Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
Papers published on a yearly basis
Papers
More filters
01 Jan 2012
TL;DR: In this paper, the combined free convective dynamic boundary layer and thermal radiation boundary layer at a semi-infinite vertical plate has been studied with variable suction, and the coupled unsteady nonlinear momentum and energy equations of the combined layer are then reduced to similarity equations by introducing a time dependent similarity parameter.
Abstract: The combined free convective dynamic boundary layer and thermal radiation boundary layer at a semi-infinite vertical plate has been studied with variable suction. The fluid is considered to be gray absorbing emitting. The coupled unsteady non-linear momentum and energy equations of the combined layer are then reduced to similarity equations by introducing a time dependent similarity parameter. The similarity equations are solved numerically by adopting shooting method using the Nachtsheirm - Swigert iteration technique. The resulting velocity and temperature distributions are shown graphically for different values of the parameters. The numerical values of the wall shear stress and the heat flux are also shown in tabular form. Finally these results are discussed.
TL;DR: In this article, the axisymmetric intrusion of a fixed volume of fluid, which is released from rest and then propagates radially at the neutral buoyancy level in a deep linearly stratified ambient fluid is investigated.
IBM1
TL;DR: In this article, it was shown that the linear diffusion equation in one dimension has two types of solutions: superpositions either of iterated error functions or of trigonometric functions, otherwise known as Fourier series.
Abstract: With iterated error functions we have already greatly expanded our vocabulary of solutions of the diffusion equation. The question is, however, whether or not any useful further expansion should be expected. The study of physical symmetries provides a partial answer, and that study is called similarity. In essence, we shall find that the linear diffusion equation in one dimension has two types of solutions: superpositions either of iterated error functions or of trigonometric functions, otherwise known as Fourier series. The strength of similarity methods lies in their applicability to nonlinear problems as well. This chapter continues with more physical examples, including exact solutions for the kinetics of certain first-order phase transformations and of diffusion problems where the diffusivity depends on the field. In contrast, Chaps. 7 and 8 describe deductive methods for the solution of diffusion problems.
01 Jan 1984
TL;DR: In this paper, a modification of the original Keller box scheme is used to approximate nonlinear parabolic partial differential equations with moving boundaries, and a comparison of numerical results with the similarity solution gives evidence of stability and convergence.
Abstract: A modification of the original Keller box scheme is used to approximate nonlinear parabolic partial differential equations with moving boundaries. The proposed scheme solves two systems of linear algebraic equations at each time-step to produce second-order approximations to the solution, its derivative (the flux) and the position of the moving boundary. The scheme is applied to a physical problem which has a known similarity solution. A comparison of numerical results with the similarity solution gives evidence of stability and convergence. (1.3) ~~~ut = (K(U) UX)X in 0 O, s - g(s, u)ux on x s(t), t> 0.