Deterioration of equivalent thermal conductivity of granite subjected to heating-cooling treatment

Understanding the thermal conductivity of granite is critical for many geological and deep engineering applications.The heated granite was subjected to air-,water-,and liquid nitrogen(LN2-)coolings in this context.The transient hot-wire technique was used to determine the equivalent thermal conductivity(ETC)of the granite before and after treatment.The deterioration mechanism of ETC is analyzed from the meso-perspective.Finally,the numerical model is used to quantitatively study the impact of cooling rate on the microcrack propagation and heat conduction characteristics of granite.The results show that the ETC of granite is not only related to the heating temperature,but also affected by the cooling rate.The ETC of granite decreases nonlinearly with increasing heating temperature.A faster cooling rate causes a greater decrease in ETC at the same heating temperature.The higher the heating temperature,the stronger the influence of cooling rate on ETC.The main explanation for the decrease in ETC of granite is the increase in porosity and microcrack density produced by the formation and propagation of pore structure and microcracks during heating and cooling.Further analysis displays that the damage of granite at the heating stage is induced by the difference in thermal expansion and elastic properties of mineral particles.At the cooling stage,the faster cooling rate causes a higher temperature gradient,which in turn produces greater thermal stress.As a result,it not only causes new cracks in the granite,but also aggravates the damage at the heating stage,which induces a further decrease in the heat conduction performance of granite,and this scenario is more obvious at higher temperatures.

A method used to determine the upper thermal boundary of subgrade based on boundary layer theory

In the numerical simulation of long-term subgrade temperature fields, the daily variation of soil temperature at a certain depth h is negligible. Such phenomenon is called the ＂boundary layer theory.＂ Depth h is defined as the boundary layer thickness and the soil temperature at h is approximately equal to a temperature increment plus the average atmosphere temperature. In the past, the boundary layer thickness and temperature increment were usually extracted from monitored data in the field. In this paper, a method is proposed to determinate the boundary layer thickness and temperature incre- ment. Based on the typical designs of highway or railway, the theoretical solution of boundary layer thickness is inferred and listed. Further, the empirical equation and design chart for determining the temperature increment are given in which the following factors are addressed, including solar radiation, equivalent thermal diffusivity and convective heat-transfer coefficient. Using these equations or design charts, the boundary layer thickness and temperature increment can be easily determined and used in the simulation of long-term subgrade temperature fields. Finally, an example is conducted and used to verify the method. The result shows that the proposed method for determining the upper thermal boundary of subgrade is accurate and practical.

Analysis of temperature field for a surface-mounted and interior permanent magnet synchronous motor adopting magnetic-thermal coupling method

Aiming at obtaining high power density of surface-mounted and interior permanent magnet synchronous motor(SIPMSM),it is important to accurately calculate the temperature field distribution of SIPMSM,and a magnetic-thermal coupling method is proposed.The magnetic-thermal coupling mechanism is analyzed.The thermal network model and finite element model are built by this method,respectively.The effects of power frequency on iron losses and temperature fields are analyzed by the magnetic-thermal coupling finite element model under the condition of rated load,and the relationship between the load and temperature field is researched under the condition of the synchronous speed.In addition,the equivalent thermal network model is used to verify the magnetic-thermal coupling method.Then the temperatures of various nodes are obtained.The results show that there are advantages in both computational efficiency and accuracy for the proposed coupling method,which can be applied to other permanent magnet motors with complex structures.

Determination of the thermal noise limit in test of weak equivalence principle with a rotating torsion pendulum

Thermal noise is one of the most fundamental limits to the sensitivity in weak equivalence principle test with a rotating torsion pendulum. Velocity damping and internal damping are two of many contributions at the thermal noise, and which one mainly limits the torsion pendulum in low frequency is difficult to be verified by experiment. Based on the conventional method of fast Fourier transform, we propose a developed method to determine the thermal noise limit and then obtain the precise power spectrum density of the pendulum motion signal. The experiment result verifies that the thermal noise is mainly contributed by the internal damping in the fiber in the low frequency torsion pendulum experiment with a high vacuum. Quantitative data analysis shows that the basic noise level in the experiment is about one to two times of the theoretical value of internal damping thermal noise.

Predictive analysis of buckling distortion of thin-plate welded structures

The welding buckling distortions of thin plated structures were investigated based on finite element methods.An engineering treatment method for predicationg the buckling distortion was proposed.The equivalent applied thermal load was used to simulate the welding residual stress,thus the calculation of complex welding distortion can be transformed into 3D elastic structural applied load analyses,which can reduce the quantities of calculating work effectively.The validation of the method was verified by comparison of the numerical calculation with experimental results.The prediction of buckling distortion for side walled structures of passenger train was performed and the calculation was in agreement with measuring results in general.It is shown that the main factors for producing the buckling are the intermittent fillet and plug weld during welding the stiffened beams and columns to the panel.

