Eventos Anais de eventos
COBEM 2017
24th ABCM International Congress of Mechanical Engineering
Integral Transform Analysis of a Simple Alcoholic Fermentation Model
Submission Author:
Helena Serrano , RJ
Co-Authors:
Helena Serrano, Leandro Alcoforado Sphaier, Isabela Florindo Pinheiro, Fernando Peixoto
Presenter: Leandro Alcoforado Sphaier
doi://10.26678/ABCM.COBEM2017.COB17-2822
Abstract
This paper analyses the specific part of the production of beer, namely the fermentation process, by the use of a hybrid methodology based on the Generalized Integral Transform Technique (GITT). A non-linear partial differential equation arises from the one-dimensional mathematical model, which describes the temperature distribution, the concentration of biomass and substrate spatially in a cylindrical fermenter vessel. The third-kind (Robin) boundary condition is established on the wall of the vessel as a general formulation is provided, involving different test-cases based on the dimensionless quantity represented by the Biot number. The solution of the governing equations was carried out within the GITT framework, for a simplified version of the problem in which the reaction rate becomes independent of temperature. The convergence behavior of the solution was analyzed, showing that in general five converged digits can be obtained with 60 terms in the truncated series. Finally, illustrative results are presented showing the evolution of temperature and concentrations at different locations.
Keywords
GITT, fermentation, mathematical model
