Energy stability bounds on convective heat transport: Numerical study

Journal Article · Sun Jun 01 04:00:00 EDT 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.55.7775· OSTI ID:530160

Doering, C R ^[1]; Hyman, J M ^[2]

---

1. Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109 (United States)
2. Theoretical Division and Center for Nonlinear Studies, MS-B284, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

The concept of nonlinear energy stability has recently been extended to deduce bounds on energy dissipation and transport in incompressible flows, even for turbulent flows. In this approach an effective stability condition on {open_quotes}background{close_quotes} flow or temperature profiles is derived, which when satisfied ensures that the profile produces a rigorous upper estimate to the bulk dissipation. Optimization of the test background profiles in search of the lowest upper bounds leads to nonlinear Euler-Lagrange equations for the extremal profile. In this paper, in the context of convective heat transport in the Boussinesq equations, we describe numerical solutions of the Euler-Lagrange equations for the optimal background temperature and present the numerical computation of the implied bounds. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 530160
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 6 Vol. 55; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONVECTION
HEAT TRANSFER
NUSSELT NUMBER
STABILITY
TEMPERATURE DISTRIBUTION
TRANSITION FLOW
TURBULENT FLOW
VARIATIONAL METHODS