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N. V. Burmasheva, E. Yu. Prosviryakov

EXACT SOLUTION FOR DESCRIBING A UNIDIRECTIONAL MARANGONI FLOW OF A VISCOUS INCOMPRESSIBLE FLUID WITH THE NAVIER BOUNDARY CONDITION. PRESSURE FIELD INVESTIGATION

DOI: 10.17804/2410-9908.2020.2.061-075

The article studies the properties of the pressure field in a unidirectional thermocapillary flow of a viscous incompressible fluid in an infinite horizontal layer of a given thickness. A distinctive feature of the considered boundary value problem is the inclusion of the Navier slip condition at the lower (solid) boundary of the layer instead of the classical condition of fluid no-slip on the solid surface. Modeling of the properties of the described flow is carried out using the system of Oberbeck-Boussinesq equations, its exact solution being obtained. The exact solution belongs to the Ostroumov-Birikh class. Hydrodynamic fields are described by polynomials. The degree of the polynomial describing the background pressure relative to the vertical coordinate is eight. The horizontal (longitudinal) pressure gradients are parabolic functions. This solution describes the multiple stratification of the pressure field. For the Navier slip condition and for special cases of no-slip and perfect slip conditions, corresponding studies are carried out to determine the number of pressure field stratification zones along the vertical coordinate.

Keywords: layered flow, Oberbeck-Boussinesq system of equations, exact solution, Ostroumov-Birikh class, unidirectional flow, counterflows, Marangoni convection, Navier condition

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Article reference

Burmasheva N. V., Prosviryakov E. Yu. Exact Solution for Describing a Unidirectional Marangoni Flow of a Viscous Incompressible Fluid with the Navier Boundary Condition. Pressure Field Investigation [Electronic resource] // Diagnostics, Resource and Mechanics of materials and structures. - 2020. - Iss. 2. - P. 61-75. -
DOI: 10.17804/2410-9908.2020.2.061-075. -
URL: http://eng.dream-journal.org/issues/2020-2/2020-2_288.html
(accessed: 12/07/2022).  

 

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