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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01 Jan 2000
TL;DR: In this article, the equation for small amplitude motions of a slender beam with a prescribed axial motion is derived from Hamilton's principle, and it is shown that under a particular set of conditions this equation admits a closed form similarity solution.
Abstract: The equation for small amplitude motions of a slender beam with a prescribed axial motion is derived from Hamilton’s principle. It is shown that under a particular set of conditions this equation admits a closed form similarity solution. For other conditions approximate solutions are obtained by the modal approach.
5 citations
TL;DR: In this paper, the effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail.
Abstract: One-dimensional unsteady adiabatic flow behind an exponential shock wave propagating in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux, which has exponentially varying azimuthal and axial fluid velocities, is investigated. The shock wave is driven out by a piston moving with time according to an exponential law. The dusty gas is taken to be a mixture of a non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The equilibrium flow conditions are maintained and energy is varying exponentially, which is continuously supplied by the piston. The heat conduction is expressed in the terms of Fourier’s law, and the radiation is assumed of diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to a power law. The effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. It is interesting to note that the similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the self gravitation, heat conduction and radiation heat flux.
5 citations
Journal Article•
5 citations
TL;DR: In this paper, an asymptotic large time solution for the thermal Stefan problem of crystal growth is presented, which is valid at large times when the growth rate of crystal is limited by the diffusion process in the environmental melt system so that a thermodynamic equilibrium state prevails at the interface.
5 citations
TL;DR: In this article, the authors describe a two-dimensional similarity solution of a viscous capillary flow in a thin film, which describes two confronted contact lines which are being gradually welded by a point that advances at constant velocity along the common contact line.
5 citations