Numerical simulation of a buried hot crude oil pipeline during shutdown

In this paper a mathematical model is built for a buried hot crude oil pipeline during shutdown, and an unstructured grid and polar coordinate grid are respectively applied to generating grids for the soil region and the three layers in the pipe （wax layer, pipe wall, and corrosion-inhibiting coating）. The governing equations are discretized using the finite volume method. The variations in temperatures of static oil and soil were investigated during pipeline shutdown in both summer and winter, in which some important parameters of the soil and crude oils of a Northeast pipeline are employed.

SIMULATION OF STEEL COIL HEAT TRANSFER IN HPH FURNACE

The mathematical model has been estublished for the simulation of steel coil＇s heat transfer during annealing thermal process in HPH （high performance hydrogen） furnace. The equivalent radial thermal conductivity is adopted by statistical analysis regression approach through the combination of a large quantity of production data collected in practice and theoretical analyses. The effect of the number of coils on circulating flow gas is considered for calculating the convection heat transfer coefficient, The temperature within the coil is predicted with the developed model during the annealing cycle including heating process and cooling process. The good consistently between the predicted results and the experimental data has demonstrated that the mathematical model established and the parameters identified by this paper are scientifically feasible and the effective method of calculation for coil equivalent radial heat transfer coefficient and circulating gas flow has been identified successfully, which largely enhances the operability and feasibility of the mathematic- model. This model provides a theoretical basis and an effective means to conduct studies on the impact that foresaid factors may imposed on the steel coil＇s temperature field, to analyze the stress within coils, to realize online control and optimal production and to increase facilily output by increasing heating and cooling rates of coils without producing higher thermal stress.

Characterization of size effect of natural convection in melting process of phase change material in square cavity

The accelerating effect of natural convection on the melting of phase change material(PCM)has been extensively demonstrated.However,such an influence is directly dependent on the size and shape of domain in which phase change happens,and how to quantitatively describe such an influence is still challenging.On the other hand,the simulation of natural convection process is considerably difficult,involving complex fluid flow in a region changing with time,and is typically not operable in practice.To overcome these obstacles,the present study aims to quantitatively investigate the size effect of natural convection in the melting process of PCM paraffin filled in a square latent heat storage system through experiment and simulation,and ultimately a correlation equation to represent its contribution is proposed.Firstly,the paraffin melting experiment is conducted to validate the two-dimensional finite element model based on the enthalpy method.Subsequently,a comprehensive investigation is performed numerically for various domain sizes.The results show that the melting behavior of paraffin is dominated by the thermal convection.When the melting time exceeds 50 s,a whirlpoor flow caused by natural convection appears in the upper liquid phase region close to the heating wall,and then its influencing range gradually increases to accelerate the melting of paraffin.However,its intensity gradually decreases as the distance between the melting front and the heating wall increases.Besides,it is found that the correlation between the total melting time and the domain size approximately exhibits a power law.When the domain size is less than 2 mm,the accelerating effect of natural convection becomes very weak and can be ignored in practice.Moreover,in order to simplify the complex calculation of natural convection,the equivalent thermal conductivity concept is proposed to include the contribution of natural convection to the total melting time,and an empirical correlation is given for engineering applications.

Numerical study on the effective thermal conductivity and thermal tortuosity of porous media with different morphologies

Effective thermal conductivity and thermal tortuosity are crucial parameters for evaluating the effectiveness of heat conduction within porous media.The direct pore-scale numerical simulation method is applied to investigate the heat conduction processes inside porous structures with different morphologies.The thermal conduction performances of idealized porous structures are directly compared with real foams across a wide range of porosity.Real foam structures are reconstructed using X-ray computed tomography and image processing techniques,while Kelvin and Weaire-Phelan structures are generated through periodic unit cell reconstruction.The detailed temperature fields inside the porous structures are determined by solving the heat conduction equation at the pore scale.The results present that the equivalent thermal conductivity of Kelvin and Weaire-Phelan structures is similar to and greater than that of the real foam structure with the same strut porosity.The thermal tortuosity of real foam structure is relatively larger and the heat conduction path becomes straighter by adopting the anisotropic design.The thermal tortuosity of the fluid channels for Kelvin,Weaire-Phelan,and real foam structures is close to one.The thermal conductivity of porous structures with heat transfer fluid increases as the thermal conductivity ratio of fluid to solid becomes larger.A small porosity of porous media leads to a larger equivalent thermal conductivity due to the dominant contribution of porous skeleton in the heat conduction process.Correlations derived from parallel and series models,as well as the Maxwell-Eucken models,provide decent predictions of effective thermal conductivity,with an average error of less than 8%in the entire range of thermal conductivity ratio.

