Calculations of Nu and Sh in Monoliths

Monolithic catalysts are continuous structures made of a large number of straight parallel and thin channels, whose walls are coated with catalyst. They are commonly used a wide range of applications, especially involving the oxidation of hydrocarbons in fast heterogeneous reactions [1-3]. Accurate modeling of monolithic reactors may be performed by means of two- and three-dimensional models. Nevertheless, for applications of real time simulations or kinetic parameters estimation, at the present computing power, non-computationally expensive one-dimensional models are required. Notwithstanding the fact that it was shown that the critical point in achieving high accuracy of 1D models consists of the correct evaluation of mass and thermal fluxes between the bulk gas phase and the surface [4], heat and mass fluxes in monolithic catalysts are presently described with correlations for heat and mass transfer coefficients, derived for flow in ducts, hence neglecting the occurrence of the superficial reaction. Such correlations are based on the solution of the Graetz problem for constant wall temperature, NuT, and constant wall heat flux, NuH [5], where NuT and NuH are given as unique functions of the dimensionless coordinate x* (x* = z / 2 Re Pe). Nevertheless, in the presence of a fast exothermic reaction at the surface, Nu and Sh numbers may be severely affected by inlet conditions [4], and by the kinetic parameters of the surface reaction [6, 7]. In our previous work [8, 9] we showed that Nu is significantly enhanced by the perturbation induced by surface reaction on the radial profiles of temperature, concentration and velocity. We found that the perturbation on mass and heat fluxes generated by the light-off at different fuel mass fractions, inlet temperatures and Re numbers, may be uniquely correlated with the adiabatic temperature of the reacting mixture via a modified Nu number (Nuad), which anchors the heat transfer efficiency to the light-off position rather than to the geometrical position (x*) [8, 9]. In the present paper we extend the previous analysis to the effect of the variation of the kinetic parameters of the superficial oxidation of propane on the heat and mass transfer efficiency, by means of a two-dimensional dynamic model of a single channel of an adiabatic monolithic reactor in which coupling between mass, energy and flow-field is solved.