Geodesic
Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient
Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 81-97

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A procedure is proposed for constructing an approximate periodic solution to the equations of motion of a viscous fluid in an unbounded region in the class of piecewise smooth functions for a given gradient of pressure and temperature for small Reynolds numbers. The procedure is based on splitting the region of the liquid into cells, and finding a solution with boundary conditions corresponding to the periodic function. The cases of two- and three-dimensional flows of a viscous fluid are considered. It is shown that the solution obtained can be regarded as a flow through a periodic system of point particles placed in the cell corners. It is found that, in a periodic flow, the fluid flow rate per unit of cross-sectional area is less than that in a similar Poiseuille flow.
Mots-clés : viscous fluid, gradient
Keywords: periodic solution, piecewise function, pressure, temperature. 
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     author = {M. S. Deryabina and S. I. Martynov},
     title = {Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient},
     journal = {Russian journal of nonlinear dynamics},
     pages = {81--97},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2018_14_1_a7/}
}
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M. S. Deryabina; S. I. Martynov. Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient. Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 81-97. http://geodesic.mathdoc.fr/item/ND_2018_14_1_a7/