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A finite-difference model for simulations of thermal wave propagation In a layered material is discussed. The method is based on the implicit scheme in solving the partial differential heat equation. According to the conventional implicit methods of solving the heat equation, a large set of equations must be solved to find the temperature distribution of the object at any time. This will cause a serious problem when working with large samples or experiments of long duration as well as generalizing the method to two and three dimensions. To avoid this complication, the concept of sparse matrices is successfully utilized to accelerate the solution of a large system of equations while simulating each time step, as well as reducing the computer memory consumption. Parker's method of evaluating the thermal diffusivity of a material is tested by this approach. The model proves to give reliable results for thermal diffusivity measurement in 1D and 2D Cartesian systems that show good agreement with experiments conducted on samples of metals and epoxy.
Ghodsi, Ghazal, "Non-destructive investigation of thermal diffusivity in a layered material using finite difference modeling" (2010). Electronic Theses and Dissertations. 8245.