梯度功能材料非定常热传导的形状效应

采用分离变量法和变量代换法，推导出无限大平板、无限长圆柱体和圆球体3种形状的梯度功能材料构件在第三类边界条件下的量纲一非定常温度场的解析解。3种形状的梯度功能材料构件的组分和热－物理性能分别服从平面对称、轴对称和球对称分布规律。通过数值计算并与无限大平板、无限长圆柱体和圆球体3种形状的均质构件对比，研究梯度功能材料构件形状以及热－物理性能分布对非定常热传导的影响。计算结果表明，梯度功能材料构件的非定常热传导具有与均质构件相似的形状效应，即圆球体的温度传播速度最快，而无限大平板的温度传播速度最慢。由表及里增大梯度功能材料构件的热导率和热扩散率，可提高温度传播速度。

Shape Effect of Unsteady Heat Conduction for Functionally Gradient Materials

The analytical formulae of the dimensionless unsteady temperature fields for an infinite plate, an infinite solid cylinder and a solid sphere made of functionally gradient materials (FGM) under convective boundary conditions are derived respectively by using the separation-of-variables method and the variable substitution method. The composition and the thermo-physical properties of the three kinds of FGM components with different shapes are of planar symmetric, axially symmetric and spherically symmetric distributions respectively. The influences of the FGM component shapes as well as the distributions of thermo-physical properties on their unsteady heat conductions are investigated via numerical calculations in contrast to homogeneous infinite plate, infinite solid cylinder and solid sphere respectively. The results reveal that the unsteady heat conductions for FGM components have a shape effect similar to that for homogeneous components, namely, the heat conduction rate is the fastest in sphere and is the lowest in plate; and that the heat conduction rate of FGM components can be improved by increasing both the thermal conductivity and the thermal diffusivity from the surface to the interior.