On the structure of a distinguished-limit quasi-isothermal deflagration for the generalized reaction-rate model

• Main Authors: Bush W. B., Krishnamurthy L.
• Format: Article
• Language: English
• Published: Hindawi Limited 1997-01-01
• Series: Mathematical Problems in Engineering
• Subjects: Activation-energy asymptotics; Cold-boundary difficulty; Laminar deflagration; Quasi-isothermal
• Online Access: http://www.hindawi.net/access/get.aspx?journal=mpe&volume=3&pii=S1024123X97000604
• ISSN: 1024-123X; 1563-5147

<p>The structure of the quasi-isothermal deflagration is examined by means of an asymptotic analysis of the physical-plane boundary-value problem, with Lewis&#8211;Semenov number unity, in the limit of the activation-temperature ratio, <math alttext="$eta = T_a /T_b $"> <mrow> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>T</mi> <mi>a</mi> </msub> <mo>&sol;</mo> <msub> <mi>T</mi> <mi>b</mi> </msub> </mrow> </math>, greater than order unity, for the generalized reaction-rate-model case of: (1) the heat-addition-temperature ratio, <math alttext="$alpha = left( {T_b - T_u } ight)/T_u $"> <mrow> <mi>&alpha;</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>T</mi> <mi>b</mi> </msub> <mo>&minus;</mo> <msub> <mi>T</mi> <mi>u</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>&sol;</mo> <msub> <mi>T</mi> <mi>u</mi> </msub> </mrow> </math>, of order <math alttext="$eta ^{ - 1/2} $"> <mrow> <msup> <mi> &beta;</mi> <mrow> <mo>&minus;</mo> <mn>1</mn> <mo>&sol;</mo> <mn>2</mn> </mrow> </msup> </mrow> </math>, less than order unity [where <math alttext="$T_a $"> <mrow> <msub> <mi>T</mi> <mi>a</mi> </msub> </mrow> </math>, <math alttext="$T_b $"> <mrow> <msub> <mi>T</mi> <mi>b</mi> </msub> </mrow> </math>, and <math alttext="$T_u $"> <mrow> <msub> <mi>T</mi> <mi>u</mi> </msub> </mrow> </math> are the activation, adiabatic-flame (and/or burned-gas), and unburned-gas temperatures, respectively]; and (2) the exponent, <math alttext="$a$"> <mi>a</mi> </math>, which characterizes the pre-exponential thermal dependence of the reaction-rate term, unity. The examination indicates that, as in the order-unity heat-addition case, this deflagration has a four-region structure: the upstream diffusion-convection and downstream diffusion-reaction regions, and the far-upstream (or cold-boundary) and the far-downstream (or hot-boundary) regions.</p>