Similarity solution

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

The solutions for the flow of micropolar fluid through an expanding or contracting channel with porous walls

Abstract: The unsteady, two-dimensional laminar flow of an incompressible micropolar fluid in a channel with expanding or contracting porous walls is investigated. The governing equations are transformed into a coupled nonlinear two-points boundary value problem by a suitable similarity transformation. Unlike the classic Berman problem (Berman in J. Appl. Phys. 24:1232-1235, 1953), three new solutions (totally six solutions) and no-solution interval, which is one of important characteristics for the laminar flow through porous pipe with stationary wall (Terrill and Thomas in Appl. Sci. Res. 21:37-67, 1969), are found numerically for the first time. The multiplicity of the solutions is strictly dependent on the expansion ratio. Furthermore, the asymptotic solutions are constructed by the Lighthill method, which eliminates the singularity of the similarity solution, for large injection and by the matching theorem for the suction Reynolds number, respectively. The analytical solutions also are compared with the numerical ones and the results agree well.

Laminar ShearStress Pattern for Nonsimilar Incompressible Boundary Layers

Abstract: A technique has been developed and applied to the solution of the laminar incompressible nonsimilar boundarylayer problem. The basic feature of this method involves the finding of a strained value of the Gortler's Principle Function such that the corresponding zero-order similarity solution provides a highly accurate approximate sheer stress result at the wall. The method can be applied locally without reference to other streamwise locations. Working charts and tables of the required universal function are provided to facilitate computations. Several examples are given to illustrate the present technique and to demonstrate its effectiveness and accuracy.

Post-breakup solutions of Navier-Stokes and Stokes threads

Abstract: We consider the breakup of a fluid thread, neglecting the effect of the outside fluid (or air). After breakup, the solution of the fluid equations consists of two threads, receding rapidly from the point of breakup. We show that the bulk of each thread is described by a similarity solution of slender geometry (which we call the thread solution), but which breaks down near the tip. Near the tip of the thread the thread solution can be matched to a solution of Stokes' equation, which consists of a finger of constant spatial radius, rounded at the end. Very close to breakup, the thread solution balances inertia, viscosity, and surface tension (Navier-Stokes case). If however the fluid viscosity is large (as measured by the dimensionless Ohnesorge number), some time after breakup the thread solution consists of a balance of surface tension and viscosity only (Stokes case), and the thread profile can be described analytically.