Based on the NCEP/NCAR reanalysis data for the period of 1948-2004 and the monthly rainfall data at 160 stations in China from 1951 to 2004, the relationships among the land-ocean temperature anomaly difference in the...Based on the NCEP/NCAR reanalysis data for the period of 1948-2004 and the monthly rainfall data at 160 stations in China from 1951 to 2004, the relationships among the land-ocean temperature anomaly difference in the mid-lower troposphere in spring (April-May), the mei-yu rainfall in the Yangtze River- Huaihe River basin, and the activities of the South China Sea summer monsoon (SCSSM) are analyzed by using correlation and composite analyses. Results show that a significant positive correlation exists between mei-yu rainfall and air temperature in the middle latitudes above the western Pacific, while a significant negative correlation is located to the southwest of the Baikal Lake. When the land-ocean thermal anomaly difference is stronger in spring, the western Pacific subtropical high (WPSH) will be weaker and retreat eastward in summer (June-July), and the SCSSM will be stronger and advance further north, resulting in deficient moisture along the mei-yu front and below-normal precipitation in the mid and lower reaches of the Yangtze River, and vice versa for the weaker difference case. The effects and relative importance of the land and ocean anomalous heating on monsoon variability is also compared. It is found that the land and ocean thermal anomalies are both closely related to the summer circulation and mei-yu rainfall and SCSSM intensity, whereas the land heating anomaly is more important than ocean heating in changing the land-ocean thermal contrast and hence the summer monsoon intensity.展开更多
Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the t...Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the thermal stress distribution during casting process,a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method(FDM),namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete.A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process.Two practical verifications were carried out,and the results from simulation basically coincided with practical cases.The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress,and to predict the occurrence of hot tearing.Because heat transfer and stress analysis are all based on FDM,they can use the same FD model,which can avoid the matching process between different models,and hence reduce temperature-load transferring errors.This approach makes the simulation of fluid flow,heat transfer and stress analysis unify into one single model.展开更多
This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip veloci...This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.展开更多
The interdecadal factors affecting the summer monsoon winds over Somalia and the South China Sea were studied. Global geopotential heights and wind velocity fields of the 850-hPa and 200-hPa pressure levels, as well a...The interdecadal factors affecting the summer monsoon winds over Somalia and the South China Sea were studied. Global geopotential heights and wind velocity fields of the 850-hPa and 200-hPa pressure levels, as well as sea surface temperature anomaly data and correlation coefficients were analyzed. The monsoons over Somalia and the South China Sea were found to be two different monsoon systems, operating on different mechanisms and being affected by different oceanatmosphere interactions. The intensity of the Asian subtropical summer monsoon is influenced by the intensity of the summer monsoon over Somalia in the month of June and by the intensity of the summer monsoon over the South China Sea in the months of June and July. The summer monsoon wind strength over Somalia is affected by regional factors, such as the heating of the Tibetan plateau, and by global mechanisms, such as the subtropical heat exchange with Antarctica. The summer monsoon over the South China Sea is affected by different ocean-atmosphere interactions. The Somalia and subtropical summer monsoons have wind blowing down the pressure gradient from area over ocean to that over land, like typical summer monsoons. The South China Sea summer monsoon has winds that blow down the pressure gradient from area over land to that over ocean. The South China Sea summer monsoon is affected by the Kuroshio Current off the east coast of Japan.展开更多
Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational s...Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational speed in numerical simulation of casting thermal stress based on FDM, one for handling of nonconstant material properties and the other for dealing with the various coefficients in discretization equations. The use of the two techniques has been discussed and an application in wave-guide casting is given. The results show that the computational speed is almost tripled and the computer storage needed is reduced nearly half compared with those of the original method without the new technologies. The stress results for the casting domain obtained by both methods that set the temperature steps to 0.1 ℃ and 10 ℃, respectively are nearly the same and in good agreement with actual casting situation. It can be concluded that both handling the material properties as an assumption of stepwise profile and eliminating the repeated calculation are reliable and effective to improve computational speed, and applicable in heat transfer and fluid flow simulation.展开更多
Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured ex...Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured experimentally. The method is a direct approach of second-order and the key advantage of the present method is that it is not required a priori knowledge of the functional form of the unknown thermal conductivity in the calculation and the thermal parameters are estimated only according to the known temperature distribution. Two cases were numerically calculated and the influence of experimental deviation on the precision of this method was discussed. The comparison of numerical and analytical results showed good agreement.展开更多
