Mass transfer is the dominant mode of structural material corrosion in energy systems employing heavy liquid metal coolant such as lead-cooled reactors. Modeling efforts in the literature have focused on materials science aspects, such as diffusive transport of alloying elements in structural materials and oxide layers, oxide layer growth and erosion, and species dissolution at the interface, but they have overlooked convective transport which is often represented by simplified one-dimensional models with no transverse convection. Here, within a Lagrangian framework, we particularly study the convective transport of dissolved elements at specimen boundaries in a flowing molten lead loop. Three-dimensional transient Reynolds-averaged Navier-Stokes simulations coupled with particle transport are carried out to compare convective transport in lead and other coolants, such as lead-bismuth eutectic, pressurized water, and sodium. Transverse convection in the narrow test section is observed to occur at a timescale comparable to longitudinal (downstream) transport and removal of particles from the test section, which highlights the need for three-dimensional modeling in the present setup. The effects of temperature, surface roughness, and mean flow velocity on convective transport in lead are investigated. While mean flow velocity is the dominant variable affecting convective mass transfer, increased surface roughness and reduced temperature are also shown herein to moderately enhance convective transfer.