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An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numericalanalytical methodology for partial differential equations. S p e c i a l e m p h a s i s i s g i v e n t o n o v e l a l g o r i t h m implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

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Like fluoride, lead (Pb) accumulates on the enamel surface pre-eruptively, but it is not yet known whether it also deposits on enamel while dental caries is developing. This study evaluates Pb distribution in bovine enamel slabs submitted to a pH-cycling regimen simulating the caries process. The slabs were subjected to 8 cycles of de- and remineralizing conditions, and Pb (as acetate salt) was added to the de- and remineralized solutions at concentrations of 30 µg/l (experimental group, E1) and 300 µg/l (experimental group, E2). The control group (C) consisted of solutions to which Pb was not added. After the pH cycling, 100-µm sections of the slabs were analyzed by polarizing microscopy, to observe the extent of caries-like lesions, and these sections were used for Pb estimation by Synchrotron radiation X-ray microfluorescence. Caries lesions were observed along all superficial enamel surfaces to an extent of 120 µm. A Pb concentration gradient was observed in enamel, which decreased toward dentine. The highest Pb signals were observed for group E2, and the differences were statistically significant at enamel depths of 0 (C vs. E2; p = 0.029) and 50 µm (C vs. E2 and E1 vs. E2; p = 0.029). In conclusion, this study suggests that if Pb is present in the oral environment, it may deposit in enamel during the caries process.