scholarly journals The Emergent Behaviour of Thermal Networks and Its Impact on the Thermal Conductivity of Heterogeneous Materials and Systems

2020 ◽  
Vol 4 (1) ◽  
pp. 32
Author(s):  
Chris R. Bowen ◽  
Kevin Robinson ◽  
Jianhui Tian ◽  
Meijie Zhang ◽  
Vincent A. Coveney ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Granular Media ◽  
Mixing Rule ◽  
Two Phase ◽  
Model Mixing ◽  
Two Phases ◽  
The Individual ◽  
Variability Region ◽  
Multi Phase

The properties of thermal networks are examined to understand the effective thermal conductivity of heterogeneous two-phase composite materials and systems. At conditions of high contrast in thermal conductivity of the individual phases (k1 and k2), where k1 << k2 or k1 >> k2, the effective thermal conductivity of individual networks of the same composition was seen to be highly sensitive to the distribution of the phases and the presence of percolation paths across the network. However, when the contrast in thermal conductivities of the two phases was modest (k1/k2 ~ 10−2 to 102), the thermal networks were observed to exhibit an emergent response with a low variability in the effective thermal conductivity of mixtures of the same composition. A logarithmic mixing rule is presented to predict the network response in the low variability region. Excellent agreement between the model, mixing rule and experimental data is observed for a range two-phase porous and granular media. The modelling approach provides new insights into the design of multi-phase composites for thermal management applications and the interpretation or prediction of their heat transfer properties.

scholarly journals Estimation of Effective Thermal Conductivity of Two-Phase Material for Hollow Circular Model

2018 ◽  
Vol 172 ◽  
pp. 02004
Author(s):  
Prateek Kumar Sahu ◽  
Nisha Netam ◽  
Lal Chandra Shah
Keyword(s):  
Thermal Conductivity ◽  
Circular Cylinder ◽  
Effective Thermal Conductivity ◽  
Complex Structure ◽  
Fundamental Property ◽  
Percentage Error ◽  
Phase System ◽  
Two Phase ◽  
Hollow Circular Cylinder ◽  
Circular Model

Two-phase materials are commonly used in engineering application because of its various properties like strength, thermal conductivity, durability and toughness etc. Effective thermal conductivity (ETC) of two-phase material is the fundamental property to predict its thermal performance. Various geometry (spheres, cylinders, irregular particles) have been considered by researchers for calculating ETC of two-phase materials. Due to complex structure, hollow circular cylinder geometry is not reported yet. In this paper, two-dimensional periodic two-phase system, with hollow circular cylinder shape is considered for calculating ETC. In present work unit cell approach method is used to derive collocated parameters model for estimation of ETC. Hollow circular cylinder model with Ψ = 0.2 gives good result for estimating ETC with average percentage error of 6.46%.

On a Spring-Network Model and Effective Elastic Moduli of Granular Materials

1999 ◽  
Vol 66 (1) ◽  
pp. 172-180 ◽  
Author(s):  
K. Alzebdeh ◽  
M. Ostoja-Starzewaski
Keyword(s):  
Granular Materials ◽  
Disordered Systems ◽  
Granular Media ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Effective Medium ◽  
Solid State Physics ◽  
Two Phase ◽  
Effective Medium Theories ◽  
The Individual

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.

Experimental and Theoretical Modeling of the Effective Thermal Conductivity of Rough Steel Spheroid Packed Beds

2003 ◽  
Vol 125 (4) ◽  
pp. 693-702 ◽  
Author(s):  
G. Buonanno ◽  
A. Carotenuto ◽  
G. Giovinco ◽  
N. Massarotti
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Solid Mechanics ◽  
Packed Bed ◽  
Elementary Cell ◽  
Upper And Lower Bounds ◽  
Packed Beds ◽  
The Finite Element Method ◽  
Two Phase ◽  
Experimental Apparatus

The upper and lower bounds of the effective thermal conductivity of packed beds of rough spheres are evaluated using the theoretical approach of the elementary cell for two-phase systems. The solid mechanics and thermal problems are solved and the effects of roughness and packed bed structures are also examined. The numerical solution of the thermal conduction problem through the periodic regular arrangement of steel spheroids in air is determined using the Finite Element Method. The numerical results are compared with those obtained from an experimental apparatus designed and built for this purpose.

The Effective Thermal Conductivity of a Multi-Phase System

1998 ◽  
Vol 51 (2) ◽  
pp. 349-360 ◽  
Author(s):  
B. M. Suleiman ◽  
S.E. Gustafsson ◽  
E. Karawacki ◽  
R. Glamheden ◽  
U. Lindblom
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Phase System ◽  
Multi Phase

Effective Thermal Conductvity of Three-Phase Soils

2012 ◽  
Author(s):  
Fabio Gori ◽  
Sandra Corasaniti
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Heat Fluxes ◽  
Water Volume ◽  
Two Phase ◽  
Empirical Constant ◽  
Three Phase ◽  
Theoretical Predictions ◽  
Porosity Ratio ◽  
Good Agreement

The aim of the present paper is to determine the effective thermal conductivity of three-phase soils, made of a quasi-spherical solid grain, and surrounded by two phase, which can be water and air or water and ice. The effective thermal conductivity is obtained theoretically by integrating the conduction equation under the thermal distribution of parallel heat fluxes in steady-state. The effective thermal conductivity is evaluated at a given degree of porosity (ratio between the void volume and the total one) and different degrees of saturation (ratio between the water volume and the void one) from dryness up to saturation. Comparisons between experimental data and theoretical predictions confirm that the present model can predict the effective thermal conductivity with a fairly good agreement without using any empirical constant.

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