Convective clouds provide an efficient mechanism for transporting aerosols to the upper troposphere. Although observational data in the upper troposphere are still limited, the few measurements available all indicate the existence of high concentrations of small particles, possibly due to the vertical transport related to deep convection. In addition, with sufficiently low temperature, high relative humidity, and relatively high concentrations of aerosol precursors; the outflow regions of convective clouds are likely areas for new aerosols to form, adding even more particles to the upper troposphere. In order to simulate convective cloud transport along with cloud processing of aerosols we have developed a 3-D cloud-resolving model with an interactive explicit aerosol module. A baseline simulation suggests good agreement in the upper troposphere between modeled and observed results including concentrations of aerosols in different size ranges, mole fractions of key chemical species, and concentrations of ice particles. A set of 34 sensitivity simulations has been carried out to investigate the sensitivity of modeled results to the treatment of various aerosol physical and chemical processes in the model. The size distribution of aerosols is proved to be an important factor in determining the aerosols' fate within the convective cloud. Nucleation mode aerosols (0< d <5.84 nm) are quickly transferred to the larger modes as they grow through coagulation and condensation of H2SO4. Accumulation mode aerosols (d >31.0 nm) are almost completely removed by nucleation and impact scavenging. However, a substantial part (up to 10% of the boundary layer concentration) of the Aitken mode aerosol population (5.84 nm< d <31.0 nm) reaches the top of the cloud and the free troposphere. The sensitivity simulations performed indicate that in order to sustain a vigorous storm cloud, the supply of CCN must be continuous over a considerably long time period of the simulation. Hence, the treatment of the growth of particles is in general more important than the initial aerosol concentration itself.