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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 , a similarity criterion for sedimentation with the electrochemical number was developed, and a new criterion equation was obtained for conditions of the saline solution natural convection, which served as the basis for heat transfer calculation during the deposits formation.
Abstract: A similarity criterion of deposit formation with the electrochemical number was developed. Experimental studies of the saline deposits effect on heat transfer were generalized, and a new criterion equation was obtained for conditions of the saline solution natural convection. The modernized criterion of sedimentation similarity served as the basis for heat transfer calculation during the deposits formation.
TL;DR: In this paper , the authors considered mathematical modeling on mixed convection MHD viscous fluid flow on the lower stagnation point of a magnetic sliced sphere and solved the similarity equations by the Keller-Box scheme.
Abstract: This paper considers mathematical modeling on mixed convection MHD viscous fluid flow on the lower stagnation point of a magnetic sliced sphere. The study began with transforming the governing equations which are in dimensional partial differential equations to non-dimensional ordinary differential equations by using the similarity variable. The resulting similarity equations are then solved by the Keller-Box scheme. The characteristics and effects of the Prandtl number, the sliced angle, the magnetic parameter, and the mixed convection parameter are analyzed and discussed.
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TL;DR: In this paper, a spatio-temporal version of the Omori-Utsu law of aftershock sequences is proposed, which satisfies a nonlinear partial differential equation (PDE).
Abstract: A spatio-temporal version of the well-known Omori-Utsu law of aftershock sequences is proposed. This 'diffusive Omori-Utsu law' satisfies a nonlinear partial differential equation (PDE). A similarity reduction is obtained that reduces the PDE to an ordinary differential equation (ODE). A nonzero constant solution of this ODE leads to the usual Omori-Utsu law. An exact and explicit similarity solution is found that corresponds to the original Omori law. An initial value problem for the 'diffusive Omori-Utsu law' is also considered, and whose spatio-temporal dynamics are described by bounding functions that satisfy nonlinear, but linearisable, PDEs. Numerical results are also provided.
12 May 2019
TL;DR: In this article, the assumption implicit in Leveque's approximation is re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution.
Abstract: In this paper, the assumptions implicit in Leveque's approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge-Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.
01 Jan 1982
TL;DR: In this article, a non-similarity solution for propagation of magnetogasdynamic blast waves in the Roche model is obtained, where the strength of the shock surface heading the disturbance as well as the total energy of the wave vary with time.
Abstract: A non-similarity solution for propagation of magnetogasdynamic blast waves in Roche model is obtained. The density outside the central core varies according to some inverse power of distance from the centre of explosion. The strength of the shock surface heading the disturbance as well as the total energy of the wave vary with time. Shock waves produced by sudden explosion have been studied by many authors, Greenspan (1962), Greifinger and Cole (1962), Christer and Helliwell (1969). Verma (1969) studied propagation of cylindrical blast wave in a plasma under an axial current and sought similarity solution of the problem for a very strong instantaneous line explosion. Carrus et al. (1951) studied propagation of explosion waves in stellar models and took the energy release of the instantaneous centre explosion into ac- count. They sought similarity solution of the problem by reducing the equations of motion to ordinary differential equations. A class of non-similarity solutions in series expansion for explosions in stars was obtained by Sakurai (1956) and also by Rogers (1956); the latter had effectively combined the methods of Sakurai (1953, 1954) and McVittie (1953). Rosenau (1977) studied the propagation of magnetogasdynamic shock waves in Roche model using the method of similarity solution and found that gravitation has an ignorable in- fluence on the past shock flow in the vicinity of the earth. The unsteady model of Roche consists of a gas distributed with spherical symmetry around a nucleus having a large mass. It is assumed that the gravitating effect of the gas itself can be neglected compared with the attraction of the heavy nucleus. Non-similarity solution for propa- gation of shock waves in Roche Model have been found under the influence of magnetic field. Ahead of the shock wave, in the undisturbed large envelope of the Roche model, the density distribution is taken to vary as inverse power of the radial distance from the point of explosion i.e.