doiSerbia

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

Laidoudi Houssem (Laboratoire des Sciences et Ingénierie Maritime (LSIM), Faculty of Mechanical engineering, USTO-MB, El-Menaouer, Oran, Algeria), houssem.laidoudi@univ-usto.dz
Helmaoui Mustapha (Laboratoire des Sciences et Ingénierie Maritime (LSIM), Faculty of Mechanical engineering, USTO-MB, El-Menaouer, Oran, Algeria)
Bouzit Mohamed (Laboratoire des Sciences et Ingénierie Maritime (LSIM), Faculty of Mechanical engineering, USTO-MB, El-Menaouer, Oran, Algeria)
Ghenaim Abdellah (Laboratoire de Mécanique et Environnement ICUBE/INSA, Institut National des Sciences Appliquées, Strasbourg, France)

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 = 0.71-100), Rayleigh number (Ra = 103-105), and inclination angle of inner cylinder (ω = 0-80°) on streamlines, isotherms, and dimensionless velocity are presented and discussed. Also, the mean average Nusselt number of inner cylinder is plotted vs. the governing parameters. All present simulations are considered in 2-D 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 Prandtl number 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 Prandtl number and Rayleigh number at ω = 0°.

Keywords: natural convection, annulus, heat transfer, Nusselt number, inclination angle, steady-state, Rayleigh number