Prediction of Equivalent Thermal Conduction Resistance of Printed Circuit Heat Exchangers

Printed circuit heat exchangers(PCHEs) have great potential to be employed in the advanced nuclear reactor systems. In this work, the equivalent thermal conduction resistance of PCHE is studied. The influences of thermal convection resistance are analyzed. The results indicate that the equivalent thermal conduction resistance of PCHEs with unequal numbers of hot plates and cold plates are sensitive to the thermal convection resistance of hot side and cold side. Specifically, for case C which has unequal number of hot and cold channels, the maximum value of equivalent thermal conduction resistance can be 1.7-2.4 times the minimum value. The equivalent thermal conduction resistance is underestimated under the isothermal boundary. In addition, the non-uniformity of the lengths of all the heat flux lines determines the influence degree of thermal convection resistance on the equivalent thermal conduction resistance. For further investigation, Latin hypercube sampling method is adopted to generate a large number of design points for each PCHE configuration. Based on the sample data, mathematical correlations and artificial neural network(ANN) for prediction of equivalent thermal conduction resistance for each case are developed. The proposed correlations of equivalent thermal conduction resistance for each case have acceptable accuracy of prediction with a wide range covering general engineering applications. The ANN model can achieve much better prediction accuracy than the proposed correlations thus it is recommended in the cases that the prediction accuracy is considered as the priority need.

Thermal performance analysis of non-uniform height rectangular fin based on constructal theory and entransy theory

A model of non-uniform height rectangular fin, in which the variation of base's thickness and width are taken into account, is established in this paper. The dimensionless maximum thermal resistance(DMTR) and the dimensionless equivalent thermal resistance(DETR) defined based on the entransy dissipation rate(EDR) are taken as performance evaluation indexes. According to constructal theory, the variations of the two indexes with the geometric parameters of the fin are analyzed by using a finite-volume computational fluid dynamics code, the effects of the fin-material fraction on the two indexes are analyzed. It is found that the two indexes decrease monotonically as the ratio between the front height and the back height of the fin increases subjected to the non-uniform height rectangular fin. When the model is reduced to the uniform height fin, the two indexes increase first and then decrease with increase in the ratio between the height of the fin and the fin space. The fin-material fraction has no effect on the change rule of the two indexes with the ratio between the height of the fin and the fin space. The sensitivity of the DETR to the geometric parameters of the fin is higher than that of the DMTR to the geometric parameters. The results obtained herein can provide some theoretical support for the thermal design of rectangular fins.

Thermal Property Measurements of a Large Prismatic Lithium-ion Battery for Electric Vehicles

Because of the high cost of measuring the specific heat capacity and the difficulty in measuring the thermal conductivity of prismatic lithium-ion batteries,two devices with a sandwiched core of the sample-electric heating film-sample were designed and developed to measure the thermal properties of the batteries based on Fourier's thermal equation.Similar to electrical circuit modeling,two equivalent thermal circuits were constructed to model the heat loss of the self-made devices,one thermal-resistance steady circuit for the purpose of measuring the thermal conductivity,the other thermal-resistance-capacitance dynamic circuit for the purpose of measuring the specific heat capacity.Using the analytic method and recursive least squares,the lumped model parameters of these two thermal circuits were extracted to estimate the heat loss and correct the measured values of the self-made devices.Compared to the standard values of the reference samples of the glass and steel plates,the measured values were corrected to improve the measurement accuracies beyond 95% through steady thermal-circuit modeling.Compared to the measured value of the specific heat capacity of the battery sample at 50% state of charge using the calorimeter,the measured value using the self-made device was corrected in order to elevate the measurement accuracy by about 90% through dynamic thermal-circuit modeling.As verified through the experiments,it was reliable,convenient,and low cost for the proposed methodology to measure the thermal properties of prismatic lithium-ion batteries.

Thermal Resistance Simulation for CoF Packages

Chip-on-Film （CoF） is a packaging technology that mounts Integrated Circuits （IC） chips directly on a flexible substrate surface. As both power and the number of pins in such packages increase, thermal conditions become more important. In this paper, the thermal resistance of CoF packages is studied using Ansys software to perform finite-element analysis. Because of circuit complexity, two equivalent methods-a length-weighted method and an image-recognition method--are proposed in place of an accurate model to get equivalent thermal conductivity of CoF package devices. In our experiments, the simulated value of thermal resistance based on the length-weighted method was 1.653 K/W, and the value based on the image-recognition method was 1.911 K/W. The real thermal resistance value of the CoF package device is 1.812 K/W. So the error between the real value measured by a tester and the simulated value based on the length-weighted method is 8.8%, and the error between the real value and the simulated value based on the image-recognition method is 5.5%. Hence, both methods can provide effective simulation results, and the image-recognition method is more accurate. In addition, we optimized the CoF package structure. From the simulation results, the drop in thermal resistance after the optimization is obvious.