Penetrative convection in slender containers

Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

“…Our main concern here is to investigate the effect of anisotropy via K ij , the changes due to the Brinkman term with coefficient μ , and the effect of the boundary conditions ( 6) or (7), upon the critical parameters of penetrative convection. Anisotropic effects upon thermal convection in saturated porous media have been the subject of many recent investigations, see e.g.…”

“…The fact that penetrative convection is of such interest is primarily due to the realization that it is an area with a multitude of real physical applications. As pointed out in Straughan [1], there are applications in planetary physics, DietrichWicht [3], van den berg et al [4], in internally cooled convection,Berlengiero et al [5], in environmental fluid mechanics, Fernando [6],Pol and Fernando [7], in the cloud cover of Venus, Imamura et al [8], in aiding the rise of volcanic plumes in the Earth's atmosphere, Kaminski et al [9], in mixing in the Laptev Sea, Kirillov et al [10], in cloud to ground discharges,Machado et al [11], Mharzi et al [12], in biochemical decay,Prudhomme and Jasmin [13], in flow in the Sun, Tikhomolov [14], and in particular in penetrative convection in a porous medium where application is to formation of stones into regular patterns, George et al [15], and in building insulation, Straughan and Walker [16]. Theoretical analyses of penetrative convection have ensued such as Veronis [2], Musman [17], Carr [18,19], Carr and Putter [20], Carr and Straughan [21], Harfash [22,23], Krishnamurti [24], Larson [25], Straughan [26][27][28].…”