ARTICLE IN PRESS Physica A ( ) – Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Generalized analytical expressions for the burning velocity in a combustion model with non-constant transport coefficients and several specific heats Toni Pujol a,∗ , Joaquim Fort b , Lino Montoro a , Joan J. Suñol b a Dept. d’Enginyeria Mecànica i de la Construcció Industrial, Escola Politècnica Superior, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia, Spain b Dept. de Física, Escola Politècnica Superior, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia, Spain article info Article history: Received 7 April 2009 Received in revised form 10 July 2009 Available online xxxx Keywords: 1D combustion model Bounds for the propagation speed Premixed laminar flame Reaction–diffusion model abstract We derive new expressions to estimate the burning velocity of a laminar gas flame in a simplified combustion model based on a one-step single reaction with transport coefficients (mass and heat) depending on temperature, and species with different specific heats. These new expressions generalize the bounds and approximations previously derived by Williams, von Karman, Zeldovich and Frank–Kamenetskii, Benguria and Depassier, and the matching asymptotic expansion method in a two zone model. The comparison of the flame speed predicted by these new analytical expressions with that numerically simulated by the full combustion model for a large variety of cases allows us to determine their range of validity. The upper bound based on the Benguria and Depassier method provides very good approximations for the actual propagation speed of combustion flames, being substantially better than the asymptotic method used in the recent papers. © 2009 Elsevier B.V. All rights reserved. 1. Introduction In laminar flame theory, the combustion of premixed gases with no energy losses develops a flame front that propagates at a constant speed [1,2]. Classical analyses carried out by several investigators (e.g., Refs. [3–5]) have provided well-known analytical expressions for predicting this laminar burning velocity on simplified combustion models. Although currently thought of having limited interest, some of these methods are still in use when investigating the essence of realistic combustion processes. A very recent example may be the analysis of the propagation of laminar premixed flames with a reversible reaction term [6]. Analytical approaches are also useful, as a first step, to test numerical codes before introducing more complicated effects (e.g., heat losses) that make analytical estimations of the flame speed impossible. Most well-known analytical expressions usually adopt a simplified one-dimensional (1D) model of a unimolecular binary mixture with a single-step reaction, with background flow at rest and with constant transport coefficients and specific heats. Some attempts to generalize these expressions to more realistic conditions have been carried out, although focusing in one particular methodology applied to solve a specific combustion problem (see, e.g., Refs. [7–10]). In contrast, the purpose of the present paper is to discuss the validity of a wide range of methodologies for estimating the burning velocity in a 1D combustion model that takes account of (1) the temperature dependence of mass and heat diffusivities and (2) the differences of specific heats between reactants and products. In addition, our model takes into consideration the very realistic case of including a non-zero flow velocity across the flame front due to density variations (see, e.g., Ref. [11]). Note that this effect has not been included in the recent studies focused on derived analytical expressions for the wavefront speed of combustion flames [1,2,5,8,9]. ∗ Corresponding author. E-mail address: toni.pujol@udg.edu (T. Pujol). 0378-4371/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2009.08.016 Please cite this article in press as: T. Pujol, et al., Generalized analytical expressions for the burning velocity in a combustion model with non-constant transport coefficients and several specific heats, Physica A (2009), doi:10.1016/j.physa.2009.08.016