第二类边界条件下固液相变问题的改进型准稳态近似解

Improved Quasi-Steady-State Approximation Analysis of Stefan Problems Under 2nd-Kind Boundary Conditions

基于准稳态近似方法,从热平衡角度出发,给出了直角坐标系和圆柱坐标系中恒定热流边界条件下传导型固液相变传热问题的无量纲近似解.对于直角坐标系情形,得到的改进型准稳态近似解精度高,且解的形式为显式表达式,相比于已有的隐式近似解更便于直接使用.对于圆柱坐标系的情形,所得到的近似解是目前文献公开报道的唯一的近似解.此改进型准稳态近似解弥补了传统准稳态近似方法不考虑显热的不足,提高了准稳态近似法的精度,丰富了固液相变传热问题的求解方法,物理意义明确,可用于实际应用问题的初步分析和计算.

Improved quasi-steady-state approximation solutions were obtained for Stefan problems under the 2nd-kind boundary conditions,both in Cartesian and cylindrical coordinates,based on the traditional quasi-steady state approximation and the 1st law of thermodynamics.For the Cartesian coordinate condition,the solution has high accuracy,and is convenient for practical use for its explicit form.For the cylindrical coordinate solution,the presented approximation solution is the only solution reported in the related literatures.The proposed improved solutions take sensible heat into consideration and greatly promote the accuracy of traditional methods,and enrich the analysis methods for the Stefan problems,with definite physical meaning of a useful reference for quick preliminary calculation of practical problems.