about λ values rather than AFR. Most practical AFR devices actually measure the amount of residual oxygen (for lean mixes) or unburnt hydrocarbons (for rich mixtures) in the exhaust gas. Fuel–air equivalence ratio (ϕ) The fuel–air equivalence ratio, ϕ (phi), of a system is defined as the ratio of the fuel-to-oxidizer ratio to the stoichiometric fuel-to-oxidizer ratio. Mathematically, where m represents the mass, n represents a number of moles, subscript st stands for stoichiometric conditions. The advantage of using equivalence ratio over fuel–oxidizer ratio is that it takes into account (and is therefore independent of) both mass and molar values for the fuel and the oxidizer. Consider, for example, a mixture of one mole of ethane () and one mole of oxygen (). The fuel–oxidizer ratio of this mixture based on the mass of fuel and air is and the fuel-oxidizer ratio of this mixture based on the number of moles of fuel and air is Clearly the two values are not equal. To compare it with the equivalence ratio, we need to determine the fuel–oxidizer ratio of ethane and oxygen mixture. For this we need to consider the stoichiometric reaction of ethane and oxygen, C2H6 + O2 → 2 CO2 + 3 H2O This gives Thus we can determine the equivalence ratio of the given mixture as or, equivalently, as Another advantage of using the equivalence ratio is that ratios greater than one always mean there is more fuel in the fuel–oxidizer mixture than required for complete combustion (stoichiometric reaction), irrespective of the fuel and oxidizer being used—while ratios less than one represent a deficiency of fuel or equivalently excess oxidizer in the mixture. This is not the case if one uses fuel–oxidizer ratio, which takes different values for different mixtures. The fuel–air equivalence ratio is related to the air–fuel equivalence ratio (defined previously) as follows: Mixture fraction The relative amounts of oxygen enrichment and fuel dilution can be quantified by the mixture fraction, Z, defined as , where , YF,0 and YO,0 represent the fuel and oxidizer mass fractions at the inlet, WF and WO are the species molecular weights, and vF and vO are the fuel and oxygen stoichiometric coefficients, respectively. The stoichiometric mixture fraction is The stoichiometric mixture fraction is related to λ (lambda) and ϕ (phi) by the equations , assuming Percent excess combustion air In industrial fired heaters, power plant steam generators, and large