Ignition of catalytic reactions in a vertical wall immersed in a combustible gas

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We study in this paper the steady-state ignition of a catalytic vertical plate immersed in a combustible gas. The set of governing equations are elliptic, including the energy equation for the plate as well as the balance equations for the laminar natural convective boundary layer. The influence of the longitudinal heat conduction through the plate is clarified, showing well-defined ignition and extinction conditions (S-shaped curve) for high activation energy. The parameter that measures the influence of the longitudinal heat conduction is the heat conduction parameter α for moderate values of the nondimensional activation energy (Ze) of the overall reaction or α ˜ = α Z e 1 / 4 for high activation energies ſ e →∞. The longitudinal heat conduction is important for large values compared with unity of the heat conduction parameter α or α ˜ for moderate or large values of the nondimensional activation energies, respectively. The heat conduction parameter can be very large compared with unity for metallic plafes or very small compared with unity for ceramic plates. Numerical and asymptotic, techniques have been used, to evaluate the ignition conditions for very good ( α , α ˜ → ∞ ) and poor ( α , α ˜ → 0 ) conducting plates. Very well-defined ignition and extinction conditions are obtained for large values of α or α ˜ and large values of the nondimensional activation energy. For small values of α or α ˜ , there is not an S-shaped, curve. The catalytic ignition is easier to achieve as the value of α increases.