Laminar Natural Convection From an Elliptic Tube With Different Orientations

Abstract

The problem of two-dimensional natural convection heat transfer from a straight tube of elliptic cross section is investigated. The tube, which has an isothermal surface, is placed with its axis horizontal in an initially quiescent fluid of infinite extent. The velocity and thermal fields are obtained by studying the time development of these fields following a sudden increase of the tube surface temperature until reaching steady state. The study is based on the solution of the full conservation equations of mass, momentum, and energy with no boundary layer simplifications. The paper focuses on the effects of the tube orientation, axis ratio, and Rayleigh number while keeping the Prandtl number unchanged (Pr = 0.7). The study revealed that the maximum average Nusselt number is obtained when the tube major axis is vertical. Within the range of axis ratios considered (Ar = 0.4 to 0.98), smaller Ar resulted in higher heat transfer rate in most cases. Higher Rayleigh number leads to higher velocities and also higher local and average Nusselt numbers in all cases considered. The details of the steady flow and thermal fields are presented in the form of local Nusselt number and surface vorticity distributions as well as streamline and isotherm patterns for some selected cases.