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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 paper, a mathematical model was developed to obtain a similarity solution for heat transfer analysis during progressive freeze-concentration-based desalination, which considered the process as a one-phase Stefan problem.
10 citations
Journal Article•
9 citations
TL;DR: In this article, the authors investigated the unsteady flow of non-Newtonian fluids of power low behavior through a porous medium in a plane radial geometry, and the equation governing the flow is a nonlinear parabolic partial differential equation with a source term whose solution satisfies certain fixed and moving boundary conditions.
Abstract: This paper investigates the unsteady flow of non-Newtonian fluids of power low behavior through a porous medium in a plane radial geometry. The equation governing the flow is a nonlinear parabolic partial differential equation with a source term whose solution satisfies certain fixed and moving boundary conditions. The attention is focused on the finding of similarity solution when the fixed boundary condition and the source term satisfy certain restrictions. In this case similarity transformations are determined and the resulting ordinary differential equations are deduced. For shear thinning fluids the existence of a pressure disturbance front moving with finite velocity is shown and expression for its location as a function of time is determined. The solutions in closed form have been given for certain particular cases where the resulting differential equations can be analytically solved. A numerical procedure has also been presented.
9 citations
TL;DR: In this paper, the authors examined the integrability of the viscous Burgers equation using the dynamics of their poles in the complex x-plane and showed that this finite-dimensional system is completely integrable, by explicit construction of a sufficient number of conserved quantities.
Abstract: Rational solutions of the viscous Burgers equation are examined using the dynamics of their poles in the complex x-plane. The dynamical system for the motion of these poles is finite dimensional and not Hamiltonian. Nevertheless, we show that this finite-dimensional system is completely integrable, by explicit construction of a sufficient number of conserved quantities. The dynamical system has a class of non-equilibrium similarity solutions for which all poles have equal real part for t sufficiently large. Within the context of the finite-dimensional dynamical system these solutions are shown to be asymptotically stable.
9 citations
TL;DR: Using the symmetry method, this article analyzed the Calogero-Degasperis-Fokas modified KdV equation, where the function f solves f '''( u )=8 a f '( u ).
Abstract: Using the symmetry method, we analyze the Calogero–Degasperis–Fokas modified KdV equation u t + u x x x - a u x 3 - f ( u ) u x =0; a ∈ R , where the function f solves f '''( u )=8 a f '( u ). The ...
9 citations