𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Nonlinear stability of the Bingham Rayleigh–Bénard Poiseuille flow

✍ Scribed by Christel Métivier; Ian A. Frigaard; Chérif Nouar

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
218 KB
Volume
158
Category
Article
ISSN
0377-0257

No coin nor oath required. For personal study only.

✦ Synopsis

A nonlinear stability analysis of the Rayleigh-Bénard Poiseuille flow is performed for a yield stress fluid. Because the topology of the yielded and unyielded regions in the perturbed flow is unknown, the energy method is used, combined with classical functional analytical inequalities. We determine the boundary of a region in the (Re, Ra)-plane where the perturbation energy decreases monotonically with time. For increasing values of Reynolds numbers, we show that the energy bound for Ra varies like (1 -(Re)/(Re EN )), where Re EN is the energy stability limit of isothermal Poiseuille flow. It is also shown that Re EN ∼ 120 √ B when B → ∞.

📜 SIMILAR VOLUMES

Parallel finite element solution of thre
Parallel finite element solution of three-dimensional Rayleigh–Bénard–Marangoni flows
✍ G.F. Carey; R. Mclay; G. Bicken; B. Barth; S. Swift; A. Ardelea 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 896 KB

A domain decomposition strategy and a parallel gradient-type iterative solution scheme have been developed and implemented for the computation of complex three-dimensional viscous flow problems involving heat transfer and surface tension effects. Special attention has been paid to the kernels for th

Effect of time-periodic vertical oscilla
Effect of time-periodic vertical oscillations of the Rayleigh–Bénard system on nonlinear convection in viscoelastic liquids
✍ P.G. Siddheshwar; G.N. Sekhar; G. Jayalatha 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 337 KB

A study of heat transport in Rayleigh-Bénard convection in viscoelastic liquids with/without gravity modulation is made using a most minimal representation of Fourier series and a representation with higher modes. The Oldroyd-B constitutive relation is considered. The resulting non-autonomous Lorenz