A Mathematical Model of Heat Transfer in Spheroplastic

Abstract

Spheroplastics are composite materials composed of a polymer or organosilicate binder and hollow spherical inclusions (mostly, of glass, but there are also of carbon, phenol, and epoxy), which are called microspheres and have a diameter within a millimeter with the wall thickness of several micrometers. To reduce the material density in watercraft constructions sometimes are used so called macrospheres of up to 40 mm in diameter and shell thickness of 0,5--1,5 mm from spheroplastic with microspheres.Microspheres may contain inert gases such as nitrogen. Many countries have commercialised quartz microspheres. The USA, in particular, produces Q-Gel microspheres with density of 300 kg / m3, the bulk density - 100 kg / m3 and the average diameter of 75 microns,characterized by a high mechanical strength and low cost. Carbon microspheres having low mechanical properties can absorb radio waves in certain frequency ranges. Spheroplastic with silicone microspheres combine relatively high mechanical and dielectric properties.In virtue of low thermal conductivity spheroplastics are used in various heat-insulating structures. As the thermal insulation coatings, the spheroplastic covers the outer surface of the pipes, in particular oil and gas pipelines in the permafrost zones, regions of swampy ground, and underwater. The effective heat conductivity factor, primarily, determines the specific application of spheroplastic as a thermal insulation material. To quantify the value of this factor is necessary to have a mathematical model describing heat ransfer in spheroplastic.The paper presents a four-phase mathematical model of the heat transfer in a representative element of a spheroplastic structure placed in an unlimited array of homogeneous material, the thermal conductivity of which is to be determined as desired characteristics of spheroplastic. This model in combination with a dual variational formulation of stationary heat conduction problem in the inhomogeneous solid first is used to define the guaranteed two-sided boundaries of the parameter space in which there are the true values of effective thermal conductivity of spheroplastic, and then to calculate the dependences of this factor on the bulk concentration of microspheres. The paper conducts a quantitative analysis of the calculated dependences and determines the values of their greatest possible accuracy, which allow us to measure a reliability degree of the predicted effective thermal conductivity of the spheroplastic.

Keywords

• spheroplastic
• microspheres
• four-phase mathematical model
• effective thermal conductivity