Air Liquide has been involved in the design of industrial furnaces (glass melting, reheating, aluminum, …) for several years. Thanks to that experience, known-how and expertise in modeling such applications have been developed. Dedicated simulation tools — 0D for global heat and mass balance, 1D for the prediction of longitudinal temperature profiles and 3D for detailed analysis — have been built. Each of them is very helpful when used relevantly and offers numerous opportunities at each step of the design of a furnace. In such kind of applications, the temperature levels are very high (up to 2500 K). As a consequence it is very crucial to simulate the radiative heat transfer as accurately as possible. This requires the use of a radiation model that can take into account complex geometries, non-isothermal media and various gas mixture compositions. Very often, three-dimensional simulations are necessary and reduction to smaller dimension problems is difficult or inadequate. The present paper introduces a new radiation model for computing two-dimensionally radiative heat transfer in an industrial furnace with a piecewise distributed load. To reduce the three-dimensional problem to two dimensions, the method consists in coupling the 2D radiation transport equation to a boundary condition based on view factors through an imaginary plane to homogenize the radiative behavior of the load surface. A solution procedure using the discrete transfer method associated to a weighted-sum-of-gray-gases database to deal with absorption and emission of a CO2-H2O mixture is proposed. Simulation results are finally compared to an analytical formula and then to a full-3D approach taking into account participating media, non-isothermal and gray walls. All tests show that this model can be used to simulate industrial configurations with a good accuracy.
Effect of solid conductivity on radiative heat transfer in packed beds
