Modeling and Measurement of Effective Thermal Conductivity of Materials Reinforced with Bars

Abstract

This article proposes new analytical dependencies for determining the thermal conductivity of materials reinforced with bars. Thermal conductivity in this case is determined in the direction parallel to the axis of the bars. According to the RVE (also called REV—representative elementary volume) method, a minimal representative volume is selected in the original reinforced material, in which the thermophysical properties of the original material are reproduced. Based on Fourier’s law, analytical dependences are derived to determine the effective thermal conductivity of the reinforced material with bars, as well as a material with cylindrical cavities. The effective thermal conductivity is affected by both the thermal conductivity of original materials and geometric parameters of the reinforcement (bar diameters and the distance between them). As part of the study, numerical simulation of the thermal conductivity process in cement reinforced with polymer bars was carried out using the Ansys software package. Graphical dependences of the effective thermal conductivity of the reinforced material depending on the bar diameters are built. A comparison is made of the effective thermal conductivity obtained using a numerical solution by the finite element method and an analytical solution. The discrepancies between the numerical and analytical methods for determining the effective thermal conductivity do not exceed 2 %. The experimental study also confirms the numerical and analytical models. Thus, in an experimental study of a polymer-reinforced sample, the effective thermal conductivity was $k_{ef} = 0.344$ W/(m·K) and in the analytical solution—$k_{ef} = 0.354$ W/(m·K). The discrepancy in this case is 3 %.