The stirred-reactor furnace model described in the previous section predicts the overall heat transfer performance of furnaces, but it gives no information on the distribution of heat flux within the furnace and it cannot account for some important design parameters, for example, the burner heat release pattern. These limitations can be serious when the furnace is long compared with its mean hydraulic radius, for example, fire-tube boilers, tunnel kilns, and metal reheating furnaces. For these cases, the plug-flow, or long-furnace, model is more appropriate.

A. Basis of model

The gas at any flow cross-section is assumed to have a reasonably uniform velocity and to be characterized by a single temperature. When combustion occurs, heat is released in such a way that the gas temperature over the furnace cross section remains reasonably uniform. Further, it is assumed that the net radiative flux in the flow direction is negligible, that all surfaces are gray, and that the refractory surfaces are in radiative equilibrium. Radiation losses through openings are neglected.

B. Model formulation

(a) Heat transfer from furnace gases