The simple model to be described in this section is found to make substantially correct predictions of the overall heat transfer performance for a wide range of furnace types. The model is quite general and can therefore be applied, in principle, to any combustion chamber configuration and to all fuels. The generality, relative simplicity, and predictive potential of the model have led to its extensive use for preliminary design of radiant sections of process heaters and boilers. The model may be readily used to estimate the effect on furnace performance of changes in furnace operational variables such as, for example, fuel flow rate, air preheat, and excess air factor.

The simplifications applied in the model are based on the same assumptions made for well stirred-reactors in chemical reactor design. The principle of separating the gas and surfaces into zones establishes the principal of the Zone method of furnace modelling, which will be developed further in the following two sections. Hence, the stirred-reactor furnace model is commonly known as the single well-stirred zone model. The model is also occasionally referred to as the zero-dimensional zone model, since there is no directional component in the model.

This section provides a manual method of calculating furnace heat transfer performance, and is a useful step in understanding the principle of the Zone method. Today, the calculations would invariably be carried out computationally enabling most of the simplifications in the approach to be relaxed. More detail on the single well-stirred zone model can be found in reference Rhine and Tucker (1991).

A. Basis of model

The furnace chamber is modeled using three zones: a single gas zone to represent the flame and combustion products within the chamber and two surface zones to represent the heat sink and refractory, respectively. It is assumed that the gas can be assigned a mean radiating temperature T_g; the heat sink surface is gray and at a specified temperature T₁; and the refractory surface is radiatively adiabatic. Radiation losses through openings in the furnace walls are neglected.