Modelling of Nonlinear Thermodiffusion for a Spherically Symmetric Case

  • Sigita Turskiene Institute of Regional Development, Šiauliai University, Lithuania
  • Arvydas J. Janavičius Institute of Regional Development, Šiauliai University, Lithuania
Keywords: nonlinear thermodiffusion, high intensity source, similarity solution, temperature profiles, spherically symmetric case


The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the heat transfer processes occurring with a finite velocity in gas from a high intensity source. In the previous papers A. J. Janavičius proposed the nonlinear diffusion equation which provided a more exact description of impurities diffusion by fast moving vacancies generated by X-rays in Si crystals. This is similar to the heat transfer in gas with constant pressure by molecules carrying a greater average kinetic energy based on the nonlinear thermodiffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. Heat transfer in gas must be compatible with the Maxwell distribution function. Heat transfer in gas described by using nonlinear thermodiffusion equation with heat transfer coefficients directly proportional to temperature . The solution of the thermodiffusion equation in gas was obtained by using similarity variables. The equation is solved by separating the linear part of the equation that coincides with Fick's second law. The obtained results coincide with Ya.B. Zeldovich’s previously published solutions of nonlinear equations by changing the respective coefficients.


Download data is not yet available.


A.J. Janavičius, Physics Letters A, 224, 159-162 (1997),

A.J. Janavičius, and A.Poškus, Acta Phys. Pol. A, 107, 519-521 (2005),

A.J. Janavičius, and S. Turskienė, Proc. of the Lithuanian Mathematical Society, Ser. A, 57, 24-28 (2016),

A.J. Janavičius, and S. Turskienė, Acta Phys. pol. A, 110, 511-521 (2006),

V.I. Rudakov, and V.V. Ovcharov, International Journal of Heat and Mass Transfer, 45(4), 743-753 (2002),

G. Joos, and I.M. Freeman, Theoretical Physics, (Dover Publications Inc., New York, 1986).

A.J. Janavičius, and S. Turskienė, Latvian Journal of physics and technical sciences, 55, 34-42 (2018),

M.E. Gliksman, Diffusion in solids, (Wiley, New York, 2000), pp. 472.

L.L Goldin, Laboratory works in physics, (Science, Novosibirsk, 1983). (in Russian)

A.J. Janavičius, G. Lūža, and D. Jurgaitis, Acta Phys. Pol. A, 105, 475-483 (2004),

Ya.B. Zeldovich, and Yu.P Raizer, Physics of Shock Waves and High-Temperature, Hydrodinamic Phenomena, (Dover Publications, 2003).

A.J. Baškys, D.J. Zanevičius, O.N. Kolomojec, and A.J. Janavičius, Algebric Devices-Technological Model for production Integral Schemes, Microelectronics Ser. 3, 4(307), 44-47 (1989). (in Russian)

A.J. Janavičius, S. Balakauskas, V. Kazlauskienė, A. Mekys, R. Purlys, and J. Storasta, Acta Phys. Pol. A, 114, 779 (2008),

A.J. Janavičius, et al, PCT publication number WO/2014/062045, PCT declaration number PCT/LT2013/000017, Declaration in USA No. 14/436,934 (2016).

C.J. van Duyn, and L.A. Peletier, Nonlinear Analysis: Theory, Methods & Applications, 1(3), 223-233 (1977),

V.D. Djordjevic, and Th.M. Atanackovic, Journal of Computational and Applied Mathematics, 222(2), 701-714 (2008),

0 article
How to Cite
Turskiene, S., & Janavičius, A. (2021). Modelling of Nonlinear Thermodiffusion for a Spherically Symmetric Case. East European Journal of Physics, (1), 13-19.