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, an analytical investigation of turbulent boundary layer flow over a flat plate in the range of Reynolds number between 10 6 and 10 9 was performed. And the authors proposed analytical expressions for the friction coefficient and the hydrodynamic boundary layer thicknesses based on the series solution.
5 citations
TL;DR: In this article, a model for forward propagation of a combustion front through a porous medium was studied and the authors proved the existence and uniqueness of solution of the model and showed that temperature is non-decreasing function of time.
5 citations
TL;DR: In this article, a nonlinear progressive wave equation (NPE) was proposed to describe the evolution of a low Mach number shock wave, which is the nonlinear time domain counterpart of the frequency domain linear parabolic wave equation for small angle propagation.
Abstract: A nonlinear progressive wave equation (NPE) describes the evolution of a low Mach number shock wave. The NPE is the nonlinear time domain counterpart of the frequency domain linear parabolic wave equation (PE) for small angle propagation. The NPE in spherical symmetry admits a similarity solution that specifies both the shape of the pulse and the shock strength as a function of range. For finite amplitude spherical waves whether self‐similar or not, the theory predicts constancy of an impulse integral corresponding to that of linear theory. For the self‐similar waves, theory and available data are in qualitative agreement in the following areas: (1) The shock strength decreases with range as an approximate power law; (2) the temporal behavior of the solution at fixed range is a shock discontinuity followed by a roughly exponential decay; and (3) the effective relaxation time behind the shock is in reasonable agreement with data for slightly more than the first decade in range.
5 citations
TL;DR: In this paper, a common numerical scheme is devised for the linear, uncoupled plane stress and plate flexure problems based on adopting the stress function and the deflection as field variables in the respective problems.
Abstract: Symmetrically laminated plates are analysed by the boundary element method. A common numerical scheme is devised for the linear, uncoupled plane stress and plate flexure problems. A generic formulation is based on adopting the stress function and the deflection as field variables in the respective problems. Their mathematical similarity allows the use of essentially the same fundamental solution and almost identical solution algorithms. The application of plane stress and flexure analyses to several benchmark problems illustrates the versatility of the formulations and the degree of accuracy achieved. In the case of flexure in particular, comparisons are made with results from earlier boundary element analyses.
5 citations
TL;DR: In this article, an analytical solution for the combined diffusive and convective mass transport from a surface film of arbitrary shape at a given uniform concentration to a pure solvent flowing in the creeping regime through microchannels is provided.
5 citations