Anyone know what this equation represent?

[Cool SH]

I came across an excel sheet, which can calculate the tube exit surface temperature in fire tube boiler.

E = exp (Surface area*U/Flue gas weight*Cp)

Where,
U = Overall heat transfer coefficient
Cp = Specific heat at constant pressure

Tube gas exit temperature = [(FEGT - Tsat)/E] + Tsat

Where,
FEGT = Furnace exit gas temperature
Tsat = Saturation temperature of water
E = from the equation shown.

I would like to know how the author come across these 2 equations. So anyone has any theory link to provide me, I am grateful for that.

 

[chicopee]

The flue gas weight is in all likely hood the mass rate (ie lbm/sec or some other similar units). As far as the two equations, they are based on the first law of thermo being that heat in minus heat out equals the heat transfer the the tubes. For an elemental tube section of dL length, {[MCpT-MCp(T+dT)]/time}=UA(T-Tw)dL. Tw=temp of water surrounding tube. When you integrate an exponential term will arise and by manipulation you can come up with similar results to the author's work.

 

[davefitz]

It is part of "compact heat exchanger theory". In the case where one of the 2 fluids has an infinite heat capacity ( boiling water, for example), the effectiveness E = 1- exp(-NTU), where NTU= number of transfer units = UA/(WCp, min). WCp, min is the flue gas flowrate and heat capacity.

The effectiveness E also equals E= (Tgi-Tgo)/(Tgi-Tsat) in the boiler case where Tsat is the saturation temp of the boiling water.This works for "boiler banks, evaporators, and fire tube boilers.Tgi= FEGT, Tgo= exit fluegas temp.

"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick