A field-validated finite element framework for predicting transient temperature fields in multilayer pavements

Shape reconstruction in transient heat conduction problems based on radial integration boundary element method

Our purpose is to establish a numerical method meeting the requirements of efficiency, stability, accuracy and easy-using. Faced with these demands, in this paper, a hybrid method combining the advantages of 2 weak-form meshless methods is proposed for solving steady and transient heat conduction problems with temperature-dependent thermophysical properties in heterogeneous media. In the process of the calculation for an arbitrary model discretized by the hybrid method, two different weak-form methods are used for the nodes categorized as: (1) boundary nodes, (2) near boundary interior nodes and (3) interior nodes. A Galerkin free element method (GFREM) is proposed for the interior nodes of the Cartesian grid; and the local radial point interpolation method (LRPIM) is used for the other two types of nodes. The GFREM using the Cartesian grid can greatly improve the accuracy and efficiency of the hybrid scheme. Special decomposition technology to determine the irregular integral domain for LRPIM can increase the flexibility for complex models. In addition, the full implicit finite difference scheme and Newton–Raphson method are used for solving transient nonlinear problems. And non-crossing interface integral domain and support domain are employed for heterogeneous media. Compared with other methods, numerical results show better accuracy, stability and efficiency from the numerical experiments.

This paper presents an efficient inverse analysis technique based on a sensitivity coefficient algorithm to estimate the unknown boundary conditions of multidimensional steady and transient heat conduction problems. Sensitivity coefficients were used to represent the temperature response of a system under unit loading conditions. The proposed method, coupled with the sensitivity analysis in the finite element formulation, is capable of estimating both the unknown temperature and heat flux on the surface provided that temperature data are given at discrete points in the interior of a solid body. Inverse heat conduction problems are referred to as ill-posed because minor inaccuracy or error in temperature measurements cause a drastic effect on the predicted surface temperature and heat flux. To verify the accuracy and validity of the new method, two-dimensional steady and transient problems are considered. Their surface temperature and heat flux are evaluated. From a comparison with the exact solution, the effects of measurement accuracy, number and location of measuring points, a time step, and regularization terms are discussed. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 345–359, 1997

Abstract. An accurate spatially continuous air temperature data set is crucial for multiple applications in the environmental and ecological sciences. Existing spatial interpolation methods have relatively low accuracy, and the resolution of available long-term gridded products of air temperature for China is coarse. Point observations from meteorological stations can provide long-term air temperature data series but cannot represent spatially continuous information. Here, we devised a method for spatial interpolation of air temperature data from meteorological stations based on powerful machine learning tools. First, to determine the optimal method for interpolation of air temperature data, we employed three machine learning models: random forest, support vector machine, and Gaussian process regression. A comparison of the mean absolute error, root mean square error, coefficient of determination, and residuals revealed that a Gaussian process regression had high accuracy and clearly outperformed the other two models regarding the interpolation of monthly maximum, minimum, and mean air temperatures. The machine learning methods were compared with three traditional methods used frequently for spatial interpolation: inverse distance weighting, ordinary kriging, and ANUSPLIN (Australian National University Spline). Results showed that the Gaussian process regression model had higher accuracy and greater robustness than the traditional methods regarding interpolation of monthly maximum, minimum, and mean air temperatures in each month. A comparison with the TerraClimate (Monthly Climate and Climatic Water Balance for Global Terrestrial Surfaces), FLDAS (Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System), and ERA5 (ECMWF, European Centre for Medium-Range Weather Forecasts, Climate Reanalysis) data sets revealed that the accuracy of the temperature data generated using the Gaussian process regression model was higher. Finally, using the Gaussian process regression method, we produced a long-term (January 1951 to December 2020) gridded monthly air temperature data set, with 1 km resolution and high accuracy for China, which we named GPRChinaTemp1km. The data set consists of three variables: monthly mean air temperature, monthly maximum air temperature, and monthly minimum air temperature. The obtained GPRChinaTemp1km data were used to analyse the spatiotemporal variations of air temperature using Theil–Sen median trend analysis in combination with the Mann–Kendall test. It was found that the monthly mean and minimum air temperatures across China were characterised by a significant trend of increase in each month, whereas monthly maximum air temperatures showed a more spatially heterogeneous pattern, with significant increase, non-significant increase, and non-significant decrease. The GPRChinaTemp1km data set is publicly available at https://doi.org/10.5281/zenodo.5112122 (He et al., 2021a) for monthly maximum air temperature, at https://doi.org/10.5281/zenodo.5111989 (He et al., 2021b) for monthly mean air temperature, and at https://doi.org/10.5281/zenodo.5112232 (He et al., 2021c) for monthly minimum air temperature.

