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Abstract To study the plane unsteady temperature field and its effect factors in the 2D-FGM plate, assuming that the thermal conductivity and volumetric specific heat capacity of the plate are the distributions of same type of exponential functions along the direction of the height and width in the plate, based on the unsteady heat conduction basic equation of the plate, the series analytical solution of the plane unsteady temperature field in the plate subjected to the different constant temperatures of initial and boundary was derived by the variable separation method. The correctness of the results of this study was verified by using the comparison of two methods. The results show as follows. (1) The isotherms in the square plate are symmetrical to the 450 diagonal of the plate when the gradient parameter ALFA=BETA, and symmetrical to the center of the plate when ALFA=BETA=0. (2) The isotherms in any plate are not symmetrical when ? ALFA is not equal to BETA. (3) With the increase of cooling time, the isotherms in the non-homogenous plate move to the lower left (or upper right) corner, and the isotherms spacing in the upper right (or lower left) corner becomes wider, and the isotherms spacing in the lower left (or upper right) corner becomes more narrow, and the cooling process of the rectangular plate is faster than that of the square plate. Thus, the suitable selection of gradient parameters and geometry can meet the need of the design, application and analysis of the thermal stress of the plate, and the analytical solution can be used as a reference standard for other approximate methods.
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Received: 15 March 2013
Published: 28 June 2014
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2014, Vol. 35 
