Micro-Macro Modelling Approach of Vegetal Wools Thermal Conductivity

Biosourced materials such as vegetal wools offer major thermal insulation advantages in the green buildings field. Experimental characterisations of vegetal wools thermal conductivity as a function of their density show the existence of an optimum conduction-radiation coupled value. This specific point, as well as the properties of vegetal wools are related to the large variability of shapes and sizes of their fibres. In order to take this specificity into account, it seems particularly relevant to use micro-macro modelling methods to predict the thermal conductivities related to both conduction and radiation heat transfer phenomena. In a first time, a self-consistent method based on a cylindrical geometry (SCMcyl) is used as a modelling approach for conduction transfers. Then, a modelling approach developed by Bankvall and based on an equivalent fibre radius value is used for radiation transfers. So, by coupling these two approaches, it is possible to obtain an equivalent thermal conductivity of fibrous materials as a function of density. Finally, this method is validated by comparison with experimental data.

An Anisotropic Equivalent Thermal Model for Shield Differential Through-Silicon Vias

An accurate equivalent thermal model is proposed to calculate the equivalent thermal conductivity (ETC) of shield differential through-silicon via (SDTSV). The mathematical expressions of ETC in both horizontal and vertical directions are deduced by considering the anisotropy of SDTSV. The accuracy of the proposed model is verified by the finite element method (FEM), and the average errors of temperature along the X-axis, Y-axis, diagonal line, and vertical directions are 1.37%, 3.42%, 1.76%, and 0.40%, respectively. Compared with COMSOL, the proposed model greatly improves the computational efficiency. Moreover, the effects of different parameters on the thermal distribution of SDTSV are also investigated. The thermal conductivity is decreased with the increase in thickness of SiO2. With the increase in pitch, the maximum temperature of SDTSV increases very slowly when β = 0°, and decreases very slowly when β = 90°. The proposed model can be used to accurately and quickly describe the thermal distribution of SDTSV, which has a great prospect in the design of 3D IC.

New Equivalent Thermal Conductivity Model for Size-Dependent Convection-Driven Melting of Spherically Encapsulated Phase Change Material

Spherically encapsulated phase change materials (PCMs) are extensively incorporated into matrix material to form composite latent heat storage system for the purposes of saving energy, reducing PCM cost and decreasing space occupation. Although the melting of PCM sphere has been studied comprehensively by experimental and numerical methods, it is still challenging to quantitatively depict the contribution of complex natural convection (NC) to the melting process in a practically simple and acceptable way. To tackle this, a new effective thermal conductivity model is proposed in this work by focusing on the total melting time (TMT) of PCM, instead of tracking the complex evolution of solid–liquid interface. Firstly, the experiment and finite element simulation of the constrained and unconstrained meltings of paraffin sphere are conducted to provide a deep understanding of the NC-driven melting mechanism and exhibit the difference of melting process. Then the dependence of NC on the particle size and heating temperature is numerically investigated for the unconstrained melting which is closer to the real-life physics than the constrained melting. Subsequently, the contribution of NC to the TMT is approximately represented by a simple effective thermal conductivity correlation, through which the melting process of PCM is simplified to involve heat conduction only. The effectiveness of the equivalent thermal conductivity model is demonstrated by rigorous numerical analysis involving NC-driven melting. By addressing the TMT, the present correlation thoroughly avoids tracking the complex evolution of melting front and would bring great convenience to engineering applications.

The Equivalent Thermal Conductivity of the Micro/Nano Scaled Periodic Cubic Frame Silver and Its Thermal Radiation Mechanism Analysis

Currently, there are few studies on the influence of microscale thermal radiation on the equivalent thermal conductivity of microscale porous metal. Therefore, this paper calculated the equivalent thermal conductivity of high-porosity periodic cubic silver frame structures with cell size from 100 nm to 100 µm by using the microscale radiation method. Then, the media radiation characteristics, absorptivity, reflectivity and transmissivity were discussed to explain the phenomenon of the radiative thermal conductivity changes. Furthermore, combined with spectral radiation properties at the different cross-sections and wavelength, the radiative transmission mechanism inside high-porosity periodic cubic frame silver structures was obtained. The results showed that the smaller the cell size, the greater radiative contribution in total equivalent thermal conductivity. Periodic cubic silver frames fluctuate more in the visible band and have better thermal radiation modulation properties in the near infrared band, which is formed by the Surface Plasmon Polariton and Magnetic Polaritons resonance jointly. This work provides design guidance for the application of this kind of periodic microporous metal in the field of thermal utilization and management.

