Conveyance tube manufacturing via a hot-finished, welded route is an energy-intensive process which promotes rapid surface oxidation. During normalisation at approximately 950 °C to homogenise the post-weld microstructure, an oxide mill scale layer grows on tube outer surfaces. Following further thermomechanical processing, there is significant yield loss of up to 3% of total feedstock due to scale products, and surface degradation due to inconsistent scale delamination. Delaminated scale is also liable to contaminate and damage plant tooling. The computational thermochemistry software, Thermo-Calc 2023b, with its diffusion module, DICTRA, was explored for its potential to investigate oxidation kinetics on curved geometries representative of those in conveyance tube applications. A suitable model was developed using the Stefan problem, bespoke thermochemical databases, and a numerical solution to the diffusion equation. Oxide thickness predictions for representative curved surfaces revealed the significance of the radial term in the diffusion equation for tubes of less than a 200 mm inner radius. This critical value places the conveyance tubes’ dimensions well within the range where the effects of a cylindrical coordinate system on oxidation, owing to continuous surface area changes and superimposed diffusion pathways, cannot be neglected if oxidation on curved surfaces is to be fully understood.