A novel and efficient analytical method for calculation of the transient temperature field in a multi-dimensional composite slab

This paper provides an efficient analytical tool for solving the heat conduction equation in a multi-dimensional composite slab subject to generally time-dependent boundary conditions. A temporal Laplace transformation and novel separation of variables are applied to the heat equation. The time-dependent boundary conditions are approximated with Fourier series. Taking advantage of the periodic properties of Fourier series, the corresponding analytical solution is obtained and expressed explicitly through employing variable transformations. For such conduction problems, nearly all the published works necessitate numerical work such as computing residues or searching for eigenvalues even for a one-dimensional composite slab. In this paper, the proposed method involves no numerical iteration. The final closed form solution is straightforward; hence, the physical parameters are clearly shown in the formula. The accuracy of the developed analytical method is demonstrated by comparison with numerical calculations.