Abstract
A one-dimensional mathematical model for heat and mass balance has been proposed to elucidate the changes occurring in the temperature and density of the evaporation-pyrolysis zone in a naturally smoldering cigarette. The model considers: (1) pyrolysis of tobacco obeying Arrhenius kinetics, (2) evaporation of water from tobacco following a mass-transfer- and rate-determined process, (3) weight loss of tobacco due to pyrolysis and evaporation, (4) internal heat transfer characterized by effective thermal conductivity, (5) heat loss attributable to free convection and radiation from the outer surface of the cigarette and endothermicity of the evaporation process, and (6) smoldering speed. These processes are expressed in a set of simultaneous ordinary differential equations that can be solved numerically by the Runge-Kutta-Gill method. The calculated distribution profiles of temperature and density in the evaporation-pyrolysis zone approximate the experimental results measured using thermocouples and a β-ray attenuation technique. On the basis of the model, the influences of several physical parameters on the shapes of the temperature and density profiles are predicted.
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