Generalization of heat-transfer results for turbulent free convection adjacent to horizontal surfaces

R. F. Bergholz, M. M. Chen, Fan-bill B. Cheung

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The common character of upward heat transfer in bottom-heated and internally heated fluid layers is demonstrated. This is accomplished by comparing their heat-transfer characteristics on the basis of a modified Nusselt number, defined in terms of an implicit length scale, in contrast to the conventional Nusselt number which contains the total layer depth. The implicit length scale is derived from dimensional considerations and depends only upon parameters relevant to the thermal boundary layer adjacent to the solid surface. The modified Nusselt number was found to have an extremely weak dependence upon the Rayleigh number, the variation being only two-fold over a 107-fold variation of Rayleigh number. More importantly, the heat transfer data for bottom-heated layers (i.e. Rayleigh-Bénard convection) were shown to be almost identical to those for internally heated layers. These results suggest that factors outside of the boundary layer, such as the method of heating, have little influence upon the heat-transfer coefficients of the two systems. The relationship between the implicit boundary-layer length scale used herein and the critical boundary-layer thickness used in the boundary-layer instability models of Howard and others is discussed. Least square correlation of the combined data for both bottom and internal heating is also presented.

Original languageEnglish (US)
Pages (from-to)763-769
Number of pages7
JournalInternational Journal of Heat and Mass Transfer
Volume22
Issue number5
DOIs
StatePublished - Jan 1 1979

Fingerprint

Natural convection
free convection
Boundary layers
Nusselt number
heat transfer
Heat transfer
boundary layers
Rayleigh number
thermal boundary layer
boundary layer thickness
heating
Heating
heat transfer coefficients
solid surfaces
convection
Heat transfer coefficients
fluids
Fluids

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

Cite this

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title = "Generalization of heat-transfer results for turbulent free convection adjacent to horizontal surfaces",
abstract = "The common character of upward heat transfer in bottom-heated and internally heated fluid layers is demonstrated. This is accomplished by comparing their heat-transfer characteristics on the basis of a modified Nusselt number, defined in terms of an implicit length scale, in contrast to the conventional Nusselt number which contains the total layer depth. The implicit length scale is derived from dimensional considerations and depends only upon parameters relevant to the thermal boundary layer adjacent to the solid surface. The modified Nusselt number was found to have an extremely weak dependence upon the Rayleigh number, the variation being only two-fold over a 107-fold variation of Rayleigh number. More importantly, the heat transfer data for bottom-heated layers (i.e. Rayleigh-B{\'e}nard convection) were shown to be almost identical to those for internally heated layers. These results suggest that factors outside of the boundary layer, such as the method of heating, have little influence upon the heat-transfer coefficients of the two systems. The relationship between the implicit boundary-layer length scale used herein and the critical boundary-layer thickness used in the boundary-layer instability models of Howard and others is discussed. Least square correlation of the combined data for both bottom and internal heating is also presented.",
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Generalization of heat-transfer results for turbulent free convection adjacent to horizontal surfaces. / Bergholz, R. F.; Chen, M. M.; Cheung, Fan-bill B.

In: International Journal of Heat and Mass Transfer, Vol. 22, No. 5, 01.01.1979, p. 763-769.

Research output: Contribution to journalArticle

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N2 - The common character of upward heat transfer in bottom-heated and internally heated fluid layers is demonstrated. This is accomplished by comparing their heat-transfer characteristics on the basis of a modified Nusselt number, defined in terms of an implicit length scale, in contrast to the conventional Nusselt number which contains the total layer depth. The implicit length scale is derived from dimensional considerations and depends only upon parameters relevant to the thermal boundary layer adjacent to the solid surface. The modified Nusselt number was found to have an extremely weak dependence upon the Rayleigh number, the variation being only two-fold over a 107-fold variation of Rayleigh number. More importantly, the heat transfer data for bottom-heated layers (i.e. Rayleigh-Bénard convection) were shown to be almost identical to those for internally heated layers. These results suggest that factors outside of the boundary layer, such as the method of heating, have little influence upon the heat-transfer coefficients of the two systems. The relationship between the implicit boundary-layer length scale used herein and the critical boundary-layer thickness used in the boundary-layer instability models of Howard and others is discussed. Least square correlation of the combined data for both bottom and internal heating is also presented.

AB - The common character of upward heat transfer in bottom-heated and internally heated fluid layers is demonstrated. This is accomplished by comparing their heat-transfer characteristics on the basis of a modified Nusselt number, defined in terms of an implicit length scale, in contrast to the conventional Nusselt number which contains the total layer depth. The implicit length scale is derived from dimensional considerations and depends only upon parameters relevant to the thermal boundary layer adjacent to the solid surface. The modified Nusselt number was found to have an extremely weak dependence upon the Rayleigh number, the variation being only two-fold over a 107-fold variation of Rayleigh number. More importantly, the heat transfer data for bottom-heated layers (i.e. Rayleigh-Bénard convection) were shown to be almost identical to those for internally heated layers. These results suggest that factors outside of the boundary layer, such as the method of heating, have little influence upon the heat-transfer coefficients of the two systems. The relationship between the implicit boundary-layer length scale used herein and the critical boundary-layer thickness used in the boundary-layer instability models of Howard and others is discussed. Least square correlation of the combined data for both bottom and internal heating is also presented.

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