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

### Abstract

The optimal spacing between finned tubes cooled by free convection is studied numerically. A row of isothermal finned 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 tube position is (0.25 ≤ δ ≤ 0.75), and the working fluid is air (Pr =0.71). The results show that the optimal spacing decreases as Rayleigh number increases for all tube positions, and the maximum density of heat transfer increases as the Raleigh number increases for all tube positions and for Ra=105 the highest value of heat transfer density occurs at tube position (δ =0.75) while the lowest value occurs at tube position (δ =0.25). The results also show that the optimal spacing remains constant with change of the tube position at constant Rayleigh number.

**Al-Nahrain Journal for Engineering Sciences**, [S.l.], v. 20, n. 4, p. 815-822, aug. 2017. ISSN 2521-9162. Available at: <https://www.nahje.com/index.php/main/article/view/303>. Date accessed: 19 sep. 2017.