A mathematical model for thermal conductivity of homogeneous composite materials (original) (raw)
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Advanced Engineering Materials, 2008
The knowledge of the effective thermal conductivity of polymer composites is becoming increasingly important in the technological developments and in many engineering applications. The composites made by incorporation of powdery metal fillers into thermoplastic polymers combine the advantageous properties of metals and plastics. The study of thermal parameters of these composites is valuable for the polymer industry. However, metal filled polymer composites are extremely useful for heat dissipation applications in electronic packaging. Dependence of the effective thermal conductivity (ETC) of these materials on porosity, shape factor and packing of the particles is also a matter of concern to engineers, mathematicians and physicists. As it is not often possible to conduct experiments to study the effect of the above parameters on the ETC, a theoretical expression is needed to predict its values. In the literature, there are many experimental as well as theoretical approaches exist on thermal conductivity of polymer composites in which the situation has been simplified by assuming that the particles are of specific shape and arranged in a particular geometries within the continuous medium. Explicit correlations of anisotropic effective conductivity are also established for composite materials with microstructures. [15] These correlations are derived in the framework of non-interaction approximation and applications to realistic microstructures containing mixtures of diverse pore shapes.
Determination of Effective Thermal Conductivity of Composites by Literature Models
International Conference on Engineering Technologies (ICENTE'21), 2021
In this work, literature was surveyed in order to find convenient models of effective thermal conductivity for composites. Five different common models were compared with each other in terms of their consistency by using the same model inputs. Three levels of matrix thermal conductivities, three levels of filler thermal conductivities, and three levels of volume fraction ratios were used as inputs. Obtained trends were graphically plotted against each other. It is seen that models including effects solid-solid interface thermal resistance are giving results distinguishing from models excluding the effects of the interface thermal resistance. It is also understood that models dealing with the thermal conductivity of composites are becoming more complex by considering filler geometries, surface properties, and other interface interactions.
JP Journal of Heat and Mass Transfer, 2018
In this work, an advanced body centered polyhedral model to simulate the periodic microstructure of hybrid composites is performed. The overall material consists of a polymeric matrix reinforced with unidirectional continuous fibers and spherical particles. According to this model, both fibers and particles are distributed inside the matrix in a deterministic manner and their configurations depend on each other. In addition, inhomogeneous interphase layers of different thicknesses are considered to surround both particles and fibers. Next, by the use of this model which takes into account the filler arrangement and contiguity along with the interphase concept, the author obtains explicit expressions to evaluate the longitudinal and transverse thermal conductivity of the composite.
Journal of Zhejiang University Science, 2009
We present an empirical model for the effective thermal conductivity (ETC) of a polymer composite that includes dependency on the filler size distribution—chosen as the Rosin-Rammler distribution. The ETC is determined based on certain hypotheses that connect the behavior of a real composite material A, to that of a model composite material B, filled with mono-dimensional filler. The application of these hypotheses to the Maxwell model for ETC is presented. The validation of the new model and its characteristic equation was carried out using experimental data from the reference. The comparison showed that by using the size distribution law a very good fit between the equation of the new model (the size distribution model for the ETC) and the reference experimental results is obtained, even for high volume fractions, up to about 50%.
Dependence of effective thermal conductivityof composite materials on the size of filler particles
A well-known Maxwell's model for evaluation of effective thermal conductivity has been modified incorporating a correction factor s. It is an important quantity, which influences the effective thermal conductivity of composite materials together with other parameters like volume fraction and thermal conductivities of the constituents. Parameter estimation technique is used to determine the value of s. Optimized value of s is used in the modified Maxwell's model to estimate effective thermal conductivity of composite materials. The effective thermal conductivity of composite materials using an artificial neural network approach has also been calculated. Materials of different sizes of filler particles/matrix have been considered for calculation of the effective thermal conductivity. Results obtained using modified Maxwell's model and artificial neural network technique have been compared with the experimental results available in the literature which shows a good fit.
