Matematika i Matematičeskoe Modelirovanie (Aug 2018)
Two-sided Thermal Conductivity Coefficient Estimates in the Porous Body Skeleton
Abstract
Porous composite materials are widely used in engineering as structural and heat-insulating materials. Pores available in such materials are due to both their manufacturing technology and the operating conditions.One of the most important factors in the process of designing products from a porous composite is a set of thermo-physical characteristics of the material. This characteristic determines the application area of the material.Among the thermo-physical properties a thermal conductivity coefficient plays a key role. For some porous materials this coefficient can be determined experimentally, however, to reduce time and resources needed, a theoretical study of this characteristic is more relevant.Theoretical investigation of the thermal conductivity coefficient of a porous composite allows us to predict its possible values depending on the composition of the material and its porosity. Such information about the composite is necessary at various processing stages of the material from its preparation to its using for the structure fabrication.There are many papers on the approaches to the theoretical estimate of the thermal conductivity coefficient of a porous material. However, due to a significant spread of its values, a relevant task is to have the guaranteed two-sided estimates of the possible values of this material characteristic.As is well known, there are some difficulties in making lower estimates of the properties of a porous material. To overcome this difficulty, the paper proposes to use a modification of the structural model of the porous body in conjunction with the dual formulation of the stationary thermal conductivity problem in an inhomogeneous solid.In the paper the structural model modification of a porous body is as follows: a solid sphere with an equal external radius replaces a hollow spherical particle. The solid sphere, in turn, is represented by a composite ball consisting of an inner ball of some conventional material and an outer spherical layer of the skeleton material of the porous body. The equivalent thermal conductivity of the material of the inner ball is to be determined.The structural model modification of the porous body proposed in the paper allowed us to obtain the two-sided estimates of the possible value of this coefficient. Also, the obtained estimates were compared with the improvable upper bound for this characteristic.The obtained results will allow us to predict two-sided estimates of the thermal conductivity coefficient of advanced heat-insulating and structural porous materials.
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