Heat-Mass-Transport and Thermal Stresses in Porous Charring Materials

Abstract

The aim of this paper is to develop a method of asymptotic averaging for processes occurring in porous charring materials under high temperatures. The advantage of the method is the ability to calculate not only averaged macrocharacteristics of the processes, namely internal gas generation, filtration and deforming processes, but also microcharacteristics, such as microstresses in phases of charring material, gas velocity in a pore, etc. To determine microcharacteristics, the method allows us to formulate special mathematical problems ‘on a periodic cell’. To calculate macrocharacteristics, such as pore pressure of filtrating gas, rate of charring and macrostresses, with the help of asymptotic averaging method, averaged ‘global’ equations are formulated. Here effective characteristics of porous medium (gas permeability coefficient, rate of charring, elasticity modulus, thermal expansion coefficient) are determined not empirically, as in most works on porous materials, but on the basis of solving the local problems. Solution of these problems over the periodic cell allows us to derive analytically the law of the Darcy type for a gas phase flow in porous media, to obtain an expression for intensive mass transfer between solid and gas phases, to set the form of constitutive relations for charring porous media, and also to calculate microstresses in a vicinity of a growing pore. As an example of solving a global averaged problem, the problem on one-sided high-temperature heating of a plate made of epoxy binder has been solved numerically.