Similarity solution

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

Boundary‐Layer Analysis of Polarization in Electrodialysis in a Two‐Dimensional Laminar Flow

Abstract: The problem of ion transfer in the fluid phase of an electrodialysis stack with parallel flow is considered for two extreme cases: (a) undisturbed laminar flow with purely diffusive mixing; and (b) perfectly mixed flow. Case (a) leads to a thin concentration boundary layer imbedded in the flow near the membrane surface. It is shown that for practically relevant parameters the solution may be approximated by a closed‐form similarity solution, and this is compared with the more exact numerical solution. Case (b), which represents the ideal situation, is presented for comparison.

Chemically reactive solute transfer in boundary layer flow along a stretching cylinder in porous medium

Abstract: This paper presents the distribution of solute undergoing first order chemical reaction in axi-symmetric laminar boundary layer flow towards a stretching cylinder embedded in porous medium. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and concentration equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that velocity decreases with increasing permeability parameter. The skin friction as well as the mass transfer rate at the surface is larger for a cylinder compared to a flat plate.

Similarity solution of two coupled reaction-diffusion rate equations.

Abstract: A coupled system of nonlinear evolution equations describing the combined effects of diffusion and reactions, e.g., fusion reactions or electron-ion recombinations, is transformed into a system of coupled similarity equations in one, two, and three dimensions. A description of the evolution of the coupled system for special though physically relevant situations, e.g., the diffusion of an ignited high-density fusion plasma (thermal-thermal reactions) of tritium and deuterium, is obtained in terms of a particular similarity solution.

Self-similar, slightly compressible, free vortices

Abstract: Exact and numerical similarity solutions for compressible perturbations to an incompressible, two-dimensional, axisymmetric vortex reference flow are presented. The reference flow consists of a set of two-dimensional, self-similar, incompressible vortices. Similarity variables, which give explicit expressions for the decay rates of the velocities and thermodynamic variables in the vortex flows, are used to reduce the governing partial differential equations to a set of ordinary differential equations. The ODEs are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are employed to study the dependences of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Additionally, several integral relations, which allow one to trace the energy transfer in a slightly compressible vortex, are derived.