Conduction of heat through slabs and walls: A differential-difference approach for design, energy analysis and building automation applications: Dissertation

Modelling thermal behaviour of buildings needs effective tools when conduction of heat through slabs or walls is computed. This paper presents a novel method for those applications. The method is based on differential equation of heat conduction modified to a differential-difference equation with continuous space variable and discretized time variable. The solution differs from conventional differential-difference solutions due to the time derivative concept and backward propagation principle. In this paper, one-dimensional problems are examined in semi-infinite, one- and multi-layer environment. Solutions are presented with the aid of past values of temperature and boundary functions. Coefficients of each time step are calculated recursively. These features make the solution straightforward, compact and easy to apply to several environments. Because differential-difference solutions are partly numerical, better accuracy is achieved by analytical methods, like the pulse transfer method. However, in a multi-layer environment the latter turns out to be more complicated, since a lot of transcendental equations must be solved for computing numerical results, contrary to the new method. The new method is also compared with numerical solutions choosing an explicit method as a typical representative. The results show that in most cases better accuracy is achieved with the differential-difference method when time steps of both methods are equal. In addition, the new method needs no nodal points inside the slab during computation of temperatures. Thus, time steps need not be adjusted according to thin layers of the wall, which makes the new method faster in multi-layer environment. The differential-difference method is also inherently stable, which is not true for all numerical methods. The new method is suggested for dynamic thermal models of buildings in which time step is less than one hour.