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An integral equation for the planar ablation problem

机译:平面烧蚀问题的积分方程

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摘要

A Laplace transform in the spatial variable is used to obtain a Volterra integral equation for the problem of determining the speed and position of the moving boundary of an evaporating surface. The integral equation is applicable for an arbitrary Stefan number and variable heat input. Asymptotic formulas for the short-time behavior are derived. The integral equation is solved numerically to illustrate several features of planar ablation. Of particular interest is the approach to a steady state, which is seen to be very slow compared to the preheat time or the characteristic diffusion time.
机译:针对确定蒸发表面的运动边界的速度和位置的问题,使用了空间变量中的拉普拉斯变换来获得Volterra积分方程。积分方程适用于任意Stefan数和可变热量输入。推导了短时行为的渐近公式。对积分方程进行数值求解,以说明平面烧蚀的几个特征。特别令人关注的是达到稳态的方法,与预热时间或特征扩散时间相比,该方法非常慢。

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