flame be denoted with subscript and similarly, the burnt gas conditions by , then we can define an equivalence ratio for the unburnt mixture as . Then the planar laminar burning velocity for fuel-rich mixture () is given by where and . Here is the thermal conductivity, is the specific heat at constant pressure and is the Lewis number. Similarly one can write the formula for lean mixtures. This result is first obtained by T. Mitani in 1980. Second order correction to this formula with more complicated transport properties were derived by Forman A. Williams and co-workers in the 80s. Variations in local propagation speed of a laminar flame arise due to what is called flame stretch. Flame stretch can happen due to the straining by outer flow velocity field or the curvature of flame; the difference in the propagation speed from the corresponding laminar speed is a function of these effects and may be written as: where is the laminar flame thickness, is the flame curvature, is the unit normal on the flame surface pointing towards the unburnt gas side, is the flow velocity and are the respective Markstein numbers of curvature and strain. Turbulent In practical scenarios, turbulence is inevitable and, under moderate conditions, turbulence aids the premixed burning process as it enhances the mixing process of fuel and oxidiser. If the premixed charge of gases is not homogeneously mixed, the variations on equivalence ratio may affect the propagation speed of the flame. In some cases, this is desirable as in stratified combustion of blended fuels. A turbulent premixed flame can be assumed to propagate as a surface composed of an ensemble of laminar flames so long as the processes that determine the inner structure of the flame are not affected. Under such conditions, the flame surface is wrinkled by virtue of turbulent motion in the premixed gases increasing the surface area of the flame. The wrinkling process increases the burning velocity of the turbulent premixed flame in comparison to its laminar counterpart. The propagation of such a premixed flame may be analysed using the field equation called as G equation for a scalar as: , which is defined such that the level-sets of G represent the various interfaces within the premixed flame propagating with a local velocity . This, however, is typically not the case as the propagation speed of the interface (with resect to unburned mixture)