Keywords: coupled heat and moisture transport, Künzel model, hydrophobic materials.

Coupled heat and moisture transport in porous materials becomes very popular and useful in many areas. Examples include building physics or the modelling of concrete creep where the influence of heat and moisture plays a significant role. This paper deals with the Künzel model introduced in reference [1]. The model assumes heat and moisture fluxes both dependent on the gradients of temperature and relative humidity. Governing equations of the transport are the heat and mass balance equations. The balance equations are discretized using the finite element method in space dimensions and by using the generalized trapezoidal rule in time. More details concerning the computer implementation of the model can be found in references [2,3].

In the case of non-conductive materials, severe difficulties with numerical solution were observed. Deeper analyses reveal significant differences of the matrix entries orders. Such matrices are hardly solvable because iterative solvers suffer from an extremely high condition number and therefore an unacceptable number of iterations are required. Application of direct methods is also questionable because of cancellation errors which were observed.

In order to avoid such badly conditioned matrices, adaptive modification of the Künzel model is introduced. Generally, it is not possible to predict which gradient, i.e. gradient of temperature or relative humidity, is dominant and which can be neglected. There are cases where both of them are comparable and both of them have to be taken into account. The matrices of such cases are relatively well conditioned and they can be solved in the classical way. On the other hand, there are cases where one of the gradients is significantly greater than the other and the associated matrices are poorly conditioned. Therefore, the heat and moisture fluxes are evaluated before element matrix assembling. If the contribution of temperature or relative humidity gradient to the fluxes is significantly smaller than the contribution of the other gradient, it is neglected which results in modification of the matrix of material conductivities. Consequently, the element matrix does not contain entries of a very low order and it leads to a better conditioned matrix for the problem.

The modification proposed leads to adaptive manipulation with degrees of freedom. If some finite elements are nearly non-conductive, they should be switched off and the appropriate degrees of freedom too. The physical meaning of this modification is an enforcing of the ideal non-conductivity. The attained values of all quantities at the nodes and on elements switched off are stored because they are required when the elements and degrees of freedom are possibly switched on. It can happen because the conductivities depend on many variables.

Selected example of a wall structure with insulation layers is described. Analysis of the conductivity matrices for particular layers is summarized. Responses of the classical and hydrophobic materials are compared.

1

H.M. Künzel, "Simultaneous Heat and Moisture Transport in Building Components", Fraunhofer Institute of Building Physics, Fraunhofer IRB Verlag Stutgart, 1995.

2

J. Kruis, T. Koudelka, T. Krejcí, "Multi-physics Analyses of Selected Civil Engineering Concrete Structures", Communications in Computational Physics, 12(3), 885-918, 2012. doi:10.4208/cicp.031110.080711s

3

J. Kruis, T. Koudelka, T. Krejcí, "Efficient computer implementation of coupled hydro-thermo-mechanical analysis", Mathematics and Computers in Simulation, 80, 1578-1588, 2010. doi:10.1016/j.matcom.2008.11.010

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £50 +P&P)