text: Shvab–Zeldovich–Liñán formulation was introduced by Amable Liñán in 1991 for diffusion-flame problems where the chemical time scale is infinitely small (Burke–Schumann limit) so that the flame appears as a thin reaction sheet. The reactants can have Lewis number that is not necessarily equal to one.
  Suppose the non-dimensional scalar equations for fuel mass fraction  (defined such that it takes a unit value in the fuel stream), oxidizer mass fraction  (defined such that it takes a unit value in the oxidizer stream) and non-dimensional temperature  (measured in units of oxidizer-stream temperature) are given by
  where  is the reaction rate,  is the appropriate Damköhler number,  is the mass of oxidizer stream required to burn unit mass of fuel stream,  is the non-dimensional amount of heat released per unit mass of fuel stream burnt and  is the Arrhenius exponent. Here,  and  are the Lewis number of the fuel and oxygen, respectively and  is the thermal diffusivity. In the Burke–Schumann limit,  leading to the equilibrium condition
  In this case, the reaction terms on the right-hand side become Dirac delta functions. To solve this problem, Liñán introduced the following functions
  where ,  is the fuel-stream temperature and  is the adiabatic flame temperature, both measured in units of oxidizer-stream temperature. Introducing these functions reduces the governing equations to
  where  is the mean (or, effective) Lewis number. The relationship between  and  and between  and  can be derived from the equilibrium condition.
  At the stoichiometric surface (the flame surface), both  and  are equal to zero, leading to , ,  and , where  is the flame temperature (measured in units of oxidizer-stream temperature) that is, in general, not equal to  unless . On the fuel stream, since , we have . Similarly, on the oxidizer stream, since , we have .
  The equilibrium condition defines
  The above relations define the piecewise function  
  where  is a mean Lewis number. This leads to a nonlinear equation for . Since  is only a function of  and , the above expressions can be used to define the function 
  With appropriate boundary conditions for , the problem can be solved.
  It can be shown that  and  are conserved scalars, that is, their derivatives are continuous when crossing the reaction sheet, whereas  and  have gradient jumps across the flame sheet.