HEAT TRANSFER IN THE RADIANT SECTION OF PETROLEUM HEATERS (part1): 1 - 2 - 3 - 4

The heat balance equation may be written: (Datum temperature = 60° F.)

(13)

By multiplying both sides of the equation by H(1 - b) we obtain:

(14)

Then

(15)

This may be transposed to:

(16)

The merit of such a relation is that the term in parentheses in the brackets is dependent on the fuel characteristics, excess air, air preheat, etc., and may be separately evaluated. After its value is determined, it may be used to establish the simple graphical relation among H (( 1 - b )) / aA_cp , q / aA_cp , t_g , in accordance with the following construction:

Since the term (t'_f  - 60) is, from its method of construction the theoretical temperature the gases would attain (a) if combustion were adiabatic except for the loss of the fraction b of the enthalpy of the fuel and (b) if the products of combustion had a mean specific heat equal to their mean value from t_g down to the base temperature, the term t'_f  may be thought of as a sort of flame temperature, referred to hereafter as the pseudo-flame temperature for short.
If now a plot is constructed with the coordinates q/aA_cp and t_g' a series of lines representing equation (12) may be placed on the plot; one for each value of surface temperature t_s (see Figures 1 and 2). On the same diagram a straight line through the value t'_f (completely determined by fuel characteristics, and presented for varying conditions of operation in Figures 3 and 4 in which the radiant section external losses have been taken as 2% of the total net heat input to the furnace) drawn through a point on the family of curves corresponding to the correct tube skin temperature, t_s , and for q/aA_cp or t_g (according to which of these is fixed) when extended to the left, will intersect the line t_g =60° at the value of H (( 1 - b )) / aA_cp .

In design calculations the temperature, t_g , of the flue gases leaving the radiant section must be estimated before the pseudo-flame temperature can be obtained. This assumed or provisional t'_f must be revised if the assumed bridge wall temperature is found to be considerablely in error. The descriptive example included at the end of this section illustrates the method of calculation.
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