Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this article, the hydrodynamic problem of twin wedges entering water vertically at constant speed is analyzed based on the velocity potential theory, and the gravity effect on the flow is ignored based upon the assumption that the ratio of the entry speed to the acceleration due to gravity is much larger than the time scale of interest.
41 citations
TL;DR: In this paper, an exact analytical solution of the famous Falkner-Skan equation is obtained, which involves the boundary layer flow over a moving wall with mass transfer in presence of a free stream with a power-law velocity distribution.
Abstract: In this paper, an exact analytical solution of the famous Falkner-Skan equation is obtained. The solution involves the boundary layer flow over a moving wall with mass transfer in presence of a free stream with a power-law velocity distribution. Multiple solution branches are observed. The effects of mass transfer and wall stretching are analyzed. Interesting velocity profiles including velocity overshoot and reversal flows are observed in the presence of both mass transfer and wall stretching. These solutions greatly enrich the analytical solution for the celebrated Falkner-Skan equation and the understanding of this important and interesting equation.
41 citations
TL;DR: In this article, the effects of compressibility on a radial laminar wall jet are investigated and a similarity solution for the velocity distribution exists, which is expressible directly in terms of the corresponding solution for an incompressible wall jet.
Abstract: The effects of compressibility on a radial laminar wall jet are investigated. On the assumption that the coefficient of viscosity is proportional to the temperature, it is shown that a similarity solution for the velocity distribution exists, which is expressible directly in terms of the corresponding solution for an incompressible wall jet. For arbitrary Prandtl number the energy equation is studied in detail and solutions are obtained for a variety of temperature conditions.
40 citations
TL;DR: It is shown that the two-dimensional mixed convection boundary-layer flow over a vertical surface with a power law temperature has an infinite number of solutions.
40 citations
TL;DR: Similarity solutions based on velocity potential theory are found to be possible in the case of an expanding paraboloid entering water when gravity is ignored in this article, and numerical solutions are obtained based on the boundary element method.
Abstract: Similarity solutions based on velocity potential theory are found to be possible in the case of an expanding paraboloid entering water when gravity is ignored. Numerical solutions are obtained based on the boundary element method. Iteration is used for the nonlinear boundary conditions on the unknown free surface, together with regular remeshing. Results are obtained for paraboloids with different slenderness (or bluntness). Flow features and pressure distributions are discussed along with the physical implications. It is also concluded that similarity solutions may be possible in more general cases.
40 citations