HEAT TRANSPORT BY TURBULENT CONVECTION,
Abstract
Upper bounds for the heat flux through a horizontally infinite layer of fluid heated from below are obtained by maximizing the heat flux subject to (a) two integral constraints, the 'power integrals', derived from the equations of motion, and (b) the continuity equation. This variational problem is solved completely, for all values of the Rayleigh number R, when only the constraints (a) are imposed, and it is thus shown that the Nusselt number N for any statistically steady convective motion cannot exceed a certain value N1(R), which for large R is approximately the square root of (3R/64). When (b) is included as a constraint, the variational problem is solved for large R, under the additional hypothesis that the solution has a single horizontal wave number; the associated upper bound on the Nusselt number is (R/248) to the 3/8 power. The mean properties of this maximizing 'flow', in particular the mean temperature and mean square temperature deviation fields, are found to resemble the mean properties of the real flow observed by Townsend; the results thus tend to support Malkus's hypothesis that turbulent convection maximizes heat flux. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 05, 1963
- Accession Number
- AD0617805
Entities
People
- Louis N. Howard
Organizations
- Massachusetts Institute of Technology