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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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G. M. Webb1
TL;DR: In this article, a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is presented, where the distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinates.
Abstract: The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J and B force (B, magnetic field induction) and the gas pressure gradient. 21 references.

17 citations

Journal ArticleDOI
TL;DR: In this article, a similarity solution is used to analyse the flow of the Oldroyd fluid B, which includes the Newtonian and Maxwell fluids, in a curved channel modelled by the narrow annular region between two circular concentric cylinders of large radius.
Abstract: A similarity solution is used to analyse the flow of the Oldroyd fluid B, which includes the Newtonian and Maxwell fluids, in a curved channel modelled by the narrow annular region between two circular concentric cylinders of large radius. The solution is exact, including inertial forces. It is found that the non-Netonian kinematics are very similar to the Newtonian ones, although some stress components can become very large. At high Reynolds number a boundary layer is developed at the inner cylinder. The structure of this boundary layer is asymptotically analysed for the Newtonian fluid. Non-Newtonian stress boundary layers are also developed at the inner cylinder at large Reynolds numbers.

17 citations

Journal ArticleDOI
TL;DR: In this article, the existence, uniqueness and behaviour of the solutions of the autonomous third-order nonlinear differential equation f(m+2)f f f −(2m+1)f′2 = 0 on ℝ+ with the boundary conditions f(0)=−γ, f′(∞)=0 and f″( 0)=−1.
Abstract: This paper is concerned with existence, uniqueness and behaviour of the solutions of the autonomous third-order non-linear differential equation f‴+(m+2)f f″−(2m+1)f′2=0 on ℝ+ with the boundary conditions f(0)=−γ, f′(∞)=0 and f″(0)=−1. This problem arises when looking for similarity solutions for boundary layer flows with prescribed heat flux. To study solutions we use some direct approach as well as blowing-up co-ordinates to obtain a plane dynamical system. Copyright © 2004 John Wiley & Sons, Ltd.

17 citations

Journal ArticleDOI
TL;DR: In this paper, the steady three-dimensional stagnation-point flow and heat transfer of a dusty fluid toward a stretching sheet is investigated by using similarity solution approach The freestream along z-direction impinges on the stretching sheet to produce a flow with different velocity components The governing equations are transformed into ordinary differential equations by introducing appropriate similarity variables and an exact solution is obtained.
Abstract: The steady three-dimensional stagnation-point flow and heat transfer of a dusty fluid toward a stretching sheet is investigated by using similarity solution approach The freestream along z-direction impinges on the stretching sheet to produce a flow with different velocity components The governing equations are transformed into ordinary differential equations by introducing appropriate similarity variables and an exact solution is obtained The nonlinear ordinary differential equations are solved numerically using Runge–Kutta fourth-order method The effects of the physical parameters like velocity ratio, fluid and thermal particle interaction parameter, ratio of freestream velocity parameter to stretching sheet velocity parameter, Prandtl number, and Eckert number on the flow field and heat transfer characteristics are obtained, illustrated graphically, and discussed Also, a comparison of the obtained numerical results is made with two-dimensional cases existing in the literature and good agreement is approved Moreover, it is found that the heat transfer coefficient and shear stress on the surface for axisymmetric case are larger than nonaxisymmetric case Also, for stationary flat plat case, a similarity solution is presented and a comparison of the obtained results is made with previously published results and full agreement is reported

17 citations

Journal ArticleDOI
TL;DR: In this paper, a new exact solution to the nonlinear diffusion-convection equation dt dx V dxjdx for two-phase fluid flow in porous media is derived.
Abstract: SUMMARY A new exact solution to the nonlinear diffusion-convection equation dt dx V dxj dx for two-phase fluid flow in porous media is derived. The solution is sought for Dirichlet boundary conditions and a diffusivity of the form D(8) = D0/(l — v6) 2. The functional form of the fractional flow function f(6) is then found from a condition which determines the integrability of the resulting nonlinear ordinary differential equation. This results in an /(0)-function of the form f(9) = (Ft + F26 + F302)/(l — v6). Asymptotic expansions are derived for the fluid flux across the surface boundary x = 0 as a function of the parameters Do and v, and the surface boundary condition. These expansions show that a Buckley-Levere tt-type profile can be obtained in the limit of v -> 1 for a saturated surface boundary condition.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850