Topic
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 article, exact boundary layer similarity solutions for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature were developed for flow and friction transfer.
Abstract: Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.
7 citations
TL;DR: In this article, the effects of Hall and ion-slip currents on a steady free convection flow and mass transfer past a semi-infinite vertical plate in a viscous incompressible electrically conducting fluid are investigated when the fluid is subjected to a strong non-uniform magnetic field.
Abstract: The effects of Hall and ion-slip currents on a steady free convection flow and mass transfer past a semi-infinite vertical plate in a viscous incompressible electrically conducting fluid are investigated when the fluid is subjected to a strong non-uniform magnetic field. The similarity solutions are obtained using a scaling group of transformations. These are the only symmetry transformations admitted by the field equations. The derived fundamental equations under the assumption of a small magnetic Reynolds number are solved numerically by employing the shooting method. The axial and transverse components of the velocity function profiles are computed for various values of magnetic parameters, Hall and ionslip current parameters.
7 citations
01 Jan 1996
TL;DR: In this article, the authors considered the special case in which the initial saturation as well as the properties of the porous medium have a single coinciding discontinuity and proposed a self-similar profile to validate numerical algorithms describing two-phase flow in porous media.
Abstract: In this paper we consider the process of one-dimensional redistribution of two immiscible and incompressible fluids in a heterogeneous porous medium. We treat in detail the special case in which the initial saturation as well as the properties of the porous medium have a single coinciding discontinuity. Then the time-dependent saturation profile is of self-similar form, i.e. depends only on $x/ sqrt{t$. This self-similar profile can be used to validate numerical algorithms describing two-phase flow in porous media with discontinuous heterogeneities. We discuss the construction of the similarity solution, in which we give special attention to the matching conditions at the interface where the medium properties are discontinuous. We also outline a numerical procedure to obtain the similarity solution and we provide applications in terms of the Brooks-Corey and the Van Genuchten model.
7 citations
01 Jan 1976
TL;DR: In this article, the temperature distribution in a laminar plane wall jet has been studied and it is found that a similarity solution of the energy equation exists, which is reduced to a hypergeometric equation by a suitable transformation of the similarity variable and the solution, for arbitrary values of the Prandtl number, is obtained.
Abstract: In the present note the temperature distribution in a laminar plane wall jet has been studied. It is found that a similarity solution of the energy equation exists. The resulting ordinary differential equation is reduced to a hypergeometric equation by a suitable transformation of the similarity variable and the solution, for arbitrary values of the Prandtl number, is obtained. It is concluded that the heat transfer at the wall at a given section and the product of volume and heat-flux through any cross-section of the boundary layer increase with the increase in the value of Prandtl number respectively.
7 citations
TL;DR: In this paper, a one-dimensional shock-reflection test problem in the case of slab, cylindrical or spherical symmetry is discussed for multi-component flows and the differential equations for a similarity solution are derived and then solved numerically in conjunction with the Rankine-Hugoniot shock relations.
Abstract: A one-dimensional shock-reflection test problem in the case of slab, cylindrical or spherical symmetry is discussed for multi-component flows. The differential equations for a similarity solution are derived and then solved numerically in conjunction with the Rankine-Hugoniot shock relations.
7 citations