PSI - Issue 65

E.Yu. Prosviryakov et al. / Procedia Structural Integrity 65 (2024) 185–190 E.Yu. Prosviryakov, O.A. Ledyankina, L.S. Goruleva / Structural Integrity Procedia 00 (2024) 000–000

190 6

2 2 C C d t z     8



2 2 C C d t z     9



8

9

,

,

2

C

C





2

C

C





d



10

10

d



11

11

,

,

2

t

z





2

t

z





2 2 C C d t z     13

2

C

C







2

C

C





d



13

14

14

,

,

,

d



12

12

2

t

z





2

t

z





0      W z

2      4 W z

1      3 W z

1 1 U V

U V

U V

0

0

0

,

,

.

4

3

3. Conclusion

A class of exact solutions to the Oberbeck-Boussinesq equations for describing convective creeping flows of binary fluids has been presented. This class of exact solutions is a generalization of the Lin-Sidorov-Aristov family. In the new class of exact solutions, the velocity field depends nonlinearly on two coordinates (horizontal or longitudinal). The form factors for the velocity field depend on the longitudinal or transverse coordinate and time. A system of equations for determining the components of hydrodynamic fields has been presented.

References

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