This study presents a novel, macrohomogeneous concept of multi-dimensional mathematical modeling of industrial-scale electrochemical systems based on a plate-and-frame design. The main idea of the model concept presented is that it considers the studied system as an anisotropic continuum in all spatial directions. The anisotropy of transport in the individual system layers is obtained by effective anisotropic transport parameters. Interlayer/interfacial fluxes are described by source terms in the conservation equations. This model concept is theoretically straightforward, avoiding both excessive simplification of the physical definition of the problem and complex numerical algorithms. It enables the calculation of the local fields of the physical properties inside the apparatus even with industrial-scale dimensions by means of conventional computational hardware. The capabilities and limits of this approach are demonstrated by two examples: (a) a stationary isothermal two-dimensional mathematical model of a high temperature polymer electrolyte membrane fuel cell stack (100 cells) with approximately 4 kW power output and (b) a stationary isothermal three-dimensional mathematical model of a pilot-scale electrodialysis unit (200 membrane pairs with a total membrane area of 82 m(2)). (C) 2015 Elsevier Ltd. All rights reserved.