Diffusion and Convection

This chapter explores the fundamental mechanisms of diffusion and convection as drivers of transport phenomena in fluids. While material variables are often assumed to be passively transported with the medium, molecular diffusion arising from random particle motion induces mixing at small scales, whereas convection dominates at larger scales through bulk transport. The combined effects are formulated via the convection-diffusion equation, which serves as the basis for a range of applications. A one-dimensional chemical reactor is analyzed, where scaling arguments reveal three distinct regimes depending on a dimensionless parameter: convection-dominated, parabolic, or hyperbolic. The framework is further applied to the case of a nuclear power plant accident, illustrating how conservation principles and fundamental solutions of the one-dimensional convection/diffusion equation can be used to evaluate the spread of radioactive material. The chapter also introduces similarity solutions, investigates nonlinear diffusion, and highlights the modeling of turbulence.