4 - Onset of rayleigh-Bénard convection in porous bodies

Abstract

The onset of the Rayleigh–Benard convection in finite porous bodies is investigated theoretically in this chapter. The phenomenon of buoyancy-induced instability is called the Rayleigh–Benard convection. The Rayleigh–Benard instability appears in its simplest version when the flow takes place in a porous medium. The chapter presents a wider class of Rayleigh–Benard problems for finite porous bodies in 3D. In general, the eigenvalue problems for such finite bodies are considerably more complicated than for the traditional case of an unlimited horizontal layer. The linear stability problem is formulated in 3D. The temperature distribution along the boundaries is prescribed as a linearly decreasing function of height and this makes the basic state motionless with uniform conduction transport of heat upwards. The thermal condition along the body contour is chosen either as zero perturbation temperature (conducting boundaries) or zero normal derivative of the perturbation temperature (insulating boundaries). The kinematic condition along the body contour is chosen either as zero normal velocity (impermeable or closed boundaries) or zero tangential velocity (open boundaries). Reference is given to existing solutions for porous cylinders and rectangular boxes. Some simplified results are found for thin porous shells.