## 824Constructing the Heat Balance Diagram

The first law of thermodynamics as applied to a steady flow-steady state system is conveniently written

where

Q = net rate of heat loss or gain, Btu/hr pi = density of ith inflow or outflow, lb/ft3

Qi = volumetric flow rate of ith inflow or outflow, scfh hi = specific enthalpy of ith inflow or outflow, Btu/lbm h'i = specific enthalpy of z'th inflow or outflow, Btu/scf

W = net rate of mechanical or electric work being transferred to or from the system, Btu/ hr n = total number of inlet or outlet paths penetrating system boundaries

Equation 8.11 constitutes the theoretical basis and the mathematical model of the heat-balance diagram shown in Figure 8.9. It corresponds to the data requirements of the survey form shown in Figure 8.8. Using the data taken from that form, we compute the separate terms of the heat balance for a hypothetical furnace as follows:

H f (fuel energy rate) = firing rate x HHV

where HHV is the higher heating value of the fuel n Btu/ft3 or Btu/gal.

Hf=403.8 X 103ft3/hr x 1030 Btu/ft3

Because this is a dual-fuel installation, we can also construct a second heat-balance diagram for the alternative fuel:

Hf.2 = 3162.6 gph x 131,500 Btu/gal = 415.9 x 106Btu/hr

Writing the combustion equation on the basis of 100 ft3 of dry flue gas from the flue-gas analysis* for natural gas (fuel no. 1):

aCh4 + BO2 + yN2 = 7.8CO2 + 6.3O2 + 0.5CO + 85.4N2 + 2aH2O

Because the chemical atomic species are conserved, we can solve for the relative quantities of air and fuel:

For nitrogen X = 85.4

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