Fusion power offers the prospect of a safe and clean sustainable energy source, and is of increasing importance for meeting the world energy demand and curbing CO2 emissions. For an indirect-driven inertial confinement cryogenic target, the D-T ice layer inside the capsule should have a uniformity more than 99% and an inner surface roughness less than a root mean square value of 1 m to avoid Rayleigh-Taylor instabilities. And this highly smooth ice layer required for ignition is considered to be affected by the thermal environment around the fuel capsule. In the present study, a numerical investigation is conducted to examine the static and dynamic characteristics of the thermal environment outside the fuel capsule. Numerical model is proposed and verified by a simplified cryogenic target, and the calculated temperature distribution around the capsule shows to be in good agreement with the experimental data. Based on the established model, the propagation of periodic disturbance of cooling wall temperature in the hohlraum is investigated, and the relations between the temperature disturbance on the cooling wall and the temperature distribution around the capsule surface are obtained. The effects of disturbance amplitude, the disturbance period, and the hohlraum gas composition on the propagation process are investigated separately. The results indicate that for stable cooling temperature, the thermal environment around the capsule shows certain dependence on the gas filled in the hohlraum. The temperature uniformity of the capsule outer surface deteriorates with the increase of fill gas pressure but can be improved by increasing the He content of the filling gas mixture. At an oscillating cooling temperature, the attenuation of amplitude is significant when the periodic disturbance propagates from the cooling rings to the hohlraum and to the capsule surface. For the sine wave form disturbance investigated in the present study, shorter disturbance period results in larger attenuation of the disturbance amplitude. Higher gas pressure leads to smaller amplitude of average temperature on the capsule outer surface. The propagation process of cooling temperature disturbance also demonstrates dependence on the filling gas composition. The higher fraction of H2 in the He-H2 mixture helps to attenuate the disturbance amplitude and suppress the propagation of the temperature disturbance. However, the temperature uniformity around the capsule exhibits different characteristics from cooling temperature disturbance. Under the oscillating cooling conditions, moderate period, lower amplitude, lower pressure and higher fraction of He in the He-H2 mixture help to improve the temperature uniformity around the capsule. The results are of guiding significance for determining the controlling scheme in experiment and further design option for the cryogenic target.

Analytical solutions to transient heat conduction problems are often obtained by superposition of a particular solution (often the steady-state solution) and an eigenfunction series, representing the terms that decay exponentially with time. Here, a finite element realization of this method is presented in which conventional finite element discretization is used for the spatial distribution of temperature and analytical methods for the time dependence. This leads to a linear eigenvalue problem whose solution then enables a general numerical model of the transient system to be created. The method is an attractive alternative to conventional time-marching schemes, particularly in cases where it is desired to explore the effect of a wide range of operating parameters. The method can be applied to any transient heat conduction problem, but particular attention is paid to the case where the Biot number is small compared with unity and where the evolution of the system is very close to that with zero heat loss from the exposed surfaces. This situation arises commonly in machines such as brakes and clutches which experience occasional short periods of intense heating. Numerical examples show that with typical parameter values, the simpler zero heat loss solution provides very good accuracy. One also shows that good approximations can be achieved using a relatively small subset of the eigenvectors of the problem.

This paper examines the potential for the use of artificial neural networks (ANNs) to estimate the reference crop evapotranspiration (ET0) based on air temperature data under humid subtropical conditions on the southern coast of the Caspian Sea situated in the north of Iran. The input variables for the networks were the maximum and minimum air temperature and extraterrestrial radiation. The temperature data were obtained from eight meteorological stations with a range of latitude, longitude, and elevation throughout the study area. A comparison of the estimates provided by the ANNs and by Hargreaves equation was also conducted. The FAO-56 Penman–Monteith model was used as a reference model for assessing the performance of the two approaches. The results of this study showed that ANNs using air temperature data successfully estimated the daily ET0 and that the ANNs with an R2 of 0.95 and a root mean square error (RMSE) of 0.41 mm day−1 simulated ET0 better than the Hargreaves equation, which had an R2 of 0.91 and a RMSE of 0.51 mm day−1.

An engineering foundation for controlling heat transfer in one-dimensional transient heat conduction problems

On the basis of reproducing kernel particle method(RKPM), the complex variable reproducing kernel particle method (CVRKPM) is discussed. The advantage of the CVRKPM is that the correction function of a 2-D problem is formed with 1-D basis function when the shape function is obtained. Then, we apply the complex variable method to two-dimensional transient heat conduction problems. In combination with the Galerkin weak form of transient heat conduction problems, the penalty method is employed to enforce the essential boundary conditions, the CVRKPM for transient heat conduction problems is investigated and the corresponding formulae are obtained. Compared with the conventional RKPM, the CVRKPM introduced in this paper has a higher precision and a lower computation cost. Some examples given in this paper verify the effectivity of the proposed method.

In this article, a domain decomposition algorithm combined with a reduced-order model (ROM) is proposed to deal with the transient heat conduction problems in multi-domain structures. Using the domain decomposition algorithm and the finite element method (FEM), the original problem is decomposed into multiple non-overlapping subdomains, which can be solved independently under appropriate boundary conditions. However, additional inter-regional connected calculation will be brought through the simple geometry decomposition. Thus, the proper orthogonal decomposition (POD), a projection-based ROM technique, is utilized to further reduce the number of unknowns and the calculation time for each subdomain. To be more specific, the local POD bases of each subdomain are obtained by decomposing a snapshot matrix that gathered according to time by the application of the virtual boundary conditions on interfaces of the adjacent subdomains and other boundaries. Furthermore, the problems under different boundary conditions can be linked by the variable condensation technique on the interfaces, which enhances the efficiency of the numerical solver dramatically. Finally, the accuracy and efficiency of the proposed method are demonstrated by comparing the results calculated using both the proposed algorithm and the direct finite element simulation.

