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 2005
TL;DR: In this paper, a micromechanics-based constitutive model for compaction of composite powders at low relative density is implemented into the finite element framework, which is capable of describing development of anisotropy, tension-compression asymmetry and variation in elastic properties during the compaction.
Abstract: A micromechanics-based constitutive model for compaction of composite powders at low relative density is implemented into the finite element framework. The micromechanical basis of the model is the mechanics of contact between individual particles, spherical but not necessarily of the same size or of the same material. The contact law is assumed to follow the similarity solution for viscoplastic particles. An appropriate averaging procedure leads to the continuum constitutive law, whereby the state of material at a point is described by the states of virtual contacts of an average particle, distributed over all directions. The outline of the finite element implementation is as follows. For numerical purposes, the continuous distribution of contacts over a unit sphere is represented by a finite number of virtual contacts, distributed so that each contact represents the same solid angle. The mathematical structure of the model is similar to the crystal plasticity model, but with some important differences. The model is capable of describing development of anisotropy, tension-compression asymmetry and variation in elastic properties during the compaction. Some computational results are presented demonstrating the feasibility if the concepts.
2 citations
TL;DR: In this paper, the point-source, spherical magnetogasdynamics shock wave moving into a constant density γ-law gas is considered in the limit of infinite shock strength, from the point of view of the Richtmyer-Von Neumann viscosity technique.
Abstract: The point-source, spherical magnetogasdynamics shock wave moving into a constant density γ-law gas is considered in the limit of infinite shock strength, from the point of view of the Richtmyer-Von Neumann viscosity technique. Numerical solutions of this problem has been obtained in viscous and non-viscous regions. A similarity solution of this problem is shown to exist. We have shown that field variables change rapidly when the magnetic field is imposed in both the viscous and the non-viscous regions.
2 citations
TL;DR: In this paper, the flow and heat transfer in a laminar condensate flim on an isothermal vertical plate is modelled mathematically and the strict Boussinesq approximation is adopted to account for buoyancy due to local temperature variations within the film.
Abstract: The flow and heat transfer in a laminar condensate flim on an isothermal vertical plate is modelled mathematically. The strict Boussinesq approximation is adopted to account for buoyancy due to local temperature variations within the film. A similarity transformation reduces the governing boundary-layer type equations to a coupled set of ordinary differential equations and the resulting three-parameter twopoint boundary value problem is solved numerically for Prandtl numbers,Pr, ranging from 0.001 to 1000 and Jakob numbers,Ja, between 0.0001 and 1.5. The principal effects of the favourable buoyancy are to reduce the thickness of the condensate film and increase the film velocity at the smooth liquid-vapour interface, whereas the friction and heat transfer at the plate are enhanced. In accordance with the classical Nusselt theory, it is found that the temperature varies nearly linearly across the film. The computed similarity profiles for velocity reveal, however, substantial departures from the parabolic distribution assumed in the simplified Nusselt analysis.
2 citations
TL;DR: In this paper, the effect of the disturbance behind a strong plane shock wave propagating in a medium with exponentially varying density in the presence of magnetic field is investigated, and a method has been developed to determine the similarity exponent α in magnetogasdynamics.
Abstract: The effect of the disturbance behind a strong plane shock wave propagating in a medium with exponentially varying density in the presence of magnetic field is investigated. The similarity solution is used to find the two interaction terms at all points of the flow. A method has been developed to determine the similarity exponent α in magnetogasdynamics.
2 citations
TL;DR: In this article, the new theory of shock dynamics proposed by Ravindran and Prasad has been considered with initial values taken from the similarity solution for a single conservation equation and the results have been compared with those obtained by Lax-Wendroff finite difference method.
Abstract: The new theory of shock dynamics proposed by Ravindran and Prasad has been considered with initial values taken from the similarity solution for a single conservation equation and the results have been compared with those obtained by Lax-Wendroff finite difference method.
2 citations