Effective thermal conductivity of isotropic polymer composites
International Communications in Heat and Mass Transfer, 1998
The effective thermal conductivity of tin powder filled high density polyethylene composites is investigated experimentally as a function of filler concentration and the measured values are compared with the existing theoretical and empirical models. Samples are prepared by compression molding process, up to 16% volumetric concentration of tin particles. The thermal conductivity is measured by a modified hot wire technique in a temperature range from about 0°C to 70°C. Experimental results show a region of low particle content, up to about 10% volume concentration, where the increase in thermal conductivity is rather slow. The filler particles are dispersed in the matrix material in this region, the thermal conductivity is best predicted by Maxwell's model and Nielsen's model with A=I.5, d~m=0.637. Whereas, at high filler concentrations, the filler particles tend to form agglomerates and conductive chains in the direction of heat flow resulting in a rapid increase in thermal conductivity. A model developed by Agari and Uno estimates the thermal conductivity in this region, using two experimentally determined constants.
International Journal of Thermophysics, 2003
The addition of conductive filler in a polymer matrix is an effective way to increase the thermal conductivity of the plastic materials, as required by several industrial applications. All quantitative models for the thermal conductivity of heterogeneous media fail for heavily filled composites. The percolation theory allows good qualitative predictions, thus selecting a range for some qualitative effects on the thermal conductivity, and providing a way to choose a range for some experimental parameters. The design of such composite materials requires a study of its thermal features combined with different mechanical, ecological, safety, technical, and economical restrictions. A specific small guarded hot plate device with an active guard, conductive grease layer, and controlled variable pressure was used for measurement of the transverse thermal conductivity on 15 mm sided samples of composite parts. Extensive thermal and composition measurements on filled thermoplastics show that the conductivity of the filler, its size and shape, and its local amount are, with the degree of previous mixing, the main factors determining the effective conductivity of composites. For injection-molded polybutylene terephtalate plates, the best filler is the short aluminum fiber. With fibers of 0.10 mm diameter, it is possible to obtain conductivities larger by factors of 2, 6, and 10 than those of polymer for aluminum contents of 20, 42, and 43.5 vol%, respectively.
Role of Filler-Polymer Interface on the Thermal Conductivity in Polymer Composites
Journal of Polymer & Composites, 2020
Polymers with high thermal conductivity are the need of modern technologies due to their robustness, cost-effectiveness and less corrosiveness. However, bare polymers are not good heat-conductors due to their molecular structures, and their non-metallic properties. Therefore, metallic fillers of different shapes and sizes have been used to enhance the thermal conductivity in polymer-composites. However, there has been search for best geometrical fillers which can maximize the thermal conductivity effectively with same volume percent. From our numerical simulations, we show that the best geometrical fillers are those which have high surface-area (S) to volume (V) ratio. In such cases, the interface of polymer-filler is maximized, which leads to the effective enhancement in the thermal conductivity. To validate our claim, we use fillers with same volume percent but maximize the surface area. We also show that there is a competition between surface and the bulk of the filler in this maximization process but surface-area dominates with an effective increase in the thermal conductivity. We use 3-dimensional models using ANSYS-Fluent to show the characteristic behaviour of thermal conductivity. Polyethylene has been used as the base polymer and aluminium (Al) has been used as filler in all our model simulation.
International Journal of Thermophysics, 2013
The thermal behavior of hollow conductive particles filled in epoxy resin has been investigated using 3D finite element computation. The effect of the filler concentrations associated with the particle/matrix interfacial resistance on the effective thermal conductivity of the composites was considered. The relationship between the out-of-plane effective thermal conductivity, the wall thickness of the hollow particles, and the ratio of the thermal conductivities of the filler to the matrix material were also taken into account. The numerical results show an increase of the effective thermal conductivity with increasing wall thickness of the hollow particles. However, for a large contact resistance and/or for a high effective thermal conductivity, it is shown that the contact resistance has a dominant influence on the effective thermal conductivity of the composites. The numerical results were also compared to some well-known analytical effective thermal conductivity models.