Description

Q2 (30 points). The derivation of the burning velocity of laminar premixed flames is based on the following equations:
• mass conservation: ˙m = ρu = const.
• species mass balance (for the simplified one-step reaction mechanism case):
,
where ˙ωi = νiWiω˙ (i = F,O2). Here νi is the stoichiometric coefficient and Wi is the molecular weight of i. The model for the reaction rate term ˙ω is

dT d2T dx dx
• energy equation in the temperature form: ˙mCp = λ 2 + Qω˙i.
Review the derivation of the burning velocity. Discuss the dependence of SL on φ (make all the necessary assumptions and simplifications if needed).
Q3 (20 points): For the non-adiabatic thermal explosion problem, use the asymptotic method (perturbation based on some small parameter), derive the temperature evolution equation.
Q4 (35 points): For the ignition/extinction problem of a well mixed flowing system,
(1) reproduce the temperature equation introduced in lecture;
1