In this paper the processes of admixture convective diffusion in two-phase structures with periodically located thin channels are investigated with taking into account a natural decay of migrating substance. With the help of application of appropriate integral transforms separately in the contacting domains, a solution of the contact initial boundary value problem of convective diffusion of decaying substance is obtained. The correlations between these integral transforms are found using the non-ideal contact conditions imposed for the concentration function. Expressions for decaying particle flows through arbitrary cross-section of the body are found and investigated, and their numerical analysis is carried out in the middle of both domains — the thin channel and basic material. It is shown that the decay intensity of the migrating substance especially affects the flow distribution in the domain of basic material.
- Fisher J. Calculation of diffusion penetration curves for surface and grain boundary diffusion. J. Appl. Phys. 22, 74 (1951).
- Klinger L., Rabkin E. Diffusion along the grain boundaries in crystals with dislocations. Interface Science. 6, 197 (1998).
- Savula Y., Koukharskiy V., Chaplia Y. Numerical analysis of advection diffusion in the continuum with thin canal. Numerical Heat Transfer. Part A. 38, 657 (1998).
- Bonelli S. Approximate solution to the diffusion equation and its application to seepage-related problems. Applied Mathematical Modelling. 33, 110 (2009).
- Chaplya Y., Chernukha O, Dmytruk V. Mathematical modeling of stationary processes of convection-diffusion mass transfer in binary periodic structures. Reports of the National Academy of Sciences of Ukraine. 7, 44 (2011).
- Chaplya Y., Chernukha O., Dmytruk V. Advective-diffusive mass transfer in binary regular structures in the steady-state regime. Applied Math. Modelling. 37, 6191 (2013).
- Goncharuk V., Dmytruk V., Chernukha O. Non-stationary processes of convection-diffusion mass transfer in a binary regular structures. Visnyk of Lviv Polytechnic National University. Physics and mathematics. 740, 79 (2012).
- Dmytruk V. Steady mass flows and distributions of admixture average concentrations in periodic structures under mixed boundary conditions. Physico-mathematical Modelling and Information Technologies. 14, 51 (2011).
- Burak Y., Chaplya Y., Chernukha O. Continuum-thermodynamics models of mechanics of solid solutions. Naukova Dumka, Kyiv (2006).
- Sneddon I. Fourier transformations. McGraw-Hill, NY, Toronto, London (1951).
- Chernukha O. Admixture mass transfer in a body with horizontally periodical structure. International Journal of Heat and Mass Transfer. 48, 2290 (2005).
- Martynenko N. Pustyl’nikov L. Finite integral transforms and their application to the study of systems with common parameters. Nauka, Moscow (1986).
- Kamke E. Handbook of Ordinary Differential Equations. Nauka, Moscow (1985).
- Handbook of Mathematical Functions. Ed. M. Abramowitz and I. Steagan. Nauka, Moscow (1979).
- Chaplya Y., Chernuha A. Physical-mathematical modeling of heterodiffusive mass transfer. SPOLOM, Lviv (2003).