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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 nonlinear diffusion equation arising from a biphasic continuum model of soft tissue, such as for articular cartilage, is studied, through the use of maximum principles and comparison theorems.
Abstract: A nonlinear diffusion equation arising from a biphasic continuum model of soft tissue, such as for articular cartilage, is studied. Through the use of maximum principles and comparison theorems, the quantitative characteristics of the solution are established, independent of the particular nonlinear constitutive equation used for the solid-fluid interaction in the tissue. In conjunction with this, similarity and asymptotic methods are employed to obtain approximate solutions to the problem.

19 citations

Journal ArticleDOI
TL;DR: In this paper, a new derivation of the Charles energy-size reduction relationship was presented, which matched the moments of particle-size distribution from the grinding equation with those computed from the empirical Gaudin-Schuhmann size distribution equation.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the three dimensional problem of steady fluid deposition on an inclined rotating disk is solved by similarity transform, and for a given spraying rate there may be one, two or no steady state solution.

19 citations

Journal ArticleDOI
TL;DR: Wei et al. as discussed by the authors studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined the self-similar evolution of advection-dominated accretion flow (ADAF) in the presence of a toroidal magnetic field and showed that the behavior of the physical quantities in a dynamical ADAF is different from that for a steady ADF or a disc using a polytropic approach.
Abstract: The present study examines the self-similar evolution of advection-dominated accretion flow (ADAF) in the presence of a toroidal magnetic field. In this research, it was assumed that angular momentum transport is due to viscous turbulence and the α-prescription was used for the kinematic coefficient of viscosity. The flow does not have a good cooling efficiency and so a fraction of energy accretes along with matter on to the central object. The effect of a toroidal magnetic field on such a system with regard to the dynamical behaviour was investigated. In order to solve the integrated equations that govern the dynamical behaviour of the accretion flow, a self-similar solution was used. The solution provides some insights into the dynamics of quasi-spherical accretion flow, and avoids many of the strictures of steady self-similar solutions. The solutions show that the behaviour of the physical quantities in a dynamical ADAF is different from that for a steady accretion flow or a disc using a polytropic approach. The effect of the toroidal magnetic field is considered using additional variable β (= P mag /P gas , where P mag and P gas are the magnetic and gas pressure, respectively). Also, to consider the effect of advection in such systems, the advection parameter f, which stands for the fraction of energy that accretes by matter on to the central object, was introduced. The solution indicates a transonic point in the accretion flow for all selected values of f and β. Also, by increasing the strength of the magnetic field and the degree of advection, the radial thickness of the disc decreases and the disc compresses. The model implies that the flow has differential rotation and is sub-Keplerian at small radii and super-Keplerian at large radii, and that different results were obtained using a polytropic accretion flow. The β parameter obtained was a function of position, and increases with increasing radii. Also, the behaviour of ADAF in a large toroidal magnetic field implies that different results are obtained using steady self-similar models in large magnetic fields.

19 citations


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Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850