The heat equation is a second-order parabolic partial differential equation, which can be solved in many ways using numerical methods. This paper provides a numerical solution that uses the finite difference method li...The heat equation is a second-order parabolic partial differential equation, which can be solved in many ways using numerical methods. This paper provides a numerical solution that uses the finite difference method like the explicit center difference method. The forward time and centered space (FTCS) is used to a problem containing the one-dimensional heat equation and the stability condition of the scheme is reported with different thermal conductivity of different materials. In this study, results obtained for different thermal conductivity of distinct materials are compared. Also, the results reveal the well-behavior properties of the materials in good agreement.展开更多
This research aims to use the outdoor thermal environment evaluation index ETFe to quantify effects on the thermal sense of the human body of a tropical region climate with small annual temperature differences, and to...This research aims to use the outdoor thermal environment evaluation index ETFe to quantify effects on the thermal sense of the human body of a tropical region climate with small annual temperature differences, and to examine seasonal differences in the thermal sense. Given that the average temperature of the earth is forecasted to rise, studying the effects on the human body from outdoor thermal environments in tropical regions is important for considering how to spend time outdoors in the future. This study clarifies seasonal differences in effects on the human body by comparing the effects on the thermal sensations of the human body from outdoor thermal environments in the winter and the dry season of Bangkok, Thailand in the tropics. The mobile measurements were carried out on the campus of Chulalongkorn University, Bangkok, Thailand. The subjects reported the thermal sensation and the thermal comfort that they experienced while exposed at the observation point. Air temperature, humidity, air velocity, short-wave solar radiation, long-wave thermal radiation, ground surface temperature, sky factor and the ratio of green and water surface solid angles were measured. We found no large seasonal difference between the winter and the dry season in skin temperature due to body temperature regulation. It is clear that in the winter season, people prefer a lower temperature than in the dry season, and in the dry season they tolerate higher temperatures than in winter. The effect of the seasonal difference appears in the amount of change to thermal sensation. We found that it is difficult for seasonal differences to greatly affect the amount of change to thermal comfort. We found that the effect of seasonal difference is that people show stronger responses to thermal comfort for thermal sensation in winter than in the dry season.展开更多
Effects of magnesia fines addition ( 4%, 6% and 8% in mass ) and spinel with different compositions (alumina-rich, magnesia-rich and stoichiometric spi-nel) on thermal expansion behavior of alumina magne-sia casta...Effects of magnesia fines addition ( 4%, 6% and 8% in mass ) and spinel with different compositions (alumina-rich, magnesia-rich and stoichiometric spi-nel) on thermal expansion behavior of alumina magne-sia castables were researched using tabular corundum, magnesia fines, spinel fines, p-A12O3, Secar-71 cement and SiO2 fume as main starting materials. The results show that: (1) thermal expansion coefficients of speci- mens with 4 mass% and 6 mass% magnesia fines have the similar change tendency, increasing slightly with temperature rising ; when magnesia addition is 8 mass% , the thermal expansion coefficient increases ob-viously at Ⅰ 050 ℃ and reaches the peak at 1 350 ℃ ; (2) when MgO content is the same, the specimen with magnesia-rich spinel has the lowest thermal expansion coefficient; (3) for the castables specimens with the same MgO content, the specimen with magnesia has higher thermal expansion coefficient than that with pre-synthesized spin, el, which is related with the secondary spinelization dttriag the heating process.展开更多
Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can c...Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can cause thermal gradients in the composite,potentially leading to undesired residual stresses which can cause shrinkage and warpage.In the present numerical study of these processes,a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization;the effect of some parameters on the thermal gradient is then analyzed,namely:the fiber nature,the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation.The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.展开更多
Using the first-principles method, we investigate the thermal stability of cation point defects in LaAlO3 bulk and films. The calculated densities of states indicate that cation vacancies and antisites act as acceptor...Using the first-principles method, we investigate the thermal stability of cation point defects in LaAlO3 bulk and films. The calculated densities of states indicate that cation vacancies and antisites act as acceptors. The formation energies show that cation vacancies are energetically favorable in bulk LaAIO3 under O-rich conditions, while the AILa antisites are stable in reducing atmosphere. However, the same behavior does not appear in the case of LaAlO3 films. For LaO-terminated LaAlOa fihns, La or AI vacancies remain energetically favorable under O-rich and O-deficient conditions. For an AlO2-terminated surface, under O-rich condition the La interstitial atom is repelled from the outmost layer after optimization, which releases more stress leading to the decrease of total energy of the system. An AI interstitial atom has a smaller radius so that it can stay in distorted films and becomes more stable under O-deficient conditions, and the Al interstitial atoms can be another possible carrier source contribution to the conductivity of n-type interface under an ultrahigh vacuum. La and Al antisites have similar formation energy regardless of oxygen pressure. The results would be helpful to understand the defect structures of LaAlOa-related materials.展开更多
