I will talk about some finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis in 90's. We proved that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Implications on the effective flame front and other related inverse type problems will also be discussed. This is a joint work with Wenjia Jing and Hung Tran.