Self-similar solution of the Navier-Stokes equations governing gas flows in rotary logarithmically spiral two-dimensional channels
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A self-similar solution of the Navier-Stokes equations governing gas flows with constant transport coefficients in rotary log-spiral two-dimensional channels is obtained and analyzed. The solution and its existence depend on the following dimensionless parameters: the Reynolds number Re; the parameterMo characterizing the channel rotation; the self-similarity parameters α and β responsible for the channel shape; the direction of channel rotation; and, finally, the wall temperature ratio. A numerical solution of the system of second-order ordinary differential equations gives the ranges of the governing parameters on which self-similar solutions for the gas flow in a rotary channel can exist.
KeywordsDifferential Equation Reynolds Number Fluid Dynamics Ordinary Differential Equation Dimensionless Parameter
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