Mixed convection from a straight isothermal tube of elliptic cross-section

The problem of laminar mixed (natural and forced) convective heat transfer from a straight isothermal tube of elliptic cross-section placed in a uniform stream is investigated. The free stream direction is horizontal and normal to the tube axis and the flow field is essentially two-dimensional. The investigation is based on a numerical solution of the conservation equations of mass, momentum, and energy. The resulting velocity and thermal fields both are found to be either steady or quasi-steady depending on vortex shedding. The parameters involved are the Reynolds number, Re, Grashof number, Gr, Prandtl number, Pr, the tube geometry represented by its axis ratio (minor to major), A_r, and its orientation represented by its angle of inclination, λ. The study focuses on the effects of Re, Gr, and λ on the heat transfer process in the Re range from 20 to 500, Gr range from 0 to 1.25 × 10⁶ and for angles of inclination varying from 0° to 180°. The average Nusselt number is found to increase considerably with the increase of the ratio Gr Re². The response of the total rate of heat transfer to changes in the inclination angle is found to depend on the Reynolds number. The results also indicate that the increase of Gr for a given value of Re tends to suppress vortex shedding. The details of the velocity and thermal fields are presented in the form of isotherm and streamline patterns in addition to the surface vorticity and local Nusselt number distributions.