Keywords: heat, moisture, differential equation, boundary conditions, Fourier flux, duct.

The description of the complex time-dependent analysis of concrete behaviour can be divided into two independent parts; coupled heat and moisture transfer and prediction of strains with the influence of temperature and humidity. This problem might be solved independently of each other. The coupled non-linear and non-stationary problem of heat and moisture transfer, which forms the input data for complex structural analysis, is described by two partial parabolic differential equations with the primary variables temperature and relative humidity. The differential equation for moisture transfer has been proposed by Prof. Bazant, [1,2] whereas the differential equation for heat transfer was considered in the basic form.

For exactness of the solution it is necessary to prescribe boundary conditions, which can be form in three types: Dirichlet, Neumann or Newton boundary condition. Dirichlet boundary condition prescribes the function of temperature or humidity on the boundary of the solved domain. Neumann and Newton conditions prescribe the moisture or temperature flux in the direction of outer normal to the boundary. Furthermore, the initial conditions of temperature and humidity must be prescribed in each node for non-stationary calculation.

A material law for coupled heat and moisture transfer in concrete, implemented in the finite element program, is based on the material relationship of the cement paste, according to Z. Bazant and Y. Xi, [1] and [2]. For the description of the material behaviour of concrete one assumption was made, that aggregate in concrete does not conduct moisture, so this model could be used for modelling of moisture transfer in concrete.

The Galerkin method has been used for deriving the system of governing equations for heat and moisture transfer. The primary variables, temperature and relative humidity, have been approximated by the linear shape functions for the finite element solution. The non-stationary algorithm has been proposed with the respect to the choice of arbitrary time discretization scheme. For the cases of the practical calculation the best results might be obtained by Crank-Nicolson scheme or Galerkin scheme.

The proposed and implemented numerical algorithm has been tested on the analysis of rectangular wall. The results has been compared with the results obtained by the commercial software . It can be claimed that compared time results gave satisfactory accordance.

A fully coupled heat and moisture transfer has been used for the the long-term analysis of the real structure -- duct. The results (relative humidity, temperature) obtained by the coupled analysis (heat and moisture transfer) have been compared with the results corresponding to the duct, which has the same cross-sectional area, except that the horizontal plate at the bottom of the structure is two times higher. The time-dependent results (humidity) are plotted in the characteristic points of the cross-sectional area, which have the same co-ordinates for both ducts. The time analysis has been done for total time, which is equal to days, when the equilibrium of relative humidity is in each characteristic point of both ducts.

1

Y. Xi, Z.P. Bazant, H.M. Jennings, "Moisture Diffusion in Cementitious Materials (Adsorption Isotherms)", Advanced Cement Based Materials, 1, 248-257, 1994. doi:10.1016/1065-7355(94)90033-7

2

Y. Xi, Z.P. Bazant, H.M. Jennings, L. Molina, "Moisture Diffusion in Cementitious Materials (Moisture Capacity and Diffusivity)", Advanced Cement Based Materials, 1, 258-266, 1994. doi:10.1016/1065-7355(94)90034-5

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