caa a22 4500 463163540 CHVBK 20180406164755.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11242-006-9000-8 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9000-8 Govender Saneshan School of Mechanical Engineering, University of Kwa-Zulu Natal, 4041, Durban, South Africa aut An analogy between a gravity modulated porous layer heated from below and the inverted pendulum with an oscillating pivot point [Elektronische Daten] [Saneshan Govender] The governing equations for the inverted pendulum is developed and shown to be analogous to the gravity modulated porous layer heated from below. In particular the temperature in a gravity modulated porous layer heated from below (R>0-unstable) is likened to the motion of an inverted pendulum (unstable). As gravity modulation stabilizes convection, Transport Porous Med. 57 (2004), 113, it is found that oscillating the pivot point of an unstable, inverted pendulum stabilizes the motion. Springer Science+Business Media B.V., 2006 Gravity modulation nationallicence Porous media nationallicence Free convection nationallicence Inverted pendulum nationallicence Latin Symbols nationallicence a : Constant in Mathieu equation nationallicence c : Damping constant for pendulum nationallicence L : Length of pendulum nationallicence g * : gravitational acceleration nationallicence m : Mass of pendulum nationallicence q : Constant in Mathieu equation nationallicence R : porous media gravitational Rayleigh number, equals, β*ΔT Cg* k c* H * / v * λ* nationallicence s : convection wave number nationallicence s x : x-component of wave number nationallicence s y : y-component of wave number nationallicence x : horizontal length coordinate nationallicence y : horizontal width coordinate nationallicence z : vertical coordinate nationallicence Greek Symbols nationallicence α : a parameter related to the wave number, equals s 2 / π2 nationallicence δ : κ FrΩ2 nationallicence γ : Va / π 2 nationallicence η : $$-{\tilde{R}}_{o} ( \alpha +1- \gamma)^{2} \left/ (4 \gamma (\alpha +1)\right. $$ nationallicence φ : Angular displacement of pendulum nationallicence σ : Mathieu exponent nationallicence ω * : vibration frequency nationallicence Ω : scaled vibration frequency, equals, $$\omega _{\ast} H_{\ast} ^{2} \left/ \lambda _{\ast}\right. $$ nationallicence Ω n : Undamped natural frequency of pendulum nationallicence ξ : scaled exponent, equals $$\sigma \left/ \sqrt{-a}\right.$$ nationallicence ξ 0 : Damping ratio for pendulum nationallicence Subscripts nationallicence o : related to unmodulated quantities nationallicence Over nationallicence ~ = : scaled quantities nationallicence Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 323-328 0169-3913 67:2<323 2007 67 11242 https://doi.org/10.1007/s11242-006-9000-8 text/html Onlinezugriff via DOI 1 brief-communication jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9000-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Govender Saneshan School of Mechanical Engineering, University of Kwa-Zulu Natal, 4041, Durban, South Africa aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 323-328 0169-3913 67:2<323 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer