Smelting furnace refractory and freeze lining heat transfer model

In this post I would like to illustrate how to model heat transfer through the refractory of a smelting furnace, and how to estimate the thickness of a freeze lining on the hot face. This is targeted at readers familiar with smelting furnaces, and would like to utilize measured data to evaluate the heat transfer performance, or alternatively to investigate refractory options. Although complex phenomena exists in the furnace influencing heat transfer and the formation of freeze lining which are in some cases  largely unknown, a simple approach is demonstrated to model the most important effects observed.