Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface
We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, prof...
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/779 |
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| author | Sergey V. Ershkov Dmytro D. Leshchenko |
| author_facet | Sergey V. Ershkov Dmytro D. Leshchenko |
| author_sort | Sergey V. Ershkov |
| collection | DOAJ |
| description | We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field <i>p</i>. The latter has been chosen for solutions correlated explicitly with the critical maximal <i>non-zero</i> level of stress τ<sub>s</sub> in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for <i>two</i> functions, <i>p</i> and τ<sub>s</sub>. As a result, a set of new semi-analytical solutions are presented and graphically plotted. |
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| id | doaj.art-ce94dd3e28894fae96af224cd0220bd4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-25T00:24:50Z |
| publishDate | 2024-03-01 |
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| spelling | doaj.art-ce94dd3e28894fae96af224cd0220bd42024-03-12T16:50:20ZengMDPI AGMathematics2227-73902024-03-0112577910.3390/math12050779Non-Newtonian Pressure-Governed Rivulet Flows on Inclined SurfaceSergey V. Ershkov0Dmytro D. Leshchenko1Department of Scientific Researches, Plekhanov Russian University of Economics, Scopus Number 60030998, 36 Stremyanny Lane, 117997 Moscow, RussiaOdessa State Academy of Civil Engineering and Architecture, 65029 Odessa, UkraineWe have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field <i>p</i>. The latter has been chosen for solutions correlated explicitly with the critical maximal <i>non-zero</i> level of stress τ<sub>s</sub> in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for <i>two</i> functions, <i>p</i> and τ<sub>s</sub>. As a result, a set of new semi-analytical solutions are presented and graphically plotted.https://www.mdpi.com/2227-7390/12/5/779rivulet flownon-Newtonian fluidcreeping viscoplastic flow |
| spellingShingle | Sergey V. Ershkov Dmytro D. Leshchenko Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface Mathematics rivulet flow non-Newtonian fluid creeping viscoplastic flow |
| title | Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface |
| title_full | Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface |
| title_fullStr | Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface |
| title_full_unstemmed | Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface |
| title_short | Non-Newtonian Pressure-Governed Rivulet Flows on Inclined Surface |
| title_sort | non newtonian pressure governed rivulet flows on inclined surface |
| topic | rivulet flow non-Newtonian fluid creeping viscoplastic flow |
| url | https://www.mdpi.com/2227-7390/12/5/779 |
| work_keys_str_mv | AT sergeyvershkov nonnewtonianpressuregovernedrivuletflowsoninclinedsurface AT dmytrodleshchenko nonnewtonianpressuregovernedrivuletflowsoninclinedsurface |