Kiln wall freeboard

Equation (7.12) is the form that is required to solve for the temperature distribution in any rectilinear block of material as those encountered in the refractory linings of rotary kilns. Consider a section of a plane wall that is some distance from any edge or corner, for example, a refractory section in the freeboard with certain thickness, receiving heat from the freeboard gas (Figure 7.3). 

The circumferential strip of the kiln freeboard (Figure 7.13) is isolated and subdivided in N small area elements. The portion of the kiln freeboard, approximately three kiln inside diameters in each axial direction viewed by these area elements, is subdivided into volume zones such as Vj comprising the freeboard gas, and the surface zones such as Aj that form the exposed bed and wall surfaces. The exchange areas between each of the zones and the elements of the circumferential strip are then evaluated and used to calculate the radiation streaming to these elements from the various volumes and surface zones, either directly or after undergoing one or two reflections. 

Figure 7.15 Predicted radiation heat transfer coefficients from freeboard gas to the exposed wall for a 41 cm diameter pilot kiln (Barr et al., 1989).

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