The theoretical foundation for mass and energy transport in one-dimensional Cartesian systems is established through differential balance laws applied to infinitesimal control volumes bounded by flat plates with infinite extent in the transverse directions. This framework derives partial diffusion equations where the temporal change of a scalar field (temperature or concentration) within an inert medium is linearly proportional to its second spatial derivative, governed by a constant diffusivity parameter such as thermal conductivity over density-specific heat capacity for energy transport. These governing relations describe how transient fields evolve from non-uniform initial states toward steady-state linear gradients defined exclusively by Dirichlet boundary conditions at the domain limits.
The theoretical foundation for mass and energy transport in one-dimensional Cartesian systems is established through differential balance laws applied to infinitesimal control volumes bounded by flat…