Abstract
Holographic interferometry has been used to measure the temperature profiles around horizontal circular cylinders immersed in a number of fluids. Air, water, silicone oils and aqueous solutions of hydroxyethyl-cellulose were studied, giving a Prandtl number range of 0.87 to 4540. The Rayleigh numbers varied from 102 to 104, whereas the Grashof number range was from 10−2 to 104. A similarity solution for the temperature and velocity distribution for high Rayleigh numbers is developed and shown to be identical to that found for high Grashof numbers. All the data are in agreement with the theory. An expression for the average Nusselt number as a function of the Rayleigh and Prandtl numbers is found from the theory.This expression is of the same form as those developed empirically and is in good agreement with numerical results. The theory indicates that the dependence of the Nusselt number on the Prandtl number decreases with increasing Prandtl number and disappears at high values. The Nusselt numbers predicted by theory and those measured experimentally appear to diverge as the Rayleigh number increases.
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