This paper is directly related to the task of modelling diffusion problems, prior to the choice of solution strategies. The approach presented is in fact a reformulation tool, aimed at reducing, as much as possible and within prescribed accuracy requirements, the number of dimensions in a certain diffusion formulation. It is shown how appropriate integration strategies can be employed to deduce mathematical formulations of comparable simplicity and improved accuracy in comparison with well-established classical lumping procedures. The approach is demonstrated through representative heat conduction problems, and the enhancement characteristics are examined against the classical lumped system analysis (CLSA) and the exact solutions of the fully differential systems.
Corrêa, E. J., & Cotta, R. M. (1998). Enhanced lumped-differential formulations of diffusion problems. Applied Mathematical Modelling, 22(3), 137–152. https://doi.org/10.1016/S0307-904X(98)00005-5