Global weak solutions for coupled transport processes in concrete walls at high temperatures

Abstract

Key wordsInitial-boundary value problems for second-order parabolic systems, nonlinear boundary conditions, global existence of weak solutions, coupled heat and mass transport.We consider an initial-boundary value problem for a fully nonlinear coupled parabolic system with nonlinear boundary conditions modeling hygro-thermal behavior of concrete at high temperatures. We prove a global existence of a weak solution to this system on any physically relevant time interval. The main result is proved by an approximation procedure. This consists in proving the existence of solutions to mollified problems using the Leray-Schauder theorem, for which a priori estimates are obtained. The limit then provides a weak solution for the original problem. A practical example illustrates a performance of the model for a problem of a concrete segment exposed to transient heating according to three different fire scenarios. Here, the focus is on the short-term pore pressure build up, which can lead to explosive spalling of concrete and catastrophic failures of concrete structures.

Homogenization of a thermo-diffusion system with Smoluchowski interactions

“…We refer to (8)-( 18) as (P ε ) -our reference microscopic model. Note that the Soret and Dufour coefficients determine the structure of the particular crossdiffusion system (see [12], [26] [2], [3], [22], [29]). The coefficients a i and b i describe the deposition interaction between u ε i and v ε i .…”

“…Accounting for the interplay between heat, diffusion, attraction-repulsion, and deposition of the colloidal particles is of paramount importance for a number of applications including the dynamics of the colloidal suspension in natural or man-made products (e.g. milk, paints, toothpaste) [12], drug-delivery systems [2], hierarchical assembly of biological tissues [27], group formation in actively interacting populations [30], or heat stocks in porous materials [4]. Further details on colloids and their practical relevance are given in [10,23], e.g.…”

“…Practical applications of our approach would include predicting the response of refractory concrete to high-temperatures exposure in steel furnaces, propagation of combustion waves due to explosions in tunnels, drug delivery in biological tissues, etc. ; see for instance [3,4,25,28,11,10]. In the paper [15] we study quantitatively some of these effects, focusing on colloids deposition under thermal gradients.…”

Analysis of non‐isothermal multiphase flows in porous media

“…41 Recently, in Amaziane et al, 42 the authors have shown the existence of weak solutions to the coupled heat transport and two-phase immiscible incompressible flows through porous materials. An existence analysis for problems with a specific structure modeling the heat and moisture transport in cementitious materials can be found in previous studies [43][44][45] (including the transport of dissolved chemical species, chemical reactions and hydration phenomena) and in Beneš, 46 where the author introduced the hygro-thermal model coupled with quasi-static evolution equations modeling elastic and inelastic mechanical deformations.…”

Structure and Stability of Steady State Bifurcation in a Cannibalism Model with Cross-Diffusion

“…Practical applications of such approach would investigate the problem of reducing a heterogeneous material to a homogeneous, specifically, predicting the response of refractory concrete to high-temperature exposure in steel furnaces. In nature, the impact of heat and mass transfer processes become particularly evident at high temperatures, where the increased pressure in pores, large temperature gradients, and temperature-induced creep may lead to catastrophic service failures [11]. Benes et al [12] discussed a nonlinear numerical scheme arising from the implicit time discretization of the Bazant-onguthai model (with crossdiffusion) for hygrothermal behavior of concrete at high temperatures.…”