Design Guidelines for High Performance Industrial Furnaces - High Temperature Air Combustion: From Energy Conservation to Pollution Reduction - page 308

Agitating fans are installed in the ceiling of the heating room to improve temper-
ature distribution.

5.4.3.1 Heat Balance and Evaluation Method of Furnace Performance

The φ CG model, which has a term of surface area of gas, is generally used for
estimation of overall heat absorptivity. With an indirect heating furnace, which uses
radiant tubes (RT), a heat transfer model is used for calculation without consideration
of gas radiation, as shown in Figure 5.68 . The φ CH model has no term of gas radiation,
in contrast to the φ CG model for direct-heating furnace. 1 Table 5.23 compares the
φ CG model, φ CH model, and the model equation. As shown in the model equations,
the φ CH model does not include terms of surface area of gas A G and emissivity of
gas ε g , and it is determined by the geometrical relation of positions of heating area
and heat-receiving area.
The φ CH can be calculated by Equation 5.3:

( )

4 4

q = φ T T (5.3)

CH H C

where q is the heat flux (W/m 2 ), T C is the average temperature of surface of the
coils, T H is the average temperature of RT, and σ is the Stefan-Boltzmann constant.
The φ CH and λ on plate-like material are factors that are concerned with elevating
the temperature of heated materials in the RT type heat treatment furnace, as shown
in Figure 5.69 . The heat flux at the surface of materials being heat-treated can be
calculated if φ CH is defined and, further, the process of elevating temperature both
of stable and of nonstable heating conditions can be calculated if the thermal
conductivity λ is defined. The calculation model of φ CH is shown in Equation 5.4
with the emissivity of surface of RT, ε H , and of surface of coil, ε C :

1 1 A

A

1 1

C

=+ 1

+−

1

φ ε ε

*

F

CH HH C

CH

=+

*

FFF F

* * * RC

CH CH RH *

1- F

(5.4) RR

FF F =+

RC

CH RH

1 F

RR

= F

CH

Calculation of the shape factor F CH of a heating surface projected from the side
of heat-treating materials is easier if the data of angles related to the tube arrays that
are listed in the heat transfer engineering handbook are used, because RT is in tube
form. 2 The thermal conductivity of materials is listed according to material compo-
sition in the related heat transfer engineering handbooks. When the heat transfer is