In extreme cold regions,a thermal insulation layer(TIL)is commonly employed to mitigate the detrimental effects of frost heaving forces in tunnels.Optimizing the laying scheme of TIL,specifically minimizing frost heav...In extreme cold regions,a thermal insulation layer(TIL)is commonly employed to mitigate the detrimental effects of frost heaving forces in tunnels.Optimizing the laying scheme of TIL,specifically minimizing frost heaving forces,holds considerable importance in the prevention of frost damage.This research developed a two-dimensional unsteady temperature field of circular tunnels by using the difference method(taking the off-wall laying method as an example)based on the law of conservation of energy.Then,the frozen circle and water migration coefficient were introduced to establish the relationship between the temperature field and frost heaving forces,and a reliable methodology for calculating these forces under the specific conditions of TIL installation was developed.Then(i)the influence of the air layer thickness of the off-wall laying method,(ii)different laying methods of TIL,(iii)the TIL thickness,(iv)the thermal conductivity of the TIL,and(v)the freeze-thaw cycles on the frost heaving force were investigated.The results showed that the frost heaving force served as a reliable and effective metric for evaluating the insulation effect in tunnels.In order to avoid frost damage in compliance with the design requirements,the insulation effects from various laying methods were established,in descending efficacy order as follows:off-wall laying,double layer laying,surface laying,and sandwich laying.Our findings revealed that the optimal thickness for the air layer in the offwall laying method was 0.10 m.The insulation effect of materials with a thermal conductivity below 0.047 W/(m·℃)was furthermore found to be good.Under freeze-thaw cycle conditions,it is concluded that to prevent frost damage,the TIL thickness should be the sum of the thickness r1 of the first freeze-thaw cycle without frost heaving forces and an additional reserve value 0.06r1 of the TIL thickness.展开更多
基金supported by the National Basic Research Program ofChina (Grant No. 2004CB418300)the National Natural Science Foundation of China (Grant No. 40675042)
文摘Based on the NCEP/NCAR reanalysis data for the period of 1948-2004 and the monthly rainfall data at 160 stations in China from 1951 to 2004, the relationships among the land-ocean temperature anomaly difference in the mid-lower troposphere in spring (April-May), the mei-yu rainfall in the Yangtze River- Huaihe River basin, and the activities of the South China Sea summer monsoon (SCSSM) are analyzed by using correlation and composite analyses. Results show that a significant positive correlation exists between mei-yu rainfall and air temperature in the middle latitudes above the western Pacific, while a significant negative correlation is located to the southwest of the Baikal Lake. When the land-ocean thermal anomaly difference is stronger in spring, the western Pacific subtropical high (WPSH) will be weaker and retreat eastward in summer (June-July), and the SCSSM will be stronger and advance further north, resulting in deficient moisture along the mei-yu front and below-normal precipitation in the mid and lower reaches of the Yangtze River, and vice versa for the weaker difference case. The effects and relative importance of the land and ocean anomalous heating on monsoon variability is also compared. It is found that the land and ocean thermal anomalies are both closely related to the summer circulation and mei-yu rainfall and SCSSM intensity, whereas the land heating anomaly is more important than ocean heating in changing the land-ocean thermal contrast and hence the summer monsoon intensity.
基金supported by the National Natural Science Foundation of China (No.50805056)New Century Excellent Talents in University (No.NCET-09-0396)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education (2009)
文摘Thermal stress simulation can provide a scientific reference to eliminate defects such as crack,residual stress centralization and deformation etc.,caused by thermal stress during casting solidification.To study the thermal stress distribution during casting process,a unilateral thermal-stress coupling model was employed to simulate 3D casting stress using Finite Difference Method(FDM),namely all the traditional thermal-elastic-plastic equations are numerically and differentially discrete.A FDM/FDM numerical simulation system was developed to analyze temperature and stress fields during casting solidification process.Two practical verifications were carried out,and the results from simulation basically coincided with practical cases.The results indicated that the FDM/FDM stress simulation system can be used to simulate the formation of residual stress,and to predict the occurrence of hot tearing.Because heat transfer and stress analysis are all based on FDM,they can use the same FD model,which can avoid the matching process between different models,and hence reduce temperature-load transferring errors.This approach makes the simulation of fluid flow,heat transfer and stress analysis unify into one single model.
文摘This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.
