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Thermal analysis of layered FGM cylindrical plates subjected to sudden cooling process at one side – Comparison of two applied methods for problem solution
The modern FGMs composite materials have a complex internal structure due to the fact that they consist of several different phases. In this paper, a sudden cooling process (thermal shock) at the upper side of FGM circular plates having discrete variation of the composite features was analysed. The samples were made of five ceramic layers (each of them 0.5 mm thick): purely Al2O3 layer and composite layers made of Al2O3 matrix and 5, 10, 15, 20 wt% content of ZrO2 (Fig. 1). The mechanical response of the plate is axisymmetric, whereas thermal properties are orthotropic. The non-stationary heat conduction equation was solved for arbitrary smooth or step variation of functions describing properties of the analysed material. The considered boundary conditions obey: perfect cooling and real cooling process of the material by introduction of heat transfer coefficient at the cooled surface. The Fourier–Kirchhoff equation for the cylindrical specimen is solved using two methods. The first one is a finite difference (FD) numerical code based on a generalized alternating direction implicit (ADI) method. In the second approach the considered problem was solved with the finite element method (FEM) of ABAQUS code. The heat transfer coefficient at the cooled surface was estimated with a linear monotonic model and with a linear model applying a step function. The solution gives the distribution of the temperature for different times. The theoretical results were compared with experimental ones [T. Sadowski, M. Boniecki, Z. Librant, A. Nakonieczny, Int. J. Heat Mass Transfer 50 (2007) 4461–4467]. Comparison between two numerical approaches was presented.
