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Local Rayleigh and Nusselt Numbers for Cartesian convection with temperature‐dependent viscosity
Author(s) -
Honda S.
Publication year - 1996
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/96gl02259
Subject(s) - nusselt number , thermodynamics , viscosity , rayleigh number , boundary layer , film temperature , natural convection , convection , mechanics , materials science , physics , reynolds number , turbulence
We present a local treatment of the heat transport efficiency of the base‐heated cartesian convection with a temperature‐dependent viscosity, which allows us to give a clearer interpretation of Nusselt ( Nu )‐Rayleigh ( Ra ) numbers relation. The “local” Nusselt ( Nu l ) and Rayleigh ( Ra l ) numbers are defined by the local values at each boundary layer except the length scale which is the total depth. We find that Nu l ‐ Ra l relation obtained for the convection with constant viscosity and free surfaces is nearly coincident with that of the bottom boundary layer. For top boundary layer, we can treat it as a constant viscosity convection with rigid surface for large enough viscosity contrast. This interpretation can be made by choosing an appropriate temperature drop and viscosity for the definitions of Nu l and Ra l .