Similarity solution

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

Entropy generation analysis for film boiling: A simple model of quenching

Abstract: In this paper, quenching in high-temperature materials processing is modeled as a superheated isothermal flat plate. In these phenomena, a liquid flows over the highly superheated surfaces for cooling. So the surface and the liquid are separated by the vapor layer that is formed because of the liquid which is in contact with the superheated surface. This is named forced film boiling. As an objective, the distribution of the entropy generation in the laminar forced film boiling is obtained by similarity solution for the first time in the quenching processes. The PDE governing differential equations of the laminar film boiling including continuity, momentum, and energy are reduced to ODE ones, and a dimensionless equation for entropy generation inside the liquid boundary and vapor layer is obtained. Then the ODEs are solved by applying the 4th-order Runge-Kutta method with a shooting procedure. Moreover, the Bejan number is used as a design criterion parameter for a qualitative study about the rate of cooling and the effects of plate speed are studied in the quenching processes. It is observed that for high speed of the plate the rate of cooling (heat transfer) is more.

Self-similar solutions of the axisymmetric shallow-water equations governing converging inviscid gravity currents

Abstract: A phase-plane approach is used to determine similarity solutions of the axisymmetric shallow-water equations which represent inwardly propagating, inviscid gravity currents. A Froude number condition characterizes the movement of the front. The unique similarity exponent is found numerically as a function of the frontal Froude number and the height and velocity profiles are presented for three different Froude numbers. The fluid speed and height are seen to increase monotonically towards the front except very close to the front where the height decreases. The maxima in both height and speed increase as the Froude number increases, reflecting the change in ambient resistance.For the Froude number that has been obtained experimentally for lock-exchange Boussinesq flows (. This similarity solution describes the formation of a shock, as well as its initial propagation.

On similarity solutions for turbulent and heated round jets

Abstract: Commonly used empirical correlations for incompressible, heated round jets are shown to represent similarity solutions of the governing jet equations. These solutions give rise to self-similar eddy viscosities. Not all the similarity solutions are physically valid because some lead to zero eddy viscosities at the jet centerline. One physically valid solution is found to correlate best with round jet measurements and it gives a Gaussian error function description for the normalized mean velocity and temperature. Heat and momentum fluxes thus calculated are also in good agreement with measurements. Therefore, in addition to the classical similarity solution obtained by assuming constant eddy viscosity, another similarity solution to the jet equations is found where the eddy viscosity is self-similar.