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 analysis of buoyancy-induced flow adjacent to a vertical surface dissipating a uniform flux in cold pure and saline water is presented, and a modified Grashof number is defined, based on the surface heat flux.
Abstract: An analysis of buoyancy-induced flow adjacent to a vertical surface dissipating a uniform flux in cold pure and saline water is presented. For these conditions a simple yet very accurate density relationship proposed by Gebhart and Mollendorf is employed to estimate the buoyancy force. To obtain a similarity solution under these conditions, the quiescent medium is considered to be at the temperature condition at which the density extremum occurs. A modified Grashof number is defined, based on the surface heat flux. The fifth-order two-point boundary value problem is solved by a fourth-order Runge-Kutta method, starting from an asymptotic solution at a large distance from the surface. Solutions are obtained for different pressure and salinity conditions over a Prandtl number range of 8.0 to 13.0, The following heat transfer correlation is proposed for all values of q(s, p) from 1.5829 to 1.8948: Nux = 0.577[Ra* x]1/(4 + q).
3 citations
TL;DR: In this article, a similarity transformation has been proposed to study the two-phase boundary layer equations derived by Wang and Beckermann for capillary porous media, and the set of governing equations and boundary conditions for the pressure-driven boiling flow over a body of arbitrary shape reduces to the one for the flow over the flat plate.
3 citations
TL;DR: In this paper, the steady surface-tension driver flows in floating rectangular cavities, and all possible solutions of the problem are classified and shown to have at most three types of solutions for A ≥ 1.
Abstract: We consider the following problem: f‴ + Q⋅[Aff″ − (f′) 2 ] = β, Q,β ∈ R , A ≥ 0), (0) = f″(1) = f″(0) + = 0, which arises from the steady surface-tension driver flows in floating rectangular cavities. In this paper, we first classify all possible solutions and obtain that the given problem can only possess, at most, three types of solutions for A ≥ 1. By the classification, we further verify that for every Q ≥ 0 or β ≥ 0, the problem has at least one solution if A ≥ 1. Moreover, if 1 ≤ A ≤ 3 2 , multiple solutions also exist for sufficiently large Q >0.
3 citations
TL;DR: In this article, a plane problem of directed mass transfer in a granular medium, induced by complex loading with continuous rotation of the principal axes of the strain tensor, is considered and a finite-element algorithm is developed for the hypoplastic model, and a numerical solution of a boundary value problem is constructed.
Abstract: A plane problem of directed mass transfer in a granular medium, induced by complex loading with continuous rotation of the principal axes of the strain tensor, is considered. It is proposed to use a hypoplastic model of a granular medium and a model of similarity of a viscous incompressible fluid to describe this effect. A finite-element algorithm is developed for the hypoplastic model, and a numerical solution of a boundary-value problem is constructed. An approximate analytical solution of the initial problem is obtained for the model of similarity of a viscous incompressible fluid. Calculations of deformation kinetics are performed for both models, and the results obtained are compared with available experimental data. Both models are demonstrated to ensure a qualitative description of the deformation process and the effect of directed mass transfer observed in experiments.
3 citations
TL;DR: In this article, the authors studied the invariance of the diffusion equation under continuous groups of transformations and showed the conditions which D ( x ) must satisfy for the existence of similarity solutions.
3 citations