Abstract Using the Laplace transform for solving a two-region (cladding/liquid) conduction problem with an exponentially increasing heat flux boundary condition, an analytic temperature profile has been found. The rate of the temperature increase in the second region (liquid) is used to determine energy deposition in the thermal boundary layer of the liquid. Energy deposition rates are then compared to the latent heat capacity of the growing thermal boundary layer to create a condition for predicting transient critical heat flux (CHF) via the heterogeneous spontaneous nucleation (HSN) trigger mechanism. These analytic predictions are then compared to existing data for exponential power ramp transients with periods ranging from 5 ms up to 10 s. Comparison with experimental data show that the trends of the expected HSN-triggered CHF are in good agreement with the magnitude being controlled by the determination of the maximum boundary layer energy. This work presents the first known attempts to derive a mechanistic CHF prediction model for HSN. Though further work is necessary to develop the HSN model (and is being pursued in parallel to this research), this work will allow for a quantitative prediction of HSN-triggered CHF. Further developments of the HSN model will inform the boundary layer energy threshold that triggers CHF.

中文翻译：

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一种通过异质自发成核触发机制预测功率瞬态 CHF 的新方法

摘要 使用拉普拉斯变换求解具有指数增加热通量边界条件的两区域（包层/液体）传导问题，已找到解析温度分布。第二区域（液体）中的温度升高速率用于确定液体热边界层中的能量沉积。然后将能量沉积速率与不断增长的热边界层的潜热容量进行比较，以创建通过异质自发成核 (HSN) 触发机制预测瞬态临界热通量 (CHF) 的条件。然后将这些分析预测与周期从 5 毫秒到 10 秒不等的指数功率斜坡瞬变的现有数据进行比较。与实验数据的比较表明，预期的 HSN 触发的 CHF 的趋势与由最大边界层能量的确定所控制的幅度非常吻合。这项工作首次尝试为 HSN 推导出机械 CHF 预测模型。尽管需要进一步的工作来开发 HSN 模型（并且正在与本研究同时进行），但这项工作将允许对 HSN 触发的 CHF 进行定量预测。HSN 模型的进一步发展将告知触发 CHF 的边界层能量阈值。尽管需要进一步的工作来开发 HSN 模型（并且正在与本研究同时进行），但这项工作将允许对 HSN 触发的 CHF 进行定量预测。HSN 模型的进一步发展将告知触发 CHF 的边界层能量阈值。尽管需要进一步的工作来开发 HSN 模型（并且正在与本研究同时进行），但这项工作将允许对 HSN 触发的 CHF 进行定量预测。HSN 模型的进一步发展将告知触发 CHF 的边界层能量阈值。