevertheless, flow maldistribution inside the heat exchanger results in uneven surface temperature field of the heat exchanger, which will ultimately limit the output capacity of the TEG. Achieving a homogeneous flow distribution within the heat exchanger while minimizing flow resistance is essential. To address this, optimization of a plate-shaped heat exchanger for the modular TEG is conducted using CFD analysis and the Taguchi method to identify the optimal combination of parameters. The optimized heat exchanger demonstrates a flow maldistribution intensity (ζ) of only 4.75 % and a low flow resistance of 1.16 kPa. Furthermore, a unit of the modular TEG is constructed using two optimized heat exchangers and commercial thermoelectric modules (TEMs), and its performance is analyzed via an analytical model. The results indicate that the power per module, net power density, and conversion efficiency reached 1.2 W, 51.4 kW/m3, and 1.92 %, respectively, at a temperature difference of 70 °C. These findings suggest that the optimized heat exchanger could provide high output performance compared with other literature, offering significant potential for low-grade heat energy recovery.

Analytical study on plastic loosening zone of weak surrounding rocks tunnel in high cold areas

AbstractThe analysis of plastic loosening zone of tunnels with cold condition, high in situ stress, and weak stratum is the key scientific problem of tunnel construction in cold areas. Based on the unified strength theory and considering the coupling effect of high in situ stress and low‐temperature field, the analytical model of the plastic loosening zone of tunnel surrounding rocks was proposed, and the influence laws of physical parameters (initial ground stress, freezing temperature, excavation radius, and intermediate principal stress) was explored. The results illustrate that: (1) with the coupling of low temperature and stress fields, the in‐situ stress has a more significant effect on the radius of the plastic loosening zone of the tunnel surrounding rocks, showing a nonlinear correlation. When the in situ stress is small, the influence of the temperature field on the radius of the plastic loosening zone is more obvious. (2) The radius of the plastic loosening zone of the tunnel surrounding rocks increases synchronously with the excavation radius and gradually decreases with the increase of the intermediate principal stress. (3) The greater the temperature difference in the low‐temperature field, the tunnel stability has a more significant response to the intermediate principal stress and is positively correlated with the coefficient of the intermediate principal stress. (4) In the actual project, the proposed model can well describe the mechanical behavior and deformation characteristics of tunnel surrounding rocks in low‐temperature environment, showing applicability. The research results are expected to provide a theoretical basis for the study of tunnel stability in cold areas.

Structural Design and Optimization on Three‐Row J‐Type Air Cooling Channel of Pouch LiB Module

To enhance the cooling efficiency of pouch lithium‐ion battery modules, a three‐row J‐type air cooling channel structure is proposed, utilizing the previously developed multiple inlet/outlet air cooling frames. The influence of the location and number of inlets and outlets on heat dissipation performance is investigated through six air cooling channel schemes, providing a baseline for the multiobjective structural optimization of the proposed structure. Three important structural parameters, , , and l, of its air convergence and divergence plenums are selected as the design variables to improve the airflow uniformity in branch channels and minimize the pressure drop between inlets and outlets. The final design exhibits superior heat dissipation performance compared to baseline. It is noted that the airflow root mean square error in branch channels is reduced by 75.64%, while the pressure drop is increased by 19.74%. These are the critical factors for ensuring the heat dissipation performance of battery module. The maximum temperature and the maximum temperature difference of battery module are reduced by 5.29% and 23.91%, respectively, which help maintain its working temperature within a reasonable range.

Optimization of cooling system parameters with temperature field of mass concrete during hydration

Embedded cooling pipe system is regarded as the primary means in mass concrete to control the temperature. The effects of three factors are investigated on the thermal field of mass concrete by the combination of measurement, theoretical analyze and numerical simulation in this paper, including cooling pipe spacing, pipe diameter and pipe arrangement. The results demonstrate that the peak temperature is reduced by the increase in both of the pipe distance and pipe diameter. The peak temperature is measured to decrease from 1 °C to 3 °C on the monitoring points, with additional 0.5 m of pipe spacing or 10 mm of pipe diameter. The serious influence is conducted by the pipe diameter on the temperature difference, and the selection of cooling pipe diameter is considered to balance multiple problems in the project necessarily. The serpentine arrangement is more widely used for better cooling and construction in the comparison of the circular arrangement. The results on the optimization of cooling system are utilized for the project to control the hydration heat accurately and reduce or even prevent the generation of cracks.

