Similarity solution

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

The Unsteady Flow of a Nanofluid in the Stagnation Point Region of a Time-dependent Rotating Sphere

Abstract: This paper deals with the unsteady boundary layer flow and heat transfer of nanofluid over a time-dependent rotating sphere where the free stream velocity varies continuously with time. The boundary layer equations were normalized via similarity variables and solved numerically. Best accuracy of the results has been obtained for regular fluid with previous studies. The nanofluid is treated as a two-component mixture (base fluid+nanoparticles) that incorporates the effects of Brownian diffusion and thermophoresis simultaneously as the two most important mechanisms of slip velocity in laminar flows. Our outcomes indicated that as

Application of the velocity‐dissipation probability density function model to inhomogeneous turbulent flows

Abstract: Recently Pope and Chen [Phys. Fluids A 2, 1437 (1990)] developed a turbulence model based on the one‐point Eulerian joint probability density function (pdf) of velocity and dissipation. The modeling is performed by constructing stochastic processes for the velocity and dissipation following fluid particles. In the original work, these models were constructed by reference to the known statistics of homogenous turbulence, and the applicability of the model was restricted to this narrow class of flows. In this paper the model is extended to inhomogeneous flows, and calculations are presented to demonstrate aspects of the model’s performance. The model equation admits a similarity solution corresponding to the log‐law region of the turbulent boundary layer, and the principal statistics obtained from this solution are in good agreement with experimental data. Application of the model to the momentumless wake and to the plane mixing layer demonstrate its ability to represent turbulent/nonturbulent intermittency in these free flows: in the intermittent regions, the pdf of dissipation is bimodal, with a spike at zero corresponding to nonturbulent fluid. Fluid‐particle paths in the turbulent mixing layer obtained from the model correspond to large‐scale coherent motions, rather than to the small‐scale incoherent motion characteristic of diffusive transport.

A note on the similarity solutions for free convection on a vertical plate

Abstract: The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x λ and when the (non-dimensional) surface heat flux is −x μ are considered. Solutions valid for λ≫1 and μ≫1 are obtained. Further, for the first problem it is shown that there is a value λ0, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for λ>λ0, and for the second problem that solutions are possible only for μ>−1 (for all Prandtl numbers). In both cases the solutions becomes singular as λ→λ0 and as μ→−1, and the natures of these singularities are discussed.

The magnetohydrodynamic effects on a fluid film squeezed between two rotating surfaces

Abstract: Considers the motion of a fluid film squeezed between two rotating parallel plane surfaces in the presence of a magnetic field applied perpendicular to the surfaces. Attention is given to the case where a similarity solution can be obtained. Approximate analytical solutions are given, and a numerical solution to the resulting nonlinear ordinary differential equations is presented. The combined effects of the magnetic forces and the centrifugal inertial forces on the velocity profiles, the load capacity and the torques that the fluid exerts on the surfaces are studied. In general, the results show that these two forces have opposite effects.