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, a generalized Leveque solution is presented for the conjugate fluid-fluid problem that arises in the thermal entrance region of laminar counterflow heat exchangers.
17 citations
TL;DR: In this article, the free convective flow of an incompressible micropolar fluid along a vertical plate under the convective boundary condition is investigated and the Lie scaling group of transformations is applied to get the similarity representation for the system of partial differential equations and then the resulting systems of equations are solved using spectral quasi-linearisation method.
Abstract: The free convective flow of an incompressible micropolar fluid along permeable vertical plate under the convective boundary condition is investigated. The Lie scaling group of transformations is applied to get the similarity representation for the system of partial differential equations and then the resulting systems of equations are solved using spectral quasi-linearisation method. A quantitative comparison of the numerical results is made with previously published results for special cases and the results are found to be in good agreement. The results of the physical parameters on the developments of flow, temperature, concentration, skinfriction, wall couple stress, heat transfer, and mass transfer characteristics along vertical plate are given and the salient features are discussed.
17 citations
TL;DR: In this article, the design of the tallest column is solved again using a different method, by the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away.
Abstract: A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the direction of the stable manifold, and solving backward numerically. This removes the need for an iterative integration method that was previously used. The method is shown to work for clamped or hinged boundary condition and can also be used for other problems involving singularities at the endpoints.
17 citations
TL;DR: In this article, an axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder is presented, where velocity slip is considered instead of the no-slip condition at the boundary.
Abstract: An axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder is presented. Velocity slip is considered instead of the no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and heat equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. It is found that the velocity decreases with increasing the slip parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to those for a flat plate.
17 citations
TL;DR: It is shown that methods such as front tracking and the level-set method are not practical for the solution of the transient problem, due to the indeterminate nature of the interface velocity, in common with similar degenerate diffusion problems.
17 citations