Resolve of inverse problem in the one-dimensional case based on the one component linear diffusion model by example of concrete composite ceramic

Abstract

Investigation of concrete ceramic is very important for understanding of humidity migration into the porous media according to classical behavior of sorption isotherms or retention and drainage curves. It is good known [1] that behavior of sorption curve according to experimental data [2] is reminds the well known Type IV sorption isotherms described by [4]. Also it was demonstrated in work [1] how the structural parameters of porous body can be obtained according to drainage or retention curves. The main purpose of this work refers to calculation of diffusion properties of water vapor component of gas mixture in the porous sample of concrete like composite ceramic under condition that results [2,3] for distribution of water saturation corresponding to the pore saturation by liquid at isothermal condition is known from experimental or computer simulation data. This method, refers to inverse mathematical problem, is first defined by the works of Liu and Simpson [5-7] and classified as ill-posed problem that is, their solution does not satisfy the general requirements of existence, uniqueness and stability under small changes of the input data [8]. The inverse method has been used with success to determine the thermal conductivity in heat conduction problem by Chen [9] or Yeung and Lan [10]. Since the governing equations for heat conduction and moisture diffusion are similar, it is only natural to use the same procedure to investigate the diffusion coefficients in the moisture resorption or desorption process of the alveolar concrete ceramic.