The rates of (a) single-step reactions, (b) reactions satis[ying the steady-state approximation, (c) 'explosive' chain reactions, may be expressed as explicit [unctions o/ temperature, i[ the diffusion coefficients o[ reactants and heat are equal. The paper provides a simple method o[ predicting the laminar burning velocities in gaseous mixtures exhibiting these reactions. Examination of exact solutions shows that burning velocity can be calculated with 1 per cent accuracy by:
(i) Plotting a curve of R versus ~, conductivity ร volumetric energy release rate where R =the conductivity of the unburnt gas, k. temperature rise and r==_ tnffxil?lunl temperature rise, T~--T,, (ii) Evaluating area beneath ttle curve, R (iii) Evaluating horizontal position, r of centroid o] area beneath R curve (iv) Evaluating ,, from ,=05--06604 (1 -re[ -04283 (1 --rc)'-' (v) Evaluating burning velocity v t, from v!=[k~R/&(Tb--T~)c:peu]ยฝ where p,,=density of unburnt gas, and c=mean specific heat at constant pressure. Graphs are given which lead to the burning velocity when the diffusion coefficients of reactant or radical are not normal. IN calculating laminar flame velocities, it frequently occurs that the local rate of reaction per unit volume can be expressed as a function of local temperature, before the main calculation begins. Cases in which the reaction rate functions are explicit in this way are: (i) the single-step reaction, (ii) chain reactions obeying the steady-state approximation, (iii) simple chain-branching reactions. It is necessary that the diffusion coefficients of all components should be 'normal'*, and that the flames should be adiabatic. Several methods exist by which the differential equations governing the flame can be solved. The present paper, however, is intended to enable flame velocities to be calculated without the necessity of solving a differential equation. The method is accurate to well within 1 per cent in most cases, and relies on a property of the flame equations discovered by examination of numerous exact solutions. Although diffusion coefficients in flames are not accurately known, so that the assumption of 'normality' usually suffices, it is important to estimate *i.e, equal to each other and to the thermal diffusivity. S~e below: "Calculation of flame speed for nonnormal reactant, and radical, diffusion'.