The power-series method, i.e., a finite analytic approach based on power-series expansion, was applied to transpiration cooling problems, and the stability and accuracy of the method were evaluated. Stability analysis using vow Neumann's method showed that the power-series method was stable for transpiration-cooling problems on the condition that Delta x >= g Delta t, where g is a mass flow rate parameter. The solutions obtained with the power-series method for typical problems were compared with those obtained with the fully implicit finite-difference method. The comparisons revealed that the power-series method yielded more accurate solutions for problems with Robin and Neumann boundary conditions, but less accurate solutions for problems with Robin and Dirichlet boundary conditions. For problems with Robin and Robin boundary conditions, the accuracy of the power-series method depended on the value of the mass flow rate parameter g.
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机译：将幂级数方法（即基于幂级数展开的有限分析方法）应用于蒸腾降温问题，并评估了该方法的稳定性和准确性。使用vow Neumann方法的稳定性分析表明，在Delta x> = g Delta t的条件下，幂级数方法对于蒸腾冷却问题是稳定的，其中g是质量流量参数。使用幂级数方法获得的典型问题的解决方案与通过完全隐式有限差分方法获得的解决方案进行了比较。比较结果表明，幂级数方法对于Robin和Neumann边界条件的问题给出了更准确的解决方案，但是对于Robin和Dirichlet边界条件的问题给出了较不精确的解决方案。对于Robin和Robin边界条件的问题，幂级数方法的准确性取决于质量流率参数g的值。
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