In the Burke-Schumann limit, the flame is considered as a thin reaction sheet outside which both fuel and oxygen cannot exist together, i.e., . The reaction sheet itself is located by the stoichiometric surface where , in other words, where
where  is the stoichiometric mixture fraction. The reaction sheet separates fuel and oxidizer region. The inner structure of the reaction sheet is described by Liñán's equation. On the fuel side of the reaction sheet ()
and on the oxidizer side ()
For given values of  (or, ) and , the flame shape is given by the condition , i.e.,
When  (), the flame extends from the mouth of the inner tube and attaches itself to the outer tube at a certain height (under-ventilated case) and when  (), the flame starts from the mouth of the inner tube and joins at the axis at some height away from the mouth (over-ventilated case).  In general, the flame height is obtained by solving for  in the above equation after setting  for the under-ventilated case and  for the over-ventilated case. 
Since flame heights are generally large for the exponential terms in the series to be negligible, as a first approximation flame height can be estimated by keeping only the first term of the series. This approximation predicts flame heights for both cases as follows
where