Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

Gur Mittelman, Aiman Alshare, Jane H. Davidson

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5 Scopus citations


A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is over(Nu, -) = fenced(frac(6.25 (1 + r), Ra sin φ{symbol}) + frac(1.64, (Ra sin φ{symbol})2 / 5))- 1 / 2, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of 30 ° ≤ φ{symbol} ≤ 90 °, this correlation predicts the available data base for 10 ≤ Ra ≤ 105 and agrees with the analytical solution for 1 ≤ Ra ≤ 102.

Original languageEnglish (US)
Pages (from-to)4689-4694
Number of pages6
JournalInternational Journal of Heat and Mass Transfer
Issue number21-22
StatePublished - Oct 2009

Bibliographical note

Funding Information:
The authors gratefully acknowledge the financial support of the National Renewable Energy Laboratory, the US Department of Energy, and the University of Minnesota through the Initiative for Renewable Energy and the Environment.


  • Free convection
  • Inclined channels
  • Uniform heat flux


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