Turbulent natural convection heat transfer from a vertical hollow cylinder suspended in air: A numerical approach

Abstract

Numerical simulations have been conducted to predict turbulent natural convection flow field and temperature distribution around an isothermal vertical solid or hollow cylinder. Continuity, momentum and energy equations have been solved along with kinetic energy and specific dissipation rate equations in the turbulent range of Rayleigh number (Ra) spanning from 1010 to 1012 and length to diameter ratio of the cylinder (L/D) from 0.125 to 20. Average surface Nusselt number and non-dimensional mass flow rate of air through the hollow cylinder have been calculated and plotted with respect to the non-dimensional input parameters such as Ra and L/D. Nu for the inner surface of the hollow cylinder is marginally lesser than that of the outer surface of the hollow cylinder for all L/D and Ra. Nu for the outer surface increases monotonically with respect to L/D however, for the inner surface, it decreases up to L/D of 10 and beyond that, it starts rising. The temperature contours and velocity vector plots have been sketched to understand the heat transfer phenomenon in a better way. Correlations for Nu and mass flow rate for hollow cylinder have been proposed in the turbulent range which could be referred in steel industries, electronics industries and academic practices. Exploiting the developed correlation, the cooling curve (temp vs time) of a hollow cylinder at various Ra and L/D has been drawn which shows a cylinder with a higher Ra with high L/D requires more time to cool down than that of a lower Ra with low L/D. The cooling curve is very much helpful in reducing the idle time in loading and unloading operations of the hot products in steel industries.