Simplification of a two-dimensional heat and mass transfer model by a transformation of coordinates

The derivation of a mathematical model for heat and mass transfer in a packed bed reactor subject to vertical fluid flow is discussed. If certain simplifying assumptions can be made, and if there is no vertical movement of the bed, then the model can be reduced to a simple form in two dimensions which can be solved by the method of characteristics. It is shown how the same simple type of model can be derived for a packed bed in which vertical movement of the solid does occur; the method is based on a transformation of the vertical coordinate. Substantial vertical movement of the granules in a packed bed does occur in many industrial reactors due to phenomena such as settling and slump. The method is being applied to the modelling of an iron ore sintering machine; slump in such a machine can cause a reduction of bed height of 20%.