A siliciclastic gas reservoir is analyzed through two seismic attributes, root mean square (RMS) ampli-tude and reservoir to shadow mono frequency (RSMF) to detect and quantify porosity and gas accumu-lation. The objectives are to apply forward modeling to design the interval for amplitude mapping to de-lineate porosity; to analyze the amplitude of the frequency to generate the RSMF map; and to validate the RMS amplitude map with porosity, and the RSMF map with gas test results. One well was modeled for two cases, a tight and porous reservoir, to establish an appropriate RMS amplitude extraction window for reservoir porosity. The amplitude around the reservoir was extracted and validated by wells. The seismic volume is decomposed in the frequency domain for the gas detec-tion technique. This technique measures the amplitude attenuation in the dominant frequency between the reservoir level and the zone just beneath it to produce the RSMF map, with the assumption that the frequency amplitude attenuation increases while passing through the gas reservoir. The RSMF map was validated by the normalized gas test results of several wells. The forward modeling indicates that up to 20 ms below the reservoir is an optimum window to corre-late the targeted reservoir with the RMS amplitude. The RMS amplitude was found to be directly pro-portional to porosity, with the modeled tight reservoir case having lower RMS amplitude than the porous reservoir case within the optimum window. The RMS amplitude response for the modeled tight reservoir case almost matches the in-situ case. There is a correlation coefficient of approximately 70% between the average reservoir porosity of the wells and the RMS amplitude map extracted from the seismic volume within the optimum window. At the dominant frequency of 20 Hz, a correlation coeffi-cient of around 82% is observed between the gas test results and amplitude attenuation. The RMS and RSMF attributes are affected by seismic amplitude preservation as well as signal-to-noise ratio, which can impact the level of uncertainty between these two attributes and the extracted maps. The integration of RMS amplitude and RSMF attributes complemented the characterization of the si-liciclastic gas reservoir for detecting high porosity zones with gas accumulations. Zones with high RMS amplitude and attenuation were highlighted to be targeted for well placement.

A new general analytical PBEM for solving three-dimensional transient nonlinear heat conduction problems with spatially-varying heat generation

The precise integration method for semi-discretized equation in the dual reciprocity method to solve three-dimensional transient heat conduction problems

Force and vibration generated in apical direction by three endodontic files of different kinematics during simulated canal preparation: An in vitro analytical study.

MODIS land surface temperature data (MODIS Ts) products are quantified from the earth surface’s reflected thermal infrared signal via sensors onboard the Terra and Aqua satellites. MODIS Ts products are a great value to many environmental applications but often subject to discrepancies when compared to the air temperature (Ta) data that represent the temperature measured at 2 m above the ground surface. Although they are different in their nature, the relationship between Ts and Ta has been established by many researchers. Further validation and correction on the relationship between these two has enabled the estimation of Ta from MODIS Ts products in order to overcome the limitation of Ta that can only provide data in a point form with a very limited area coverage. Therefore, this study was conducted with the objective to assess the accuracy of MODIS Ts products, i.e., MOD11A1, MOD11A2, MYD11A1, and MYD11A2 against Ta and to identify the performance of a modified Linear Scaling using a constant and monthly correction factor (LS-MBC), and Quantile Mapping Mean Bias Correction (QM-MBC) methods for lowland area of Peninsular Malaysia. Furthermore, the correction factor (CF) values for each MBC were adjusted according to the condition set depending on the different bias levels. Then, the performance of the pre- and post-MBC correction for by stations and regions analysis were evaluated through root mean square error (RMSE), percentage bias (PBIAS), mean absolute error (MAE), and correlation coefficient (r). The region dataset is obtained by stacking the air temperature (Ta_r) and surface temperature (Ts_r) data corresponding to the number of stations within the identified regions. The assessment of pre-MBC data for both 36 stations and 5 regions demonstrated poor correspondence with high average errors and percentage biases, i.e., RMSE = 3.33–5.42 °C, PBIAS = 1.36–12.07%, MAE = 2.88–4.89 °C, and r = 0.16–0.29. The application of the MBCs has successfully reduced the errors and bias percentages, and slightly increased the r values for all MODIS Ts products. All post-MBC depicted good average accuracies (RMSE and MAE < 3 °C and PBIAS between ±5%) and r between 0.18 and 0.31. In detail, for the station analysis, the LS-MBC using monthly CF recorded better performance than the LS-MBC using constant CF or the QM-MBC. For the regional study, the QM-MBC outperformed the others. This study illustrated that the proposed LS-MBC, in spite of its simplicity, managed to perform well in reducing the error and bias terms of MODIS Ts as much as the performance of the more complex QM-MBC method.