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Przybliżone równania dyfuzji masy i przewodzenia ciepła z członem źródłowym

Gwadera M., Kupiec K., Neupauer K.

Przemysł Chemiczny

2016

T. 95, nr 10

1988--1993

Przedstawiono przybliżone rozwiązania równania dyfuzji oparte na aproksymacji ułamkami łańcuchowymi. Omówiono algorytmy obliczeń numerycznych dla różnych przypadków oraz porównano wyniki obliczeń przybliżonych ze ścisłymi. Przedstawiono ogólny przypadek nieustalonej dyfuzji z reakcją chemiczną oraz szczególne przypadki obejmujące adsorpcję w zbiorniku oraz nieustalone przewodzenie ciepła.

Approximate solns. of the diffusion equation based on the continued fraction approximation were used to consider transient diffusion with chem. reaction and specific cases of adsorption in a tank and of transient heat transfer. Algorithms of numerical calculations for particular cases were discussed and the results of calculations were compared with the exact solns. A good agreement of the data was obsd.

Modelling of mass transport in watercourses considering mass transfer between phases in unsteady states. Part II. Mass transport during absorption and adsorption processes

Bielski A.

Environment Protection Engineering

2011

Vol. 37, nr 4

71-89

Equations describing the rate of adsorption and absorption processes and those based on Whitman's model have been analyzed. In the case of unstable states, the mass flux penetrating to the layer of the river sediment and calculated by means of these equations differs from the mass flux calculated from the mass diffusion equation. In order to minimize the discrepancies between the flux determined by Whitman's model and a real flux, the correction factor has been introduced into the concentration gradient equation originated from Whitman's model. This correction factor can be expressed as a time dependence of the product of a certain parameter and the concentration derivative at the phase boundary (solid phase side). The corrected equation for the concentration gradient has been used to derive another equation, describing a general rate of the absorption and adsorption processes at the linear interfacial equilibrium and the chemical reactions occurring in the liquid and solid phases; the chemical reactions follow the first order monomolecular mechanism in unstable states with reference to the liquid phase. Knowing the general rate of the earlier mentioned processes it is possible to construct an advective-dispersion model of mass transport in a river including these particular processes. Such a model contains a term defined as a correction factor referring to the time dependence of the concentration derivative with respect to time. The described model may be also used for simulation of the transport of pollutants undergoing adsorption and absorption in the layer river sediment; the processes occur with a finite and infinitely large rate through the equilibrium states.