TRANSLATIONAL-OSCILLATORY MOTION OF A SPHERICAL POROUS BODY IN A VISCOUS FLUID 

Taktarov Nikolay Grigor'evich, Doctor of physical and mathematical sciences, professor, sub-departament of mathematics and methods of mathematics teaching, Mordovia State Pedagogical Institute named after M. E. Evsevyev (11a Studencheskaya street,
Saransk, Russia), n.g.taktarov@mail.ru
Khramova Nadezhda Aleksandrovna, Assistant, sub-departament of mathematics and methods of mathematics teaching,
Mordovia State Pedagogical Institute named after M. E. Evsevyev (11a Studencheskaya street, Saransk, Russia), nadegdalem@mail.ru
Runova Ol'ga Aleksandrovna, Candidate of physical and mathematical sciences, sub-departament of mathematics and methods of mathematics teaching, Mordovia State Pedagogical Institute named after M. E. Evsevyev (11a Studencheskaya street, Saransk, Russia), runova.olga@list.ru

532.685

10.21685/2072-3040-2018-1-5

Background. The study of the motion of continuous and porous solids in a viscous fluid is of significant due to various applications in technological processes and natural phenomena. The present paper considers the effect of the translational-oscillatory motion
of a spherical porous body in a viscous fluid on the said fluid flow.
Materials and methods. The methods of mathematical physics and numerical methods were used to solve the problem. The problem was solved in a motionless spherical coordinate system with the origin that coincides with the sphere’s center at the present time.
Results. The fields of fluid velocities inside and outside of the porous body are found. The fluid stream lines are shown on the graphs.
Conclusions. The article shows that the fields of fluid velocities and stream lines in the cases of the porous body considerable differ from the ones of an impermeable body.

viscous fluid, translational-oscillatory motion of a spherical porous body, Brinkman equation

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