In many electrochemical cells, the flow of electrolyte has an influence on cell behavior and this investigation concerns a cell (a zinc-air cell) where that flow occurred through natural convection. The zinc was present in the form of a bed of particles, connected at its top and bottom with channels forming reservoirs of electrolyte. Dissolution of the zinc caused density differences between electrolyte in the bed interstices and that in the reservoir; flow of the electrolyte ensured. In Part I of this two-part paper, a mathematical model for this cell is developed. The model employs the well-known Newman/Tobias description of a porous electrode and treats flow through the bed using the Blake-Kozeny equation. A fourth-order Lax-Wendroff algorithm, thought to be original, is used to solve the convective diffusion equation within the model. Sample computed results are presented.