Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

On nonlinear diffusion in fractal structures

Abstract: An exact similarity solution for nonlinear diffusion in fractal sructures, in the presence of absorption, is presented and disscused. The concentration distribution in a spherical symmetry geometry for the Cauchy problem, corresponding to an instantaneous point source solution, reveals the occurence of traveling wave characteristics. The conditions for the existence of these diffusive waves are shown in terms of nonlinear and fractal effects. The absorption effect gives rise to a spatial localization of the moving concentration front.

An approximate similarity solution for spatial fractional boundary-layer flow over an infinite vertical plate

Abstract: In this paper, an approximate similarity solution of a fractional laminar boundary layer of viscous fluid flow over an infinite vertical plate has been presented. We introduce new fractional similarity transformations to convert the partial differential equation into a similarity ordinary differential equation with a fractional context. The viscous term of the flow momentum equation is written based on the Caputo fractional derivative. The proposed analytical solution has been developed using fractional power-series technique, and the convergence of the solution has been examined. The velocity distributions with the similarity variable are plotted against different values of the fractional order to illustrate the effects of fractional argument on the velocity behavior.

Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids

Abstract: Three local self-similar solutions are obtained for the laminar planar jet flow of viscoelastic fluids, described by the FENE-P constitutive equation, through an order of magnitude simplification of the governing equations. The more general solution is shown to be more accurate than two further simplified solutions, here called the delta and the Olagunju-type solutions, at least for the profiles of conformation tensor components. In the limit of vanishing viscoelasticity, all conformation tensor components reduce to the same low elasticity asymptotic behavior, and the polymer stresses become Newtonian-like. The general solution is then used to obtain the laws of the decay of the centerline velocity and of the growth of the jet half-width and to ascertain the effects of the Weissenberg number, maximum polymer extensibility parameter and the ratio of polymer to total viscosities upon the flow characteristics. The general local self-similar solution compares well with results of numerical simulations obtained by the RheoFoam module of the freeware OpenFoam code.

Role of Buoyancy and the Boussinesq Approximation in Horizontal Boundary Layers

Abstract: The effect of buoyancy on the shear and heat transfer in a horizontal boundary layer is studied for a fluid which has a linear density, viscosity and conductivity variation with temperature. It is shown that the problem admits a similarity solution for arbitrary buoyancy when the external stream is accelerated as the one-fifth power of the distance from the leading edge. This case is solved numerically for both the complete and the Boussinesq approximation to the boundary-layer problem. It is shown that the Boussinesq approximation gives quite accurately a correction to the shear and heat-transfer coefficient due to buoyancy, except in the case of cooled flows where the boundary layer tends to a buoyancy-induced separation. A perturbation expansion to the Boussinesq equations for small buoyancy which admits a family of self-similar solutions for flows accelerated or decelerated as powers of the distance is derived and the coupling between pressure gradient and (small) buoyancy effects is discussed.