The theoretical framework establishes that linear partial differential equations governing unsteady transport phenomena can be reduced to ordinary differential equations via similarity variables when convection-diffusion balances exhibit specific scaling properties, such as in semi-infinite domain approximations. This reduction relies on the assumption of constant velocity and negligible downstream diffusion relative to transverse convection, permitting analytical solutions through analogy between transient diffusion and steady convective transport. The method yields concentration profiles governed by error function integrals within defined parameter regimes characterized by high Péclet numbers, providing a mechanistic basis for deriving Sherwood number correlations in mass transfer theory.
The theoretical framework establishes that linear partial differential equations governing unsteady transport phenomena can be reduced to ordinary differential equations via similarity variables when…