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# Accession Number:

## AD0617805

# Title:

## HEAT TRANSPORT BY TURBULENT CONVECTION,

# Descriptive Note:

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE DEPT OF MATHEMATICS

# Report Date:

## 1963-04-05

# Pagination or Media Count:

##
28.0

# 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 N1R, which for large R is approximately the square root of 3R64. 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 R248 to the 38 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 Malkuss hypothesis that turbulent convection maximizes heat flux. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#