Laminar mixed convection in vertical elliptic ducts

Abstract

A control volume based numerical solution is described for the fully developed mixed convection in vertical ducts of elliptic cross-section. The duct wall is supplied with a uniform axial heat rate while the thickness and thermal conductivity of the duct wall are such that the wall temperature is circumferentially uniform. Results for velocity and temperature distributions, friction factor, Nusselt number and critical Rayleigh number are presented for a wide range of duct aspect ratios and Rayleigh numbers. It is found that during mixed convection, fluid with a higher axial velocity exists around the foci of the elliptical cross-section, leading to substantial heat transfer enhancement in this region of the duct. The ratio of friction factor during mixed convection to that during forced convection is low in elliptical ducts compared to that in a circular duct. Also, the ratio of Nusselt number to friction factor is higher for elliptic ducts compared to that for a circular duct, irrespective of the value of the Rayleigh number. The critical Rayleigh number, at which flow reversal is initiated in the core region, is higher for elliptic ducts compared to that for a circular duct.