Similarity solution

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

Lie group invariance properties of radiation hydrodynamics equations and their associated similarity solutions

Abstract: The Lie group invariance properties of the one‐dimensional radiation hydrodynamic equations with the equilibrium diffusion approximation, a local thermodynamical equilibrium assumption, and an arbitrary material equation of state are derived. These properties are used systematically to generate similarity solutions of these equations for a given form of the equation of state. A comprehensive list of allowed similarity solutions for a perfect gas is presented. Several special cases that have been found previously by other authors appear in the list. Many other cases not reported previously are also presented. An example numerical solution is given for a piston‐driven shock with a thermal precursor.

Transient Heat Transfer in Superfluid Helium — Part II

Abstract: Three classical problems associated with the ordinary diffusion equation concern the temperature in (1) a half-space with clamped heat flux at the free face, (2) a half-space with clamped temperature at the free face, and (3) an infinite medium with a pulsed plane heat source. These problems are also important for the nonlinear diffusion equation based on the Gorter-Mellink relation, which describes heat transport in superfluid helium. A similarity solution to problem (1) , the champed-flux problem, has already been found1 and compared, with goou agreement, with experimental data of van Sciver.2 [A similarity solution is one in which the profiles of temperature rise AT versus distance Z at different times t can be obtained from one another by suitable (different) stretching of the temperature and distance axes.] In this paper, I give similarity solutions in analytic form to problems (2) and (3) , the clamped-temperature and pulsed-source problems.

Effect of Double Dispersion on Mixed Convection Heat and Mass Transfer in Non-Darcy Porous Medium

Abstract: Similarity solution for the problem of hydrodynamic dispersion in mixed convection heat and mass transfer from vertical surface embedded in porous media has been presented. The flow induced by the density variations is comparable with the freestream flow. The heat and mass transfer in the boundary layer region for aiding and opposing buoyancies in both aiding and opposing flows has been analyzed. The structure of the flow, temperature, and concentration fields in the Darcy and non-Darcy porous media are governed by complex interactions among the diffusion rate (Le) and buoyancy ratio (N) in addition to the flow driving parameter (Ra/Pe). The flow, temperature, and concentration fields are analyzed and the variation of heat and mass transfer coefficients with the governing parameters are presented

Evolution of supernovae-driven superbubbles with conduction and cooling

Abstract: We use spherically symmetric hydrodynamic simulations to study the dynamical evolution and internal structure of superbubbles (SBs) driven by clustered supernovae (SNe), focusing on the effects of thermal conduction and cooling in the interface between the hot bubble interior and cooled shell. Our simulations employ an effective diffusivity to account for turbulent mixing from nonlinear instabilities that are not captured in 1D. The conductive heat flux into the shell is balanced by a combination of cooling in the interface and evaporation of shell gas into the bubble interior. This evaporation increases the density, and decreases the temperature, of the SB interior by more than an order of magnitude relative to simulations without conduction. However, most of the energy conducted into the interface is immediately lost to cooling, reducing the evaporative mass flux required to balance conduction. As a result, the evaporation rate is typically a factor of $\sim$3-30 lower than predicted by the classical similarity solution of Weaver et al. (1977), which neglects cooling. Blast waves from the first $\sim$30 SNe remain supersonic in the SB interior because reduced evaporation from the interface lowers the mass they sweep up in the hot interior. Updating the Weaver solution to include cooling, we construct a new analytic model to predict the cooling rate, evaporation rate, and temporal evolution of SBs. The cooling rate, and hence the hot gas mass, momentum, and energy delivered by SBs, is set by the ambient ISM density and the efficiency of nonlinear mixing at the bubble/shell interface.

Surface tension dominated impact

Abstract: We study the impact of a line mass onto a liquid-gas interface. At early times we find a similarity solution for the interfacial deformation and show how the resulting surface tension force slows the fall of the mass. We compute the motion beyond early times using a boundary integral method, and find conditions on the weight and impact speed of the mass that determine whether it sinks or is trapped by the interface. We find that for given impact speed there is a critical weight above which the mass sinks, and we investigate the asymptotic behavior of this critical weight in the limits of small and large impact speeds. Below this critical weight, the mass is trapped by the interface and subsequently floats. We also compare our theoretical results with some simple tabletop experiments. Finally, we discuss the implications of our work for the vertical jumps of water-walking arthropods.