Heat and mass transfer correlations and bifurcation analysis of catalytic monoliths with developing flows

We review and compare the literature correlations for estimating the heat and mass transfer coefficients as well as pressure drop in catalytic monoliths with simultaneously developing velocity, concentration and temperature profiles. We present accurate correlations for estimating the local Nusselt and Sherwood numbers for developing flows with constant flux (slow reaction) and constant wall concentration or temperature (fast reaction) cases for a channel of arbitrary shape. These new correlations need only a single parameter, namely, the asymptotic value, which depends on the channel geometric shape. We establish the accuracy of the proposed correlations by comparing the predicted values with the exact numerical values available for a few cases. We use the new correlations to analyze the effect of flow conditions near the inlet of the channel on the ignition and extinction behavior of catalytic monoliths used in combustion and after-treatment applications as well as laboratory experiments. It is shown that the bifurcation behavior, such as the number and location of the ignition/extinction points, the number of stable steady-states and the hysteresis locus is sensitive to the flow conditions in the entry region, and hence the heat and mass transfer correlations used, especially for large values of the transverse Peclet number (high space velocities or very short monoliths) or adiabatic temperature rise or when the axial catalyst loading is not uniform.