Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

Invariance analysis and similarity solution of heat transfer for MHD viscous power-law fluid over a non-linear porous surface via group theory

Abstract: A B S T R A C T In this paper general group symmetry analysis so-called deductive group-theoretical method is applied to analyze the boundary layer flow of electrically conducting viscous fluid over with heat transfer over a non-linear surface. The symmetry groups admitted by the corresponding boundary value problem are obtained. With the use of the entailed similarity transformations the governing equations reduce to a set of non-linear ordinary differential equations. The system of equations is solved numerically using MATLAB coding. The effect of various flow parameters is studied for both Newtonian and Non-Newtonian power-law fluids in case of stretching and shrinking sheet.

A similarity transformation for inviscid non–Boussinesq gravity currents

Abstract: We propose a similarity transformation to investigate the motion of inviscid gravity currents in the similar phase. With this similarity transformation, the shallow water equations can be solved without needing to consider the front condition Eq. (1) downstream of the gravity current, and the parameter β of Eq. (1) becomes a part of the similarity solutions. It is shown that the resultant similarity solutions are in good agreement with the experimental results of both the dam-break and the lock-exchange non-Boussinesq currents, which have a density much larger than the ambient fluid.

Note on the Axisymmetric Sonic Jet.

Abstract: The axisymmetric sonic jet is considered in transonic small disturbance theory. A new hodograph equation is derived from which it can be deduced that there is a local similarity solution describing the final state. From this similarity solution it follows that the uniform sonic state is reached at a finite distance from the orifice.

Entropy generation due to a moving isothermal wavy surface in nanofluid

Abstract: The aim of current investigation is to analyse the irreversibility phenomenon, in the presence of nanoparticles in the base fluid, in viscous flow caused by the uniform motion of a wavy plate. The utilised model for the presentation of nanofluid is the Bonjourno model in which the Brownian motion and thermophoresis effects are considered. The non-flat surface texture of the wavy plate does not allow the similarity solution to exist due to which the problem is non-similar in nature. The study of entropy generation phenomenon in such non-similar boundary layer flows is very rare in literature. An implicit finite difference scheme (the Keller-box method) is utilised to obtain the numerical solution and the results have been presented through several graphs. The impact of various controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, wavy amplitude, Lewis number, Prandtl, and Brinkman numbers on Bejan number and entropy production number are examined. It is found that entropy production increases by increasing the concentration of nanoparticles.