This document contains a question from a midterm exam in mechanical engineering about determining the adiabatic flame temperature of a furnace operating with preheated air. The question provides the mass air-fuel ratio, temperatures of the entering air and fuel, and simplified thermodynamic properties. To solve it, the student sets up an energy balance equation accounting for the enthalpies of the products, fuel, and air. They plug in the known values and solve for the adiabatic flame temperature, determining it to be 2543 K. The student also notes they could solve similar problems in Excel by changing variables like the air-fuel ratio or heat capacities.

1. UNIVERSITY OF GAZIANTEP
ENGINEERING FACULTY
MECHANICAL ENGINEERING DEPARTMENT
ME 438 THEORY OF COMBUSTION
TAKE HOME MIDTERM
SUBMITTED TO: Dr. AYŞEGÜL ABUŞOĞLU
SUBMITTED BY:
ÖZGECAN ARACI
BURAK BARLAS
YÜKSEL ERASLAN
İBRAHİM İLKER ERDEM
YAŞAR GÜRBÜZ
ZÜHEYİR NURAL
ERDİ KARAÇAL
DECEMBER 2013

2. QUESTION 2
A furnace uses preheated air to improve its fuel efficiency.Determine adiabatic flame
temperature when the furnace is operating at a mass air fuel-ratio of 16 for air preheated to 600 K.
The fuel enters at 300 K.Assume the simplified thermodynamic properties as follows;
Tref=300 K
MWfuel=MWair=MWprod=29 kg/mol
Cp,fuel=Cp,air=Cp,prod=1200 J/kg.K
hf0,air=hf0,prod=0
hf0,fuel=4x10^7 J/kg

3. When we look at the question it is the simple first law analysis of thermodynamic.
After that we can write the energy equation; There is no heat transfer or no work in the system.
ܳ.
−ܹ.
=ܪ.
௣ −ܪ.
ோ ܳ.
.
= 0 and ܹ
= 0
For A/F ; we can write these equations to use in the enthalpy equation
݉.
୮୰୭ୢ =݉.
୤୳ୣ୪ ∗ (1 +
ܣ
ܨ
)
݉.
ܣ
ܨ
ୟ୧୰ =݉.
୤୳ୣ୪ ∗ (
)
݉.
୤୳ୣ୪ =݉.
୤୳ୣ୪ ∗ 1
We can write the equation as followings;
ܪ.
୔୰୭ୢ୳ୡ୲ =ܪ.
ୖୣୟୡ୲ୟ୬୲
(݉.
௣ ∗ ℎ)୔୰୭ୢ୳ୡ୲ = (݉.
௙ ∗ ℎ)୊୳ୣ୪ + (݉.
ୟ୧୰ ∗ ℎ)୅୧୰
݉.
௙ ∗ (1 +
ܣ
ܨ
) ∗ [(ℎ௙
଴) + ܥ௣ ∗ (ܶୟୢ − ܶ୰ୣ୤)]௉
=݉.
௙ ∗ [(ℎ௙
ܣ
ܨ
଴) + ܥ௣ ∗ (ܶ୤୳ୣ୪ − ܶ୰ୣ୤)]୊୳ୣ୪ +݉.
௙ ∗ (
) ∗ [(ℎ௙
଴) + ܥ௣ ∗ (ܶୟ୧୰ − ܶ୰ୣ୤)]ୟ୧୰
When we write the known values into the equation ;
17 ∗ [0 + 1200 ∗ (ܶୟୢ − 300)]୔୰୭ୢ୳ୡ୲
= 1 ∗ [4 ∗ 10଻ + 1200 ∗ (300 − 300)]୊୳ୣ୪ + 16 ∗ [0 + 1200 ∗ (600 − 300)]ୟ୧୰
After that point solving for Tad will give us the solution.
Tad=2543 K
In our Excel program we can solve the adiabatic flame temperature with the changeable
values.For example we can change the A/F ratio or Cp of any substance or supply temperatures of air
and fuels.