Chronobiological perspectives and meteorological associations in symptomatic popliteal artery aneurysms

ABSTRACT The potential influence of circadian rhythm, seasonal variations, and alterations in meteorological parameters has been studied across various vascular events. However, there is a lack of evidence on the potential chronobiological impacts on thromboembolic events related to the most common peripheral aneurysm, the popliteal artery aneurysm (PAA). Data was obtained from a German PAA registry and the German Meteorological Service (Deutscher Wetterdienst). In this observational cohort study seasonality and chronobiology as well as associations with meteorological parameters of symptomatic PAA were investigated. In a multivariate logistic regression analysis, it was further analyzed whether meteorological parameters could distinguish asymptomatic from symptomatic patients in the registry. Of 1200 registered PAA, n = 142 PAA presented with acute limb ischemia between February 2011 and September 2022. More symptomatic patients (57.0%) presented to the hospital between January and June than in the second half of the year with a nadir in the fall season. Symptom onset was predominantly in the morning hours (39.5%). Atmospheric pressure and humidity values from the index dates diverged from a normal distribution showing a bimodal (“double-peak”) configuration. Most patients developed symptoms after a reduction in temperatures compared to 1 or 2 d prior to the index date. However, we found evidence for an interaction between age and temperature difference, where the effects of a decreasing temperature fade with increasing age. Facing the complexity of individual-environment interactions, further investigations are needed to determine whether meteorological parameters are true risk modifiers or surrogates for seasonal differences and altered behaviors.

Analysis and Verification of cooling structure of superconducting motors for electrical aircraft propulsion

The hydrogen-powered aviation hybrid technology is one of the important directions of the development of electrical aircraft propulsion. Superconducting motors (SCMs) are the core components of a hydrogen-powered aircraft due to their high power-to-weight ratio. Among SCMs, partial SCMs with superconducting armature windings and permanent magnets (SC-PMMs) are the research front and hotspots. This study focuses on the key issue of cooling the superconducting (SC) coils of SC-PMMs. The advantages and disadvantages of three cooling structures, namely core conduction cooling, coil immersion cooling, and core and coil immersion cooling, are compared. The temperature of the SC coils in different cooling structures is simulated and analyzed in detail. The obtained results show that the temperature of the coils in the core and coil immersion cooling structure is not much different from that in the coil immersion cooling structure, with a temperature difference of about 1.5 K only. However, the implementation of the core and coil immersion cooling structure is much easier. Therefore, an SC-PMM prototype is developed using it as the cooling structure, and the temperature change in the prototype under different operating conditions is investigated experimentally. The obtained results show that the final stable temperature during the cooling process is 76.8 K, and the coil on the top is more likely to quench than that at the bottom. The maximum frequency and maximum current at which the prototype can operate stably for a long time are 200 Hz and 49 A, respectively. This study verifies the effectiveness of the core and coil immersion cooling structure, obtains the quench prone area in SC-PMMs, and lays the foundation for the development of high-performance and highly reliable SCMs.

Fracture and fractal characteristics of high-temperature granite under confined space water jet impact

In the application of jet assisted deep drilling technology, the fracture mode and rock fragment characteristics of high-temperature rock in the confined space of jet drilling are not yet clear. We analyzed the fragmentation and debris distribution of high-temperature granite under confined space jet action using 3D reconstruction technology and statistical fractal theory to examine their fragmentation patterns and fractal characteristics. The results show that high-temperature rocks exhibit obvious thermal fracturing characteristics under the impact of confined water jet, and as the rock temperature increases, vertical compression shear cracks connect with radial tensile cracks. The maximum damage area is located near the bottom of the confined hole, and the distribution of cracks is more complex. As the degree of jet confinement decreases, the rock cracking form changes from radial tensile cracking to vertical compression shear cracking. As the rock temperature increases and the confined space size decreases, the total mass and large debris mass percentages of rock debris increase. The particle size distribution of rock debris follows an Rosin-Rammler (R-R) distribution and has obvious fractal characteristics. The fracture and fragmentation of high-temperature rocks under confined water jet impact are mainly caused by the combination of jet impact stress waves and thermal stress. The temperature difference of rocks affects the heat transfer between jet and rock, and the confined space size directly affects the heat transfer efficiency between jet and rock, which is manifested in different numbers of fracture cracks, internal damage area, and rock debris size distribution. These findings can provide a theoretical and parameter optimization basis for jet-assisted deep reservoir drilling applications.

Thermomechanobiology as a new research field in soft tissues

During intense galloping, the difference in temperature between the external and the central part of an equine superficial digital flexor tendon can be as high as 7°C. Thirty minutes of jogging modifies the temperature in human knee cartilage from 32°C to 37°C. Intrinsic dissipative phenomena related to the viscoelastic behavior of soft tissues have been identified to be primarily responsible for the observed temperature increase, a situation referred to as self-heating in mechanics. While a 5°C increase may be considered negligible from a mechanical point of view in the cartilage at first sight, it can have a significant biological impact. It has been recently proposed that self-heating and the resulting increase of temperature in cartilage following mechanical stimulation can be necessary for its maintenance. This new concept complements the general acceptance that mechanobiology is central to the homeostasis of musculoskeletal tissues. In most biomechanical and biological studies on cartilage or other soft tissues, the temperature is set at 37°C and considered constant, despite human knee cartilage at rest being around 32°C, for example. Therefore, there is a deficit of information on the role and effect of physiological temperature variation induced through mechanical loading in soft tissues, opening a new research avenue that we coin thermomechanobiology.

Calorimetric Measurements of a High-Power RF Signal

Development of a high-power RF signal meter based on the method of calorimetric measurements, which in some cases is the only possible one is presented. The device is as a system of elements exchanging either energy or information, the operation and interconnection of which ensures the stability of its functioning. The main elements of the device are: a coordinated load and a two-circuit water-air cooling system that convert RF energy first into thermal electrical energy, and then into internal energy of the coolant (working fluid). The measurement and control system provides information display on the monitor and generation of internal control signals. The work focuses on the process of converting electromagnetic energy into internal energy of the coolant, since the matched RF load is integrated into the cooling system and requires special design and technological solutions to ensure efficient operation. A cooling and measurement system has been designed to test the developed RF absorber with a power of up to 5 kW. The parameters of the cooling system were determined based on minimizing the time to achieve thermal equilibrium (time to establish readings) and the set parameters (input temperature no more than 35 °С, temperature difference no more than 40 °С). Based on calculations of the electrodynamic model constructed by the partial domain method, the geometric dimensions were determined at which the voltage standing wave ratio of the load in the operating frequency range (from DC to 1300 MHz) will be the smallest. The article presents the results of designing a high-frequency wattmeter cooled by a liquid (water), examines the thermophysical processes occurring in it and the influence of the presence of a coolant in the cooling circuit.

Experimental analysis of glass failure criteria under different thermal conditions

The initiation of the first crack mainly determines the criteria for glass failure. However, the extended consequences of cracking, with the formation of multiple cracks merging, result in fallout conditions under varying thermal loads that become more critical. Point-supported glass arrangements are globally used in high-rise and energy-efficient buildings for architectural ingenuity aimed at a low budget. However, the formation of cracks due to thermal load resulting in glass breakage could infuriate the overall fire dynamics of the enclosed area. Therefore, experimental study and prediction of glass failure become very crucial. The present experimental study focuses on finding the most critical parameter that may quantify the cause of glass failure and further breakage in fallout conditions under varying thermal loads. 45 experiments were carried out on float glass of 300 × 300 mm2 with 4 mm, 6 mm, 8 mm, 10 mm, and 12 mm with continuous fuel supply arrangements. Critical parameters analysed were the time of crack initiation, glass temperature at the time of cracking, maximum temperature difference at glass failure, and thermal strain caused by the temperature difference on the glass surface. The range of minimum and maximum temperature difference recorded on the glass surface for the present study was between 30–35°C and 55–60°C at the breakage time for all the experiments. The Maximum temperature difference measured was 56.99°C on the 12 mm glass surface, and the corresponding maximum thermal strain found was 482 × 10−6 mm/mm. The maximum heat release rate was found to be approximately 200 kW. Maximum heat flux was found in the range of 10.33 kW/m2 to 21.14 kW/m2. A correlation was also developed using the least square method for all the thicknesses, which is well correlated with the glass thickness per unit length.

