TITLE:
Simple Models for Diffusion in Thin Plates or Membranes
AUTHORS:
Jorge Corrêa de Araújo, Rosa García Márquez
KEYWORDS:
Simplified Model, Theoretical Model, Membrane, Mean Concentration
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.7,
July
24,
2019
ABSTRACT: Two simplified models, linear and nonlinear, were used in a cementation process on a homogeneous thin carbon steel plate. The parameters for these models, as obtained by the least squares’ method the first one in a global way while the other parameters refer to the second model—were estimated by a set of local minimums. To compare the performance of these models we used theoretical data, for the same diffusion problem obtained by a one-dimensional transient model considering the concentrations in the mean plane of the plate. The results for carbon concentrations in weight percentage in the plate (%pC) as a time-only dependent function with these simplified models to represent the analyzed diffusion process were in good agreement with those from a stricter model. The diffusion flows of these models were determined and a reasonable agreement can be seen in relation to the flow obtained by the theoretical model on the surface of the plate. This study shows that it is possible to use this methodology with the given restrictions adopted here to describe the concentration and the diffusion flow of other solutes in thin membranes.