Abstract: The problem of the motion of a fluid layer over a solid substrate inclined at an angle to the horizontal is studied. The classical equation [3] that relates the fluid flow rate and the thickness of the flowing layer has long been known. This equation was derived from an exact solution of the fluid-layer motion problem for the case of constant viscosity. For most common fluids, viscosity depends significantly on temperature. It is shown that if this dependence is represented by Padé approximants, then an exact solution of the problem under variable viscosity can also be constructed. Exact solutions of hydrodynamic problems play an important role in research and engineering applications. They are used in stability analysis of flows, for testing numerical methods and computational codes, and for obtaining closed-form analytical expressions that determine integral characteristics of the process. An equation relating the thickness of the flowing layer and the fluid flow rate for variable viscosity is obtained; a comparison with the classical result is presented. It is noted that even moderate temperature variations lead to substantial changes in the flow rate due to viscosity variation. An equation for the thickness of a thin film is derived for the case where viscosity depends on temperature, analogous to equations previously obtained for constant viscosity. Under additional assumptions an exact solution of the derived equation is constructed.

Cite: Kuznetsov V.V.
Exact Solutions to the Problems of Flowing of Fluid Layers and Films at Variable Viscosity
Theoretical Foundations of Chemical Engineering. 2025. V.59. N3. P.615-620. DOI: 10.1134/s0040579525602043

Dates:

Submitted:	Nov 15, 2024
Accepted:	Jan 27, 2025

Identifiers: No identifiers

Citing: Пока нет цитирований

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