Two-sided Estimates of Thermal Conductivity Coefficient of a Porous Body Skeleton

Abstract

Porous composite materials are widely used in engineering as structural and heat-insulating materials. The presence of pores in such materials is due to both the technology of their manufacture and the operating conditions.One of the most important factors in the process of designing products from a porous composite is the complex of thermophysical characteristics of the material. This characteristic determines the application area of the material.Among the thermophysical properties the leading role is played by the coefficient of thermal conductivity. This coefficient for some porous materials can be determined experimentally, however, in order to reduce the 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 stages of working with the material from its preparation to the construction of a structure from it.There are many works devoted to approaches to the theoretical evaluation of the coefficient of thermal conductivity of a porous material. However, due to a significant spread of its values, an actual task is to construct guaranteed two-sided estimates of the possible values of this material characteristic.As is well known, there are some difficulties in constructing lower estimates of the properties of a porous material. In this paper, to overcome this difficulty, a modification of the structural model of the porous body was used in conjunction with the dual formulation of the stationary heat conduction problem in an inhomogeneous solid.The modification of the structural model of a porous body in this paper is as follows: a hollow spherical particle is replaced by a solid sphere with an equal external radius. 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 carcass material of the porous body. The equivalent thermal conductivity of the material of the inner ball is to be determined.The modification of the structural model of the porous body proposed in the work allowed to obtain two-sided estimates of the possible value of this coefficient. Also, the obtained estimates were compared with unimprovable upper bound for this characteristic.The obtained results will allow us to predict two-sided estimates of the thermal conductivity coefficient of perspective heat-insulating and structural porous materials.