text: For simplicity, assume combustion takes place in a single global irreversible reaction
  where  is the ith chemical species of the total  species and  and  are the stoichiometric coefficients of the reactants and products, respectively. Then, it can be shown from the law of mass action that the rate of moles produced per unit volume of any species  is constant and given by
  where  is the mass of species i produced or consumed per unit volume and  is the molecular weight of species i.
  The main approximation involved in Shvab–Zeldovich formulation is that all binary diffusion coefficients  of all pairs of species are the same and equal to the thermal diffusivity. In other words, Lewis number of all species are constant and equal to one. This puts a limitation on the range of applicability of the formulation since in reality, except for methane, ethylene, oxygen and some other reactants, Lewis numbers vary significantly from unity. The steady, low Mach number conservation equations for the species and energy in terms of the rescaled independent variables
  where  is the mass fraction of species i,  is the specific heat at constant pressure of the mixture,  is the temperature and  is the formation enthalpy of species i, reduce to
  where  is the gas density and  is the flow velocity. The above set of  nonlinear equations, expressed in a common form, can be replaced with  linear equations and one nonlinear equation. Suppose the nonlinear equation corresponds to  so that
  then by defining the linear combinations  and  with , the remaining  governing equations required become
  The linear combinations automatically removes the nonlinear reaction term in the above  equations.