基金This research was supported by the National Natural Science Foundation of China(No.40136010)carried out at the Ocean University of China as part of the US National Science Foundation REU in M arine Science and Engineering in China,under Grant Number OISR-0229657.
文摘The interdecadal factors affecting the summer monsoon winds over Somalia and the South China Sea were studied. Global geopotential heights and wind velocity fields of the 850-hPa and 200-hPa pressure levels, as well as sea surface temperature anomaly data and correlation coefficients were analyzed. The monsoons over Somalia and the South China Sea were found to be two different monsoon systems, operating on different mechanisms and being affected by different oceanatmosphere interactions. The intensity of the Asian subtropical summer monsoon is influenced by the intensity of the summer monsoon over Somalia in the month of June and by the intensity of the summer monsoon over the South China Sea in the months of June and July. The summer monsoon wind strength over Somalia is affected by regional factors, such as the heating of the Tibetan plateau, and by global mechanisms, such as the subtropical heat exchange with Antarctica. The summer monsoon over the South China Sea is affected by different ocean-atmosphere interactions. The Somalia and subtropical summer monsoons have wind blowing down the pressure gradient from area over ocean to that over land, like typical summer monsoons. The South China Sea summer monsoon has winds that blow down the pressure gradient from area over land to that over ocean. The South China Sea summer monsoon is affected by the Kuroshio Current off the east coast of Japan.
基金supported by National Natural Science Foundation of China (Grant Nos. 50827102 and 50931004)National Basic Research Program of China (Grant No. 2010CB631202 and No. 2006CB605202)High Technology Research and Development Program of China (Grant No. 2007AA03Z552)
文摘Finite difference method (FDM) was applied to simulate thermal stress recently, which normally needs a long computational time and big computer storage. This study presents two techniques for improving computational speed in numerical simulation of casting thermal stress based on FDM, one for handling of nonconstant material properties and the other for dealing with the various coefficients in discretization equations. The use of the two techniques has been discussed and an application in wave-guide casting is given. The results show that the computational speed is almost tripled and the computer storage needed is reduced nearly half compared with those of the original method without the new technologies. The stress results for the casting domain obtained by both methods that set the temperature steps to 0.1 ℃ and 10 ℃, respectively are nearly the same and in good agreement with actual casting situation. It can be concluded that both handling the material properties as an assumption of stepwise profile and eliminating the repeated calculation are reliable and effective to improve computational speed, and applicable in heat transfer and fluid flow simulation.
文摘Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured experimentally. The method is a direct approach of second-order and the key advantage of the present method is that it is not required a priori knowledge of the functional form of the unknown thermal conductivity in the calculation and the thermal parameters are estimated only according to the known temperature distribution. Two cases were numerically calculated and the influence of experimental deviation on the precision of this method was discussed. The comparison of numerical and analytical results showed good agreement.
文摘The heat equation is a second-order parabolic partial differential equation, which can be solved in many ways using numerical methods. This paper provides a numerical solution that uses the finite difference method like the explicit center difference method. The forward time and centered space (FTCS) is used to a problem containing the one-dimensional heat equation and the stability condition of the scheme is reported with different thermal conductivity of different materials. In this study, results obtained for different thermal conductivity of distinct materials are compared. Also, the results reveal the well-behavior properties of the materials in good agreement.
文摘This research aims to use the outdoor thermal environment evaluation index ETFe to quantify effects on the thermal sense of the human body of a tropical region climate with small annual temperature differences, and to examine seasonal differences in the thermal sense. Given that the average temperature of the earth is forecasted to rise, studying the effects on the human body from outdoor thermal environments in tropical regions is important for considering how to spend time outdoors in the future. This study clarifies seasonal differences in effects on the human body by comparing the effects on the thermal sensations of the human body from outdoor thermal environments in the winter and the dry season of Bangkok, Thailand in the tropics. The mobile measurements were carried out on the campus of Chulalongkorn University, Bangkok, Thailand. The subjects reported the thermal sensation and the thermal comfort that they experienced while exposed at the observation point. Air temperature, humidity, air velocity, short-wave solar radiation, long-wave thermal radiation, ground surface temperature, sky factor and the ratio of green and water surface solid angles were measured. We found no large seasonal difference between the winter and the dry season in skin temperature due to body temperature regulation. It is clear that in the winter season, people prefer a lower temperature than in the dry season, and in the dry season they tolerate higher temperatures than in winter. The effect of the seasonal difference appears in the amount of change to thermal sensation. We found that it is difficult for seasonal differences to greatly affect the amount of change to thermal comfort. We found that the effect of seasonal difference is that people show stronger responses to thermal comfort for thermal sensation in winter than in the dry season.
