Non-Darcian Convection in Cylindrical Packed Beds

Non-Darcian transport describes the nonuniform flow and thermal anomalies often found in flow through packed beds. These effects include the high-flow-rate inertial pressure loss, near-wall porosity variation, solid-boundary shear, and thermal dispersion. Inclusion of these effects significantly alters the velocity and temperature profiles from those predicted by models using uniform or Darcian flow. In this paper, the non-Darcian formulation is used to predict the heat transfer rates for cylindrical packed beds such as chemical reactors. Traditional analyses of chemical reactors assume slug flow and must include a temperature-slip boundary condition to predict the measured temperature profiles. The present analysis predicts similar temperature variations by allowing the velocity and diffusivity to vary across the bed. The results agree with experimental data for chemical reactors and do not depend on the extensive experimental relations needed in conventional reactor models.