One-, two- and three-dimensional steady-state heat conduction

transfer meets the theory of mass transfer, and in which there is much analogy, is the field of air permeation and air exchange in building structures and buildings.

One-, two-and three-dimensional steady-state heat conduction

Heat transfer through conduction can now be modelled with relatively high accuracy by numerical calculations based on Fourier's laws of heat flux and steady heat conduction. The body under study (building construction) is translated by a raster, whose individual nodes correspond to the temperature distribution at a certain time instant. Such a raster is called a temperature field. For a temperature field, the temperature at each of its nodes is a function of position and time:

 = f(x,y,z,t)

We also call it a non-steady (transient) temperature field. If the function of time drops out of the above equation for the temperature at a node of the temperature field and the temperature depends only on position, the temperature field is called steady (stationary). Depending on whether we examine heat conduction in one, two or three dimensions, we speak of one-, two- and three-dimensional temperature fields. Two- and three-dimensional temperature fields are used when the heat flow through the structure is not ideally unidirectional. Such fields are also called deformed temperature fields or thermal bridges. The accuracy and speed of calculation of heat conduction in a deformed temperature field depends on the density of its grid. This should be freely definable, i.e. without limits from the side of the numerical calculation method used, although every software ultimately has some limits. In principle, materials with higher thermal conductivity can have a thinner raster and materials with lower thermal conductivity should in turn have a denser raster [4]. Some boundary conditions (e.g., convective heat transfer coefficients or temperature-dependent equivalent thermal conductivity coefficients), nonlinear radiative heat transfer, or transient heat conduction (by principle) require iterative calculations [4]. The results from individual iterative steps for individual nodes or even the entire temperature field should not differ by more than a predetermined deviation to ensure sufficient stability of the calculation. For example, EN ISO 10211:2008 specifies in its normative annex the requirements for the validation of numerical calculation methods. These should be met by any program for the calculation of 2- or 3-dimensional heat conduction.

In several countries, 2- or 3-dimensional steady-state heat conduction calculations are mainly used for:

• Assessment of the resistance of the constrcution to heat transfer, • Assessment of temperatures on internal surfaces of constructions containing thermal bridges in terms of the critical temperature for mould formation and the dew point temperature, • Assessment of the impact of thermal bridges on the heat loss of the building or room under study.