Conduction of heat through one- and multilayer slabs: A differential-difference approach

A novel method for calculating transient heat flow through slabs and walls is presented. The method is based on differential-difference equation of heat conduction with continuous space variable and discretized time variable. The method needs no nodal points inside the slab during computation of temperatures. Thus the time step need not be adjusted according to the thin layers of the wall. Because differential-difference solutions are partly numerical, better accuracy is achieved by analytical methods. However, in multilayer environments the new method turns out to be more straightforward, since no transcendental equations need to be solved numerically, contrary to analytical methods.