Double Diffusive Convection with LTNE

Abstract

In the standard Bnard problem the instability is driven by a density difference caused by a temperature difference between the upper and lower planes bounding the fluid. If the fluid layer additionally has salt dissolved in it then there are potentially two destabilizing sources for the density difference, the temperature field and the salt field. A similar scenario could be witnessed in isothermal conditions but with two dissolved salts such as sodium and potassium chloride. When there are two effects such as this the phenomenon of convection which arises is called double diffusive convection. For the specific case involving a temperature field and sodium chloride it is frequently referred to as thermohaline convection. There are many recent studies involving three or more fields, such as temperature and two salts, for example, NaCl, KCl. For the three or greater field case we shall refer to this as multi-component convection. The driving force for the interest in double diffusive or multi-component convection is largely physical applications. In this chapter we investigate double diffusive convection in a porous material taking into account local thermal non-equilibrium conditions. We study the stability of this problem in the case of a Darcy porous medium allowing for inertia (acceleration) effects. We also study the analogous problem in a Brinkman theory with inertia. Afterward, rotation is added to double diffusive convection in both Darcy and Brinkman theories and the literature on this is discussed. We also look at the problem of double diffusive convection in a porous material when a chemical reaction is taking place.