Passively aerated compost piles are built on a base of porous materials, such as straw or wood chips, in which perforated air supply pipes are distributed. The piles are not turned during composting, nor is forced-aeration equipment used, which significantly reduces the operating and capital expenses associated with these piles. Currently, pile configurations and materials are worked out by trial and error. Fundamentally based design procedures are difficult to develop because the natural convection air flow rate is not explicitly known, but rather is closely coupled with the pile temperature. This paper develops a mathematical model to analytically determine the maximum upward air flow velocity over an air supply pipe and the drop in vertical velocity away from the pipe. This model has one dimensionless number, dependent on the pile and base properties, which fully characterizes the velocity profile between the pipes.