Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient

    Received 10 November 2017; accepted 05 March 2018

    2018, Vol. 14, no. 1, pp.  81-97

    Author(s): Deryabina M. S., Martynov S. I.

    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.
    Keywords: viscous fluid, periodic solution, piecewise function, gradient, pressure, temperature
    Citation: Deryabina M. S., Martynov S. I., Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  81-97
    DOI:10.20537/nd1801008


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