Natural convection from narrow horizontal plates at moderate Rayleigh numbers
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Date
2003
Authors
Martorell, Ingrid
Herrero, Joan
Grau, Francesc X.
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Abstract
The present work deals with the natural convection flow and heat transfer from a horizontal plate cooled from
above.Experiments are carried out for rectangular plates having aspect ratios between / ¼ 0:036 and 0.43 and Rayleigh
numbers in the range 2906Raw 63:3 105.These values of Raw and / have been selected below those commonly
considered in previous research in view of a future application to the design of printed circuit boards.The plates are
made of two different metals, copper and steel.The choice of a metal is relevant to the present problem because the
plates are heated by means of an electric current.Important variations of the surface temperature are observed along
the transverse direction for the steel plates.The surface of the copper plates is almost isothermal because of the high
thermal conductivity of the metal.
Calculations for a semi-infinite plate are carried out to predict the transverse profiles of the surface temperature and
heat flux and to visualize the structure of the flow.Three-dimensional calculations are also used at a qualitative level to
observe the changes in the flow structure due to the finite length of the plate.Present results are compared with both
previous experimental work and analyses that are based on boundary layer theory.It is shown that analyses for an
infinite boundary layer are not completely applicable to the present problem because of its different physics.The most
relevant feature of the natural convection flow, which is not predicted by boundary layer analyses, is a thermal plume
rising near the center of the plate.
Present heat transfer results differ from previous experimental work because of the lower Rayleigh numbers and
aspect ratios investigated here.The Nusselt number is found to depend on Ran
w, with the exponent n ¼ 0:17 being lower
than most of the values reported in the literature.This comparatively low value is related to the transverse conduction
of heat through the air, which becomes increasingly significant as Raw approaches zero.It is shown that such a low-Raw
effect can be accounted for in a physically consistent manner by adding a constant term to the heat transfer correlation.
On the other hand, it is found that the Nusselt number does not significantly depend on the aspect ratio in the range of
/ investigated contrary to what has been previously reported for wider plates.
Citation
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International Journal of Heat and Mass Transfer, 2003, vol. 46, p. 2389-2409