Liñán's equation
In the study of diffusion flame, Liñán's equation is a second-order nonlinear ordinary differential equation which describes the inner structure of the diffusion flame, first derived by Amable Liñán in 1974. The equation reads as d 2 y d ζ 2 = ( y 2 − ζ 2 ) e − δ − 1 / 3 ( y + γ ζ ) {\displaystyle {\frac {d^{2}y}{d\zeta ^{2}}}=(y^{2}-\zeta ^{2})e^{-\delta ^{-1/3}(y+\gamma \zeta )}} subjected to the boundary conditions ζ → − ∞ : d y d ζ = − 1 , ζ → + ∞ : d y d ζ = + 1 {\displaystyle {\begin{aligned}\zeta \rightarrow -\infty :&\quad {\frac {dy}{d\zeta }}=-1,\\\zeta \rightarrow +\infty :&\quad {\frac {dy}{d\zeta }}=+1\end{aligned}}} where δ {\displaystyle \delta } is the reduced or rescaled Damköhler number and γ {\displaystyle \gamma } is the ratio of excess heat conducted to one side of the reaction sheet to the total heat generated in the reaction zone.