Electric Process Furnace Modeling Using Algebraic Geometric Reduction of the Radiant Heat Transfer Problem

Electrically heated high temperature process furnaces, when powered by renewable energy, are a promising technology for decarbonized chemical production. Although heat transfer, and in relevant cases coupled reaction modeling, is a well-known problem, the geometrical complexity of using (potentially miles of) resistive heating elements to generate heat for large industrial production furnaces makes the problem computationally intractable for multi-physics software and computer hardware affordable for use in furnace design. The so-called “effective emissivity” concept—the value of a flat radiant wall that would predict the electric heating element temperature were the heating elements to be included—simplifies the model for practical use. It allows prediction of the heating element temperature, which is critical to the element's operating life. A method to directly determine this parameter was developed by examining the mathematical structure of the radiant heat transfer problem. With this method, the effective emissivity is only a function of the problem geometry and the emissivity of the electric heating element material. The geometry inputs are in the form of surface areas and view factors. The method fully accounts for the 3-dimensional structure of commercial electric heating solutions.