Prediction of mechanical and thermal properties of particle reinforced hydrogel composites using the structural genome approach

In this paper, the structural genome approach is used for multiscale analyses to predict the mechanical and thermal properties of particle reinforced hydrogel composites. First, the structure genome model of particle reinforced hydrogel composites is created by the random sequential adsorption algorithm. Then the mechanical properties and equivalent thermal conductivity of hydrogel composites are numerically studied by the structural genome approach. The effects of particles with different volume fractions and material properties on their mechanical and thermal properties are investigated. From the simulation results, it can be found that within a certain range of volume fraction, the mechanical properties and equivalent thermal conductivity of hydrogel composites are positively correlated with the volume fractions of particles. We also find that with the increase of the mechanical properties and thermal conductivity of particles, the properties of hydrogel can be improved and eventually reach stabilization. The structural genome approach shows excellent efficiency in multiscale structure analysis. It is a convenient method for the simulation of complex soft material composites.

MathConnex mathematical package for calculating the equivalent thermal conductivity of a strip coil

When heating complex metal loads (layered, fibrous, granular), the gas gaps in them increase the temperature difference across the charge section and lead to an increase in the duration of its heating. Optimizing the time of complex loads heating, which helps to reduce fuel consumption and improve the heated metal quality, requires knowledge of temperature fields in them, which, in turn, depend on the equivalent thermal conductivity of the complex load. For their calculations mathematical modeling can be used, which requires a highly qualified researcher. Carrying out of laboratory and experimental researches takes a lot of time and demands big material expenses, thus the received results are applicable only to a concrete charge. A number of authors give formulas for calculating the equivalent thermal conductivity of the strip coil. However, the practical use of such formulas is difficult due to the presence of difficult to determine parameters: the degree of the strip layers contact, thermal conductivity of different layers of strip and gas gaps between them, heat transfer coefficients by radiation in the gaps between layers. In this case, different formulas for calculating the equivalent thermal conductivity give signifi cantly different results. In the present work, for 20 steel strip coils with height, inner and outer diameters, respectively, 1; 0.4–0.966 m; with a strip thickness of 0.001; 0.003; 0.006 m, the number of layers per side 17; 25 and 50, for the coefficients of strip coil filling 0.70; 0.75; 0.80; 0.85; 0.90; 0.95; 0.97; 0.99, 0.999, the degrees of the strip layers contact 2.8–3.0% and different heated media (air, nitrogen, hydrogen), the reduced thermal conductivity coefficients were calculated according to various formulas using the MathConnex mathematical package (part of MathCadPro). On the basis of the conducted researches the formula for calculation of equivalent thermal conductivity of strip coils is chosen. The results of the calculation are in good agreement with the literature data, it can be used to calculate temperature fields and thermophysical parameters in layered metal loads, as well as to calculate their heating time and furnace performance.

A novel fractal model for the prediction and analysis of the equivalent thermal conductivity in wood

This study proposes a new fractal model to improve the accuracy of equivalent thermal conductivity (ETC) prediction for wood and determine how the wood’s pore structure influences ETC. Using fractal theory and mercury injection porosimetry data, a fractal model for the geometry of the wood’s pore structure was built. The geometric model was then transformed into an equivalent thermal resistance model to calculate ETC. The calculations produced an explicit expression for ETC derived from the wood’s structural parameters including the minimum and maximum pore apertures, aperture distribution, porosity, and fractal dimension. The model also includes a probability factor. The simulated ETC produced by the model was validated by experiments and it was found to be in good agreement with these. These simulation results will be used to study the influence of several factors on ETC. The proposed model has the potential to be able to predict and analyzing other wood properties such as its electrical conductivity, diffusivity, and permeability and the model can likely also be used to analyze other porous materials.

Development of a Turbine Generator Stator 3D Thermal Model Taking into Account Gas Dynamics

The construction of a thermal model of a fully air cooled turbine generator stator with taking into account gas dynamics is considered. The complete mathematical model includes various physical subsystems with multiphysical relationships. The study is based on accurate 3D models with the use of the modern and proven COMSOL Multiphysics software, in which the finite element method is used for calculation. The equivalent thermal conductivity of the gap between the winding bar copper conductors and stator iron is studied. The gap in question consists of the winding bar main insulation and a gap filled with additional semiconducting gaskets or similar materials. The above-mentioned physical parameter has a strong influence on the temperature distribution, because the main part of the heat releasing in the bar is transferred to the stator core through these elements. The optimal minimum equivalent thermal conductivity coefficient is analyzed and selected. A model of a turbine generator stator symmetric element together with a turbulent cooling air flow is developed and analyzed. The development of such integrated models will make it possible not only to simplify the design process, but also to analyze various insulation systems. For example, air-cooled turbine generators initially use the Global VPI insulation system; however, after replacing---for economic reasons---the stator winding, another insulation system is used, namely, the Resin Rich system. For correctly making a transition to another insulation system, integrated calculations, including thermal ones, should be carried out. In practice, after changing the insulation system, which may entail certain thermal limitations, it may be necessary to decrease the turbine generator rated power output for its further operation without overheating the stator winding, which can be obtained on the basis of simulation. In this regard, the equivalent thermal conductivity coefficient also plays an important role; its value can be preliminarily analyzed to select the necessary materials in terms of their thermal properties, and their filling factor to retain the turbine generator nominal parameters after its rewinding.