Maximization of heat transfer density from radially finned tubes in cross-flow using the constructal design method

The maximization of volumetric heat transfer density from radially finned tubes in cross-flow is investigated in this study based on the constructal design method. A row of radially finned tubes is placed in cross-air flow. The tubes and the radial fins are heated at uniform temperatures and cooled by the air cross-flow. The cross-air flow is generated by a finite pressure difference. Two dimensionless pressure differences (Bejan number) are considered (Be = 10³ and Be = 10⁵). The objective function, the degrees of freedom, and the constraints in the constructal design method should be identified. The objective function is the maximization of the heat transfer density from the finned tubes. The degrees of freedom are; the fin tip-to-fin tip spacing, the number of fins, the tube diameter, the fin thickness, and the angle between the fins. The constraints are the length and height of the space occupied by the finned tubes. The pressure-driven flow and energy equations (steady, two-dimensional, and incompressible) are solved by means of the finite volume method. The ranges of the dimensionless fin tip-to-fin tip spacing are (0.2 ≤ S ≤ 1 for Be = 10³ and 0.05≤ S ≤ 0.3 for Be = 10⁵). The number of fins is changed as (N = 2, 4, 6, 8, 10, and 12). The dimensionless tube diameter is changed as (D = 0.25, 0.5, and 0.75). The dimensionless fin thickness is changed as (T = 0.001, 0.01, and 0.05). The results showed that for both (Be = 10³) and (Be = 10⁵), the highest value of the maximum volumetric heat transfer density is for (N = 2) and decreases as the number of fins increases. In addition, the minimum values of the maximum volumetric heat transfer density occur when the vertical fins exist at (N = 4, 8, and 12).