Transport Analogies Comparison Matrix

The Transport Analogies Comparison Matrix serves as a cornerstone in transport phenomena education and research by exposing deep structural symmetries between momentum, heat, and mass transfer. Each domain obeys a conservation principle — mass continuity, momentum balance (Navier–Stokes), and energy/species balance — coupled with linear phenomenological laws relating fluxes to driving gradients (velocity gradient, temperature gradient, concentration gradient). The matrix organizes these correspondences into rows (governing equations, boundary conditions, flux definitions) and columns (momentum, heat, mass), revealing identical forms when expressed in nondimensionalized or similarity-variable form. Key insights include the equivalence of the Reynolds number (Re) in momentum transfer, Péclet number (Pe) in heat transfer, and Sherwood number (Sh) in mass transfer — all representing ratios of convective to diffusive transport. Practically, this analogy allows engineers to leverage solutions from one domain (e.g., heat exchanger correlations) to model analogous systems (e.g., membrane separation or aerodynamic heating), significantly reducing computational and experimental effort. Moreover, it underpins analog modeling techniques such as thermal–hydraulic scaling and electrochemical impedance mapping, where electrical circuits simulate transport behavior via Ohm’s-law-like equivalences.