Self-similar solution of the Navier-Stokes equations governing gas flows in rotary logarithmically spiral two-dimensional channels

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 parameterM _o characterizing the channel rotation; the self-similarity parameters and 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.Perm'-Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 44–50, November–December, 1995.