初始和边界不同恒温时二维梯度板瞬态温度场

为了研究二维功能梯度板的平面瞬态温度场及影响因素,假设热导率和容积比热容在板的高和宽方向为同一类型指数函数分布,基于该板的瞬态热传导基本方程,采用分离变量法,导出在初始和边界不同恒温时该板平面瞬态温度场的级数解析解.通过两种方法的对比,验证了论文研究结果的正确性.结果表明:方板内的等温线,在梯度参数α=β时,对称于板的45°对角线分布,在α=β=0时,对称于板的中心分布;在α≠β时,板的等温线不具对称性;随着冷却时间的增加,非均匀板的等温线向左下(或右上)角移动,右上(或左下)角等温线间距变宽,左下(或右上)角等温线间距变窄,且矩形板的冷却过程比方板更快.因此,可选择适合的梯度参数和几何形状来满足设计、应用和热应力分析的需要,该解析解可作为检验其他近似方法的参考标准.

Unsteady temperature fields in the 2D-FGM plate under different constant temperatures of initial and boundary

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.