Numerical Study on Flow and Thermal Fields of Mixed Convection in a Concentric Inclined Annulus

Laminar upward mixed convection in an inclined concentric straight annulus is studied numerically in this paper. The governing equations including for continuity, the three-dimensional Navier-Stokes, and the energy equations in cylindrical coordinates, are solved by means of a second-order finite-difference method based on the projection algorithm. To discretize conveniently, the governing equations in the annulus domain are obtained in cylindrical coordinates, using a uniform staggered grid. The Boussinesq approximation is employed to implement the natural convection term in the equations of motion. Developing hydrodynamic and thermal conditions are considered to survey the effect of different parameters such as the radius ratio, inclination, and Reynolds and Richardson numbers on flow field and thermal characteristics, while the outer wall is insulated and the inner one is at constant heat flux. It has been found that the heat transfer coefficient decreases as the inclination angle increases from the horizontal position. Also, a numerical relation is developed to predict the Nusselt number value, which is validated in the studied ranges.