Similarity solution

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

Similarity solutions for phase-change problems

Abstract: A modification of Ivantsov's (1947) similarity solutions is proposed which can describe phase-change processes which are limited by diffusion. The method has application to systems that have n-components and possess cross-diffusion and Soret and Dufour effects, along with convection driven by density discontinuities at the two-phase interface. Local thermal equilibrium is assumed at the interface. It is shown that analytic solutions are possible when the material properties are constant.

Pressure diffusion in unsteady non-Darcian flows through porous media

Abstract: The pressure diffusion in unsteady non-Darcian flows through a porous medium is studied analytically. The exact similarity solutions for the pressure and velocity distributions for the Cauchy problem, (i.e. the case of source type solution) are presented and graphically illustrated. Two classes on non-Darcian flows are investigated. The class of unsteady turbulent gas flows with polytropic thermodynamic evolution, and the class of non-Newtonian fluid flows of power law behavior. The derived governing pressure-diffusion equations belong to a class of nonlinear degenerate parabolic equations having solutions with compact support. It is shown that due to the nonlinear effects associated with non-Darcian flows, the pressure and velocity distributions exhibit traveling wave characteristics. The conditions for the existence of these diffusive waves are found, and expressed in terms of the properties of the fluid and the porous medium. (authors). 11 refs., 5 figs.

Stability of gravity currents generated by finite-volume releases

Abstract: We generalize the linear stability analysis of the axisymmetric self-similar solution of gravity currents from finite-volume releases to include perturbations that depend on both radial and azimuthal coordinates. We show that the similarity solution is stable to sufficiently small perturbations by proving that all perturbation eigenfunctions decay in time. Moreover, asymmetric perturbations are shown to decay more rapidly than axisymmetric perturbations in general. An asymptotic formula for the eigenvalues is derived, which indicates that asymptotic rates of decay of perturbations are given by t -σ where 0 < σ < 1/4 as the Froude number decreases from √2 to 0. We demonstrate that this formula agrees closely with numerically calculated eigenvalues and, in the absence of azimuthal dependence, it reduces to an expression that improves on the asymptotic formula obtained by Grundy & Rottman (1985). For two-dimensional (planar) currents, we further prove analytically that all perturbation eigenfunctions decay like t -1/2 .

Non-Darcy Mixed Convection with Thermal Dispersion-Radiation in a Saturated Porous Medium

Abstract: In the present work melting with thermal dispersion and radiation on non-Darcy, mixed convective heat trans- fer from an infinite vertical plate embedded in a saturated porous medium is studied. Both aiding and opposing flows are examined. Forchheimer extension for the flow equations in steady state is considered Similarity solution for the governing equations is obtained .The equations are numerically solved using Runge-kutta fourth order method coupled with shooting technique. The effects of melting (M), thermal dispersion (D), radiation(R) inertia (F) and mixed convection (Ra/Pe) on velocity distribution, temperature and Nusselt number are examined. It is observed that the Nusselt number decreases with increase in melting parameter and increases with increase in the combined effect of thermal dispersion and radiation.