The core theoretical mechanism presented is the similarity solution method for unidirectional transport phenomena in Cartesian coordinates, which reduces parabolic partial differential equations (PDEs) governing heat and mass diffusion to ordinary differential equations via a dimensionless group derived from dimensional analysis. This technique applies specifically under conditions of infinite domain approximation where boundary effects are confined by finite penetration depths proportional to the square root of time or diffusivity. The theory establishes that when no inherent length or time scales exist in an unsteady problem, transport profiles depend exclusively on this single similarity variable, enabling universal solutions across thermal conductivity and mass diffusion contexts provided material properties remain position-independent.
The core theoretical mechanism presented is the similarity solution method for unidirectional transport phenomena in Cartesian coordinates, which reduces parabolic partial differential equations (PDE…