论文标题
与空间相关的潜热的一阶段类似Stefan的问题的近似解决方案
Approximate solutions to one-phase Stefan-like problems with space-dependent latent heat
论文作者
论文摘要
本文的工作涉及研究与空间依赖性潜热的一维单相类似Stefan样问题的不同近似值的研究。它被认为是两个不同的问题，它们在固定面上施加的边界条件下彼此不同：Dirichlet和Robin条件。通过应用热平衡积分法（HBIM），一种修改的热平衡积分方法，即改进的积分方法（RIM）来获得近似解决方案。利用精确的分析解决方案，我们比较并测试了近似解决方案的准确性。使用无尺寸的广义Stefan编号（Ste）和Biot号（BI）进行分析。当BI在对流条件下到达无穷大时，还研究了这种情况，当在固定面上施加温度条件时恢复了近似溶液。提供了一些数值模拟，以断言哪些近似积分方法被证明是最佳的。此外，我们基于最小化最小二乘误差的构成近似技术，还获得了经典Stefan问题的近似解决方案。
The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), a modified heat balance integral method, the refined integral method (RIM) . Taking advantage of the exact analytical solutions we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalized Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimizing the least-squares error, obtaining also approximate solutions for the classical Stefan problem.
