Journal of T.~ermalAnalysis, Vol. 34 (1988) 871-873 ON TIME-DEPENDENT HEAT CONDUCTION IN LAYERED MATERIALS Towards solving the infinite series problem P. Enders AKADEMIE DER WISSENSCHAFTEN DER DDR, ZENTRALINSTITUT FOR OPTIK UND SPEKTROSKOPIE, BERLIN-1199, G.D.R. (Received May 29, 1987) The asymptotic behaviour of the temperature decay constants in Fourier's' series is shown to be a powerful tool for a simplification of the latter, which may considerably save computing time, simplify the alternative series obtained from the Laplace transformation, thus, solve, at least in principle, the convergence problem of both standard series and lift the problem of matching both ones. The time-dependent heat conduction in layered media faces one with the (an)harmonic Fourier analysis, i.e. with infinite series of decay terms [1, 2]. These series converge ill either for large, or for short times. But good convergence is necessary to recognize individual layers in the temperature or effusivity curve [3-5]. Thus, for practical purposes, it is highly desirable to get a systematic evaluation of the cut-off time, below (above) which the other series becomes preferable, or, alternatively, to improve the convergence of the known series. The goal of this note is to report on the first step in this direction. The basic idea consists in transforming the Fourier series into a lattice sum by using the asymptotics of the temporal decay constants, z,, reported recently [5] and then performing the theta function transformation (which is otherwise only applicable, when the Fourier series is harmonic). Let us assume, that the heat conduction is quasi-onedimensional and that the tenlperature decay at a given point after Dirac-pulse excitation is described by the Fourier series O(t) = ~ F(z.)e -'/'" (1) n=O John Wiley & Sons, Limited, Chichester Akad~miai Kiadr, Budapest