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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 series of transient problems in the flows of concentrated suspensions were investigated to test the effects of particle migration on the evolution of concentration and velocity profiles, and the authors reported a similarity solution to a Rayleigh problem, where the boundary of the infinite half space is given a velocity proportional to the square root of time.
Abstract: We have investigated a series of transient problems in the flows of concentrated suspensions to test the effects of particle migration on the evolution of concentration and velocity profiles. First, we report a similarity solution to a Rayleigh problem, where the boundary of the infinite half space is given a velocity proportional to the square root of time. Next, the classical Rayleigh problem, where the boundary is impulsively started initially at a constant velocity, is examined. The structure of the kinematics resembles that obtained in the first problem, but the concentration does not have a similarity form, and tends asymptotically to a uniform profile at large time. Finally, we solve the flow of a suspension past a semi-infinite plate, and discuss its connection to the Rayleigh problem. In all three cases, our calculations reveal Newtonian kinematics in the practical limit of a L ⪡ 1 , where a is the particle size, and L is a viscous diffusion length scale. In addition we see vastly different time and length scales in the evolution of the velocity and the concentration profiles. The velocity develops faster in time (by O( a L ) 2 ), and extends further in space (by O( L a ) ) than the concentration profile.
2 citations
01 Jan 2002
TL;DR: In this paper, a two dimensional channel flow is considered under the action of periodic oscillatory pressure field, where the flow is assumed to be fully developed laminar and incompressible, so that dimensionless form of the momentum equation has been solved analytically by using similarity transformation.
Abstract: Two dimensional channel flow is considered under the action of periodic oscillatory pressure field. The flow is assumed to be fully developed laminar and incompressible, so that dimensionless form of the momentum equation has been solved analytically by using similarity transformation. Variations of the velocity profiles and skin friction coefficient over a cycle have been obtained together with behavior of the flow for various oscillation frequencies. Results were also compared to numerical values of the two dimensional laminar flow equations, based on the finite volume technique.
2 citations
TL;DR: Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed in this paper, where the plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary.
Abstract: Similarity solution of unsteady convective boundary layer flow along isothermal vertical plate with porous medium is analyzed. The plate surface is reactive with the fluid and generates inert specie which diffuses inside the boundary. The flux of the specie at the plate is proportional to specie concentration at the plate. The governing equations of continuity, momentum, energy and specie diffusion are transformed into ordinary differential equation by using the similarity transformation and solved numerically by using free parameter method along with shooting technique. The dimensionless velocity, temperature and concentration profiles are obtained and presented through figures for different parameters entering into the problem. The local Skin-friction co-efficient, Nusselt number and Sherwood number at the plate for physical interest are also discussed through tables.
2 citations
TL;DR: The similarity solution of the inclined wall plume is obtained analytically in this article, where the authors used the continuity equation of flow, the momentum balance equation in the flow direction, diffusion equation of concentration, equation of kinetic energy of turbulence and the equation of viscous dissipation rate of turbulence.
Abstract: The similarity solution of inclined wall plume is obtained analytically. The mathematical model used herein consists of the continuity equation of flow, the momentum balance equation in the flow direction, the diffusion equation of concentration, the equation of kinetic energy of turbulence and the equation of viscous dissipation rate of turbulence. It is shown that this set of equations has the similarity solution which can be solved numerically for each angle of the inclined wall. This numerical model is applied to the wide range of the slope angle, which includes the plume along the vertical wall for the special case and along the nearly horizontal wall. The velocity and concentration profiles of the inclined wall plume are explained well by the similarity solution.
2 citations
01 Jan 2013
TL;DR: Similarity equations for both two-dimensional and three-dimensional flow for ten different models of non-Newtonian fluids are presented in this paper, and it is observed that similarity solution exists for the flow past a 90 degree wedge when shearing stress of the fluids is related to the rate of strain by an arbitrary continuous function.
Abstract: Similarity equations for both two-dimensional and three-dimensional flow for ten different models of non-Newtonian fluids are presented. It is observed that, for non-Newtonian fluids of any models, similarity solution exists for the flow past 90 degree wedge when shearing stress of the fluids is related to the rate of strain by an arbitrary continuous function. Similarity solution for the flow past a wedge inclined at any arbitrary angle, exists only in the case of Ostwald-de-Waele Power-law fluids, for which shearing stress can be expressed as an implicit function of rate of strain.
2 citations