We discuss the problem of determining optimum thicknesses for the refractory and thermal insulation layers to minimize the total cost of the lining and the fuel used to compensate for thermal losses. The proposed methodology (with the required temperature at the boundary of the lining layers specified as an additional condition) reduces the 2D constrained optimization problem for a cost function with a locus of discontinuity but no unconstrained minima to the problem of determining the minimum of a unimodal 1D cost function. The work described in this paper is highly relevant because a major furnace overhaul may involve the use of new materials and costs can be optimized by using new data on available materials and their pricing.

中文翻译：

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加热炉最佳衬里厚度的确定

我们讨论确定耐火层和隔热层的最佳厚度的问题，以最大程度地减少衬里和用于补偿热损失的燃料的总成本。拟议的方法（将衬砌层边界处的所需温度指定为附加条件）减少了具有不连续点但不存在约束最小值的成本函数的二维约束优化问题，从而确定了单峰最小值一维成本函数。本文所述的工作具有高度的相关性，因为大修炉可能涉及使用新材料，并且可以通过使用有关可用材料及其价格的新数据来优化成本。