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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). [ABSTRACT FROM AUTHOR]

The density of heat transfer rate from a vertical array of flat tubes in cross flow is maximized under fixed pressure drop using constructal design. With the constructal design, the tube arrangement is found such that the heat currents from the tubes to the coolant flow easily. The constraint in the present constructal design is the volume where the tubes are arranged inside it. The two degrees of freedom available inside the volume are the tube‐to‐tube spacing and the length of the flat part of the tubes (tube flatness). The tubes are heated with constant surface temperature. The equations of continuity, momentums, and energy for steady, two‐dimensional, and laminar forced convection are solved by means of a finite‐volume method. The ranges of the present study are Bejan number (dimensionless pressure drop) (103 ≤ Be ≤ 105) and tube flatness (dimensionless length of the tube flat part) (0 ≤ F ≤ 0.8). The coolant used is air with Prandtl number (Pr = 0.72). The results reveal that the maximum heat transfer density decreases when the tube flatness decreases at constant Bejan number. At constant tube flatness, the heat transfer density increases as the dimensionless pressure drop (Bejan number) increases. Also, the optimal tube‐to‐tube spacing is constant, irrespective of the tube flatness at constant Bejan number. [ABSTRACT FROM AUTHOR]

In the present paper, the heat transfer density rate from a multi-scale diamond-shaped pin fins cooled by mixed convection is maximized under fixed pressure drop based on constructal design. Instead of Richardson number, the ratio of Rayleigh number to Bejan number (Ra/Be) arises due to the imposed pressure drop. Two sizes of diamond-shaped pin fins are placed in a fixed volume in vertical cross flow. The smaller fins are placed in the entrance region of the unused fluid between the larger fins with the same leading-edge of the larger fins. All the larger and the smaller fins are kept at constant temperature. The equations of the buoyancy-pressure driven flow are solved by finite volume method (FVM) for steady, two-dimensional, laminar, and incompressible flow. The leading-edge angles of the larger and the smaller fins are varied from (30°) to (60°). Rayleigh number is kept constant at (Ra = 105), the range of Bejan number is (104 ≤ Be ≤ 106), the range of the ratio of Rayleigh number to Bejan number is (0.1 ≤ Ra/Be ≤ 10), and the air is used as a working fluid with (Pr = 0.71). The heat transfer density is maximized twice, the first maximization is done for the larger fins in the absence of the smaller fins, and the second maximization is done with the presence of the smaller fins at constant leading-edge angle of the larger fins (λ = 30°). The optimal spacing between the larger fins is found in the first maximization, and the optimal height of the smaller fins is found in the second maximization. In the first maximization, the design indicated that the optimal spacing between the larger fins is constant for all fin angles (λ) at constant (Ra/Be). And based on this indication, the number of fins installed in fixed area must be reduced as (λ) increases. As well as, the results show that the heat transfer density can be maximized twice for all the studied angles of the smaller fins (30°, 45°, and 60°), and for all ratios (Ra/Be = 0.1, 1, and 10). Also, the highest value of the second maximized heat transfer density is found at the angle of the smaller fins (λ 1 = 30°) for all ratios (Ra/Be). [ABSTRACT FROM AUTHOR]