Abstract
The shifting function method is utilized to find the exact solution for the one dimensional heat conduction of a slab at two surfaces with time-dependent boundary conditions of the first kind. The proposed method is shown to be simple and accurate. Two examples chosen from the literature are given to reveal the methodology. The convergence rate of the present analysis is very fast and we find that when the dimensionless Fourier number is greater than 1.0, the error for the three-term approximation solution of the infinite series solution can be less than 2%. Moreover, we use alternative shifting functions to solve the problem, but we find that more terms of the infinite series solution are required for numerical calculation.
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