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In this paper, we performed a numerical simulation of natural convection of  Newtonian fluids between two cylinders of different cross-sectional form.  The inner cylinder is supposed to be hot and the outer cylinder is assumed  to be cold. The diameter of inner cylinder to the diameter of outer cylinder  defines the radii ratio (RR= 2.5). The governing equations describing the  physical behavior of fluid flow and heat transfer are solved using finite  volume method. The effects of Prandtl number (Pr = 0.71 to 100), Rayleigh  number (Ra = 103 to 105) and inclination angle of inner cylinder (ω = 0° to  80°) on streamlines, isotherms and dimensionless velocity are presented and  discussed. Also, the mean average Nusselt number of inner cylinder is  plotted versus the governing parameters. All present simulations are  considered in two-dimensions for steady laminar flow regime. The obtained  results showed that the flow between cylinders is more stable for the  inclination angle ω = 0°. Increase in Rayleigh number increases the heat  transfer rate for all values of inclination angle. Furthermore, the effect  of Prandtl number on the mean average Nusselt number becomes negligible when  Pr is over the value 7.01. For example at Pr = 0.71 and Ra =105, increase in  inclination from 0° to 40°decreases the average Nusselt number by 5.4%. A  new correlation is also provided to describe the average Nusselt number as  function of Pr and Ra at ω = 0°.

Natural-convection of Newtonian fluids between two concentric cylinders of a special cross-sectional form