Low sintering shrinkage and high strength of porous mullite–zirconia ceramics: Effect of AlF3 and ZrSi2 contents

AbstractLow‐shrinkage porous mullite–zirconia ceramics were prepared using Al and ZrSi2 as raw materials and AlF3 as the whisker catalyst through foam‐gelcasting and freeze‐drying methods. The oxidation of Al and ZrSi2 combined with the Kirkendall effect and volume expansion was employed to reduce the sintering shrinkage, while the mullitization was promoted by the reaction between AlF3 and extra ZrSi2, and ZrO2 were generated to enhance the compressive strength as the reinforcing phase. The effect of AlF3 and ZrSi2 content on the microstructure and properties of porous mullite‐zirconia were explored. These ceramics exhibited high porosity (73.75%–85.02%) and compressive strength (2.98–17.71 MPa), low shrinkage (0.47%–10.89%) and thermal conductivity (0.228–0.462 W/(m·K)). In particular, the porous mullite–zirconia ceramics with great compressive strength (4.01 MPa) companied with near‐zero shrinkage (0.47%) at the AlF3 content of 15 wt% and extra ZrSi2 content of 20 wt% by introducing the reinforcing phase (ZrO2). Additionally, the temperature difference around 950°C of the porous ceramics during the heating test proved the exceptional application on thermal insulation.

Investigation into the nonuniform temperature effect of a large-span stainless steel roof system under solar radiation

Metal roof systems have been widely used in various landmark buildings. The effect of the temperature of a large-span metal roof system under solar radiation is significant. As the latest roof form, the continuous welded stainless steel roof (CWSSR) system shows many unknown behaviors under the action of temperature. The purpose of this work is to analyse the temperature field and temperature effect of the CWSSR system under solar radiation and to select the appropriate support layouts to reduce the temperature effect of the CWSSR system. First, an experimental study on the temperature field of the CWSSR system was carried out. Finite element analysis of the temperature field distribution was then performed, and the validity of the finite element method was verified by comparing the experimental results. Finally, the influence of different support layouts on the temperature effect of the CWSSR system was researched. The results show that there is an obvious nonuniform distribution of the temperature field and temperature effect of the CWSSR system under solar radiation. The maximum temperature difference between the roof panel and the ambient temperature is 39.4 °C. By using arrangements of cross-support and segmented support, the stresses of the roof panel and support can be effectively reduced, and the maximum reductions are 14.4 % and 38.9 %, respectively. The investigation results contribute the most to the safe design of metal roof systems and are expected to provide guidelines for future applications of the CWSSR system.

Analytical generalized thermal resistance model for conductive heat transfer in pebble beds based on heat flux weighted temperature difference

A novel model for inter-particle contact thermal resistance based on analytical solutions is proposed. By applying the concept of heat flux weighted temperature difference in thermal resistance modeling for the first time, this model offers greater physical significance than traditional thermal resistance models. It effectively describes the dissipation in the heat transfer process and the influence of particle radius on thermal resistance, making it a generalized thermal resistance model suitable for multi-dimensional systems. The impact of applying different levels of uniform heat flux boundary conditions on thermal resistance is analyzed from the perspective of energy dissipation, revealing that a more uniform heat flux input results in lower thermal resistance. The effects of contact radius and particle size on the dimensionless generalized thermal resistance of inter-particle contact were studied, showing that the dimensionless resistance increases with larger particle contact radius and smaller particle size. Using the thermal discrete element method, the thermal resistance model with uniform heat flux density boundary conditions was applied to calculate the effective thermal conductivity of the pebble bed. Considering the distribution of contact radius, differences in effective thermal conductivity at various heights of the pebble bed due to different contact radii were examined and compared with the traditional fixed-coefficient contact resistance model. It was found that the difference between the two models decreases as the contact radius decreases. Finally, multiple sets of fixed contact radii were established under three different particle sizes, revealing that as the contact radius increases, the deviation between the new generalized resistance model and the traditional fixed-coefficient model rises from 8.18 % to 14.64 % for different particle radii.