Numerical investigation of generalized Graetz problem in circular tube with a mass transfer coupling between the solid and the liquid

The average plasticizer concentration in the liquid behaves following two main regimes as a function of the migration strength. When α is much smaller than one, the average plasticizer concentration in the liquid is an algebraic function of the axial coordinate, z, at the power two third and increases linearly with time. Conversely, when α is much larger than one, the average plasticizer concentration is linear as a function of axial distance and increases as a function of the square root of time. Moreover, the concentration is much smaller of few orders of magnitude in dynamic condition than in static working showing that in the context of food contamination the dynamic approach is more appropriate and relevant for demonstration of compliance with the safety authorities requirements.