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 paper, a similarity type of general solution for the one-dimensional heat equation in spherical coordinates was developed, and the solution was then applied to establish analytical solutions of finite line source problems and moving boundary problems.
6 citations
01 Jan 2012
TL;DR: In this article, a similar analysis of the three dimensional incompressible laminar boundary layer flow of general class of non-Newtonian fluids is presented. But the analysis is restricted to the case of flow over wedge.
Abstract: Similarity analysis is made of the three dimensional incompressible laminar boundary layer flow of general class of non-Newtonian fluids. This work is an extension of previous analysis by Na and Hansen (1967), where the similarity solution of laminar three dimensional boundary layer equations of Power-law fluids was investigated. For the present flow situation, it is observed that the similarly solutions exist only for the case of flow over wedge. Further, it is also observed that for the more general case of the boundary layer flow of non-Newtonian fluids over anybody shapes yields non –similar solutions. Present similarity equations are well agreed with those available in literature.
6 citations
Abstract: Heat transfer by natural convection occurs in many physical and engineering applications. Governing equations of these problems are non-linear and need special methods for being solved. This paper aims to conduct an analytical analysis on the natural convection of a non-Newtonian fluid flow between two infinite vertical flat plates within a porous medium considering a variable heat source. The addition of porous medium and heat source marks the difference between the present work and previous researches. In the first phase of the current analysis, the governing equations including partial differential equations (PDE) are turned into ordinary differential equations (ODE) utilizing the similarity solution. Afterwards, a system of differential equations is solved using the Least Square Method (LSM), and reliable functions for the temperature and velocity distributions are presented. In order to investigate the accuracy of this method, the governing equations are also solved using numerical solutions. Proper agreement is observed between the analytical and numerical results. Regarding the very small errors observed in the results yielded by the LSM method, it can be concluded that this method is an efficient and reliable approach for solving non-linear ordinary differential equations. Finally, the effects of two main parameters, namely porosity and heat source parameters, are meticulously discussed. It is shown that as the value of the heat source parameter increases, the values of velocity and temperature decrease. Also, the results indicate that by enhancing the porosity parameter the flow velocity decreases, whereas there is no change in temperature. The results could be helpful for systems such as geothermal systems, heat exchangers, petroleum reservoirs and nuclear waste repositories in which natural convection is important.
6 citations
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01 Jan 1994
TL;DR: In this paper, the authors used conservation laws of porous media to construct one-phase and two-phase models, which lead to the same partial differential equation for saturation of a phase, which has an equilibrium and a non-equilibrium form.
Abstract: The flow in porous media is hard to describe. Based on a representative elementary volume, we use conservation laws of porous media to construct one-phase models (which models the flow through a porous medium where only one liquid or gas is present) and two-phase models. Both lead to the same partial differential equation for the saturation of a phase, which has an equilibrium and a non-equilibrium form. We analytically solve the equilibrium form using similarity solutions, this gives us useful results. For the non-equilibrium form we use a numerical approach to find a similarity solution. With the results we can say how the water distributes in some porous media.
6 citations
TL;DR: In this article, a class of similarity solutions for radial motions of spherical and cylindrical bodies made of a certain type of compressible hyperelastic materials is obtained for radii.
Abstract: A class of similarity solutions is obtained for radial motions of spherical and cylindrical bodies made of a certain type of compressible hyperelastic materials. The equations satisfied by the infinitesimal generators of the symmetry group of the unified governing first order field equations for spheres and cylinders are found. It is shown that these equations admit a special class of solutions which generate a five-parameter group of transformations. The form of the strain energy function Σ corresponding to the resulting symmetry group is evaluated. The similarity variable is determined and ordinary differential equations satisfied by similarity solutions are obtained. Numerical solutions are given for a Ko material which falls into the class of admissible materials.
6 citations