基于状态空间理论的功能梯度圆球瞬态热传导分析1)

基于状态空间理论研究功能梯度圆球的球对称瞬态热传导问题。根据热传导方程和热流密度的定义,取温度场和热流密度为系统的状态向量,通过将圆球分层和在时域内应用差分格式对控制方程进行离散,建立了系统的状态方程,给出了功能梯度圆球瞬态热传导问题的半解析解。算例分析表明：本文解不但结果正确、计算效率高,而且适用于材料参数沿径向任意梯度变化的圆球瞬态热传导分析。

AN ANALYSIS OF TRANSIENT HEAT CONDUCTION FOR FUNCTIONALLY GRADED SPHERES BASED ON STATE SPACE THEORY1)

Based on the state space theory, the spherically symmetric transient heat conduction is analyzed for functionally graded spheres. According to the heat conduction equation and the heat flux definition, the temperature field and the heat flux are taken as the state vector for the system. By dividing the sphere into spherical subshells and using the finite difference scheme in the time domain to discretize the governing equations, the state equation is established and a semi-analytical solution is obtained for the transient heat conduction problem of functionally graded spheres. The numerical examples show that the present solution is not only correct and efficient, but also can be applied to the transient heat conduction analysis for arbitrarily graded spheres.