Penetrative Convection with LTNE

Abstract

AbstractIn many natural phenomena the process of thermal convection involves a penetrative motion into a stably stratified fluid. Examples of penetrative convection are to be found in several areas of geo- and astrophysical fluid dynamics. For example, the Earth’s atmosphere is bounded below by the ground or ocean; this bounding surface is heated by solar radiation, and the air close to the surface then becomes warmer than the upper air, and so a gravitationally unstable system results. When convection occurs, the warm air rises and penetrates into regions that are stably stratified. Penetrative convection is important in solar pond design, in atmospheric physics, in building design, in convective motion in the Sun, in assisting the rise of volcanic plumes into the Earth’s atmosphere, in the Laptev Sea coastal pycnocline layer, in the deep mantle of exosolar planets, in clouds surrounding Venus, and in connection with cloud to ground electrical discharges. In addition, internal heat source penetrative convection is important when the heat source occurs in a porous biological material due to organic decay involving microbial activity. In this chapter we present a model for penetrative convection in a local thermal non-equilibrium Darcy porous medium when the penetration effect is due to the density in the buoyancy force being a quadratic function of the fluid temperature. We also describe work in local thermal non-equilibrium convection in a Darcy porous medium which has employed a uniform heat source in the energy balance equations. A model for penetrative convection in a local thermal non-equilibrium scenario in a Darcy porous medium where the penetration effect is due to internal heat sinks is also presented.KeywordsRayleigh NumberBuoyancy ForceThermal ConvectionInternal Heat SourceSolar PondThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.