文摘Effects of magnesia fines addition ( 4%, 6% and 8% in mass ) and spinel with different compositions (alumina-rich, magnesia-rich and stoichiometric spi-nel) on thermal expansion behavior of alumina magne-sia castables were researched using tabular corundum, magnesia fines, spinel fines, p-A12O3, Secar-71 cement and SiO2 fume as main starting materials. The results show that: (1) thermal expansion coefficients of speci- mens with 4 mass% and 6 mass% magnesia fines have the similar change tendency, increasing slightly with temperature rising ; when magnesia addition is 8 mass% , the thermal expansion coefficient increases ob-viously at Ⅰ 050 ℃ and reaches the peak at 1 350 ℃ ; (2) when MgO content is the same, the specimen with magnesia-rich spinel has the lowest thermal expansion coefficient; (3) for the castables specimens with the same MgO content, the specimen with magnesia has higher thermal expansion coefficient than that with pre-synthesized spin, el, which is related with the secondary spinelization dttriag the heating process.
文摘Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can cause thermal gradients in the composite,potentially leading to undesired residual stresses which can cause shrinkage and warpage.In the present numerical study of these processes,a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization;the effect of some parameters on the thermal gradient is then analyzed,namely:the fiber nature,the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation.The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.
基金Supported by the Hebei Provincial Young Top-Notch Talent Support Program under Grant No BJRC2016the Innovative Funding Project of Graduates of Hebei University under Grant No hbu2018ss62the Midwest Universities Comprehensive Strength Promotion Project
文摘Using the first-principles method, we investigate the thermal stability of cation point defects in LaAlO3 bulk and films. The calculated densities of states indicate that cation vacancies and antisites act as acceptors. The formation energies show that cation vacancies are energetically favorable in bulk LaAIO3 under O-rich conditions, while the AILa antisites are stable in reducing atmosphere. However, the same behavior does not appear in the case of LaAlO3 films. For LaO-terminated LaAlOa fihns, La or AI vacancies remain energetically favorable under O-rich and O-deficient conditions. For an AlO2-terminated surface, under O-rich condition the La interstitial atom is repelled from the outmost layer after optimization, which releases more stress leading to the decrease of total energy of the system. An AI interstitial atom has a smaller radius so that it can stay in distorted films and becomes more stable under O-deficient conditions, and the Al interstitial atoms can be another possible carrier source contribution to the conductivity of n-type interface under an ultrahigh vacuum. La and Al antisites have similar formation energy regardless of oxygen pressure. The results would be helpful to understand the defect structures of LaAlOa-related materials.
基金the financial support provided by the National Natural Science Foundation of China(Nos.52078061,51878074)the Huaihua University Scientific Research Project,China(No.HHUY 2022-26)+1 种基金the Postgraduate Research and Innovation-funded Project of Hunan Province,China(No.CX20220885)。
文摘In extreme cold regions,a thermal insulation layer(TIL)is commonly employed to mitigate the detrimental effects of frost heaving forces in tunnels.Optimizing the laying scheme of TIL,specifically minimizing frost heaving forces,holds considerable importance in the prevention of frost damage.This research developed a two-dimensional unsteady temperature field of circular tunnels by using the difference method(taking the off-wall laying method as an example)based on the law of conservation of energy.Then,the frozen circle and water migration coefficient were introduced to establish the relationship between the temperature field and frost heaving forces,and a reliable methodology for calculating these forces under the specific conditions of TIL installation was developed.Then(i)the influence of the air layer thickness of the off-wall laying method,(ii)different laying methods of TIL,(iii)the TIL thickness,(iv)the thermal conductivity of the TIL,and(v)the freeze-thaw cycles on the frost heaving force were investigated.The results showed that the frost heaving force served as a reliable and effective metric for evaluating the insulation effect in tunnels.In order to avoid frost damage in compliance with the design requirements,the insulation effects from various laying methods were established,in descending efficacy order as follows:off-wall laying,double layer laying,surface laying,and sandwich laying.Our findings revealed that the optimal thickness for the air layer in the offwall laying method was 0.10 m.The insulation effect of materials with a thermal conductivity below 0.047 W/(m·℃)was furthermore found to be good.Under freeze-thaw cycle conditions,it is concluded that to prevent frost damage,the TIL thickness should be the sum of the thickness r1 of the first freeze-thaw cycle without frost heaving forces and an additional reserve value 0.06r1 of the TIL thickness.