激光辐照下多层圆柱体中三维瞬态温度场的解析解

Analytical solutions of 3D transient temperature field in a multilayer cylinder irradiated by high power laser beam

考虑外表面的气流影响和层间温度与传热的协调关系,建立了激光辐照下,层合圆柱体中的三维瞬态热传导解析模型。利用特征值法和Bessel函数,导出了各层柱体中三维瞬态温度场的封闭解析解。以一维轴对称问题为例计算了柱体中的瞬态温度场,给出了柱体内部温度随时间的变化和柱体表面换热系数对温度场的影响规律。本文的理论解可进一步用于分析层合圆柱体中的三维瞬态热-力效应,并可作为相应问题的数值模拟中数值模型的修正依据。

A theoretical model of 3D transient heat conduction in a multilayer cylinder irradiated by high power laser was developed in which the action of air flow around the exterior surface and the compatibilities of both temperature and heat transfer at the interfaces were taken into consideration. By using eigenvalue method and Bessel functions, the closed solutions of 3D transient temperature field in each layer of the cylinder were deduced. As a simple example, the axisymmetric transient tem- perature field was analytically computed and the effect rules of some parameters such as surface heat- exchange coefficient on the temperature field were obtained. The theoretical solutions of transient temperature field can be further used to analyze 3D thermo-mechanical effects of multilayer cylinders and can also be used as basis of modification of numerical models in related numerical simulations.