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Cláudia Drumond |
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| Title |
Analysis of the predictive ability of a simplified mathematical model to describe loss/uptake of solute from/to a solid immersed in a fluid in situations of significant external resistance. |
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| Abstract | Mass transfer of solutes from/to a solid immersed in a fluid can often be described by analytical solutions of Fick’s second law. The important parameters of these solutions are the diffusion coefficient and the external mass transfer coefficient, the former related to the internal resistance and the latter related to the external resistance to mass transfer. Estimation of parameters considering both internal and external resistances is cumbersome, due to the high correlation between the model parameters, which jeopardises regression procedures. An alternative solution consists in describing the process as being controlled by internal resistance only, and estimating an apparent diffusion coefficient, lower than the true one, that accounts for the effects of the external resistance and that might be used for predictive purposes provided the same hydrodynamic conditions prevail. The main objective of this work was to theoretically evaluate the predictive ability of such approach. Apparent diffusion coefficients were estimated, using a design based on equally spaced values of fractional mass loss/uptake (Mt/M ) generated by the model that accounts for both internal and external resistances to mass transfer. Values of Mt/M predicted by the simplified model, using the apparent diffusion coefficients, were compared with the “true” values of Mt/M . The average of the absolute values of the relative errors of Mt/M was lower than 5% for Biot numbers above 17.5, and lower than 1% for Biot numbers above 102. The absolute values of the relative errors were found to be higher in the initial part of the uptake/loss process, that is, for low values of Mt/M . For example, for a Biot number of 30, the absolute values of the relative errors were around 5% and 45% for values of Mt/M equal to 0.5 and 0.1, respectively. | ||
| Authors | Abreu, I.C.; Oliveira, F.A.R. and Drumond, M.C. | ||
| Institution |
Escola Superior de Biotecnologia, Universidade Católica Portuguesa |
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