The Optimal Spacing between Elliptic Tubes Cooled by Free Convection Using Constructal Theory

Abstract

The optimal spacing between elliptic tubes cooled by free convection is studied numerically. A row of isothermal elliptic tubes are installed in a fixed volume and the spacing between them is selected according to the constructal theory (Bejan's theory). In this theory the spacing between the tubes is chosen such that the heat transfer density is maximized. A finite volume method is employed to solve the governing equations; SIMPLE algorithm with collocated grid is utilized for coupling between velocity and pressure. The range of Rayleigh number is (103 ? Ra ? 105), the range of the axis ratio of the tubes is (0 ? ? ? 0.5), and the working fluid is air (Pr =0.71). The results show that the optimal spacing decreases as Rayleigh number increases for all axis ratios, and the maximum density of heat transfer increases as the Raleigh number increases for all axis ratios and the highest value occurs at axis ratio (? =0) (flat plate) while the lowest value occurs at (? =0.5) (circular tube). The results also show that the optimal spacing is unchanged with the axis ratio at constant Rayleigh number.