Development of wall and free plumes above a heated vertical plate

E. M. Sparrow, S. V. Patankar, R. M. Abdel-Wahed

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Abstract

An analysis has been made to determine the successive stages of development as the natural convection boundary layer on a steadily heated vertical plate evolves into a plume. Both the wall plume and the free plume are investigated. The wall plume develops along an adiabatic wall which is the vertical extension of the heated plate. The free plume is created as the boundary layer streams away from the upper edge of the plate. Since the plate is heated on only one of its faces, the free plume is initially unsymmetric. The development of these plumes does not admit similarity-type boundary layer solutions, and numerical techniques were, therefore, employed, with results being obtained for Prandtl numbers of 0.7, 2, 5, and 10. It was found that at sufficient downstream distances both plumes attain their respective fully developed behaviors (i.e., similar profiles at successive streamwise stations). For the wall plume, the development for all Prandtl numbers is completed at a position that is about five plate lengths above the leading edge of the heated plate. The development length for the free plume for Pr = 0.7 is about the same as that for the wall plume, but about 30 plate lengths are required for the development of the free plume when Pr = 10. The fully developed free plume is symmetric.

Original languageEnglish (US)
Pages (from-to)184-190
Number of pages7
JournalJournal of Heat Transfer
Volume100
Issue number2
DOIs
StatePublished - May 1978

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    Sparrow, E. M., Patankar, S. V., & Abdel-Wahed, R. M. (1978). Development of wall and free plumes above a heated vertical plate. Journal of Heat Transfer, 100(2), 184-190. https://doi.org/10.1115/1.3450779