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Constructal design of vertical multiscale triangular fins in natural convection is investigated in this paper. The design consists of two parts. The first part is for single‐scale triangular fins. The objective in the first design is to reach to the highest heat transfer density from the fins for three fin angles (15°, 30°, and 45°). The single‐scale fins are placed in a horizontal array and considered as isothermal fins. The degrees of freedom are the fin angle, and the fin‐to‐fin spacing. The constraint is the fin height. The second part is for multiscale fins where small fins are placed between the large fins which are optimized in the first part. In the second part, the angles of the large and small scales fins are kept constant at (15°). The optimal fin‐to‐fin spacing which is obtained in the first part is considered a constraint in the second part. The Rayleigh numbers in this design are (Ra = 103, 104, and 105). The two‐dimensional mass, momentum, and energy equations for natural convection are solved with the finite volume method. The results show that there is a benefit of placing the small‐scale fins where the percentage increase in the heat transfer density is (10.22%) at (Ra = 103), and (50.6%) at (Ra = 105) due to existence of the small fins between the large fins. [ABSTRACT FROM AUTHOR]

A set of vertical flat tubes cooled by natural convection and placed in a finite size space is designed based on the constructal law. The constraint in this design is the size of the space where the tubes are placed. The freedom inside the space is the distance between the tubes. When the constructal law is applied, the optimal distance between the tubes is determined. Rayleigh numbers are taken as (Ra = 10³, 104, and 105 ). The dimensionless tube diameter (tube diameter/tube height) is changed from (D* = 0.2) to (D* = 1) (circular tube). All the tubes are heated to the same wall temperature. The air used to cool the tubes has a Prandtl number (Pr = 0.72). The equations of conservation of mass, momentum, and energy for steady, two‐dimensional, and incompressible flow are solved by the finite volume method. The result showed that the best or optimal distance at a given Rayleigh number remains constant for all tube diameters. The result also showed that the number of the small diameter tubes must be more than the number of the large‐diameter tubes for the same Rayleigh number and the same size of the space to make the heat flow from the tubes to the coolant easier. [ABSTRACT FROM AUTHOR]

The optimal spacing between elliptic tubes cooled by free convection is studied experimentally and 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. For the numerical study, the range of Rayleigh number is (103 ≤ Ra ≤ 105), the range of the axis ratio of the tubes is (0 ≤ ϵ ≤ 0.5), and the working fluid is air (Pr =0.71). Eexperimental study is also carried out in order to demonstrate the existence of the optimal spacing. The experimental Rayleigh number is (3.5x104 ) and the axis ratio of the elliptic tube is .The numerical 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 (ϵ =0) (flat plate) while the lowest value occurs at (ϵ =0.5) (circular tube). The results also show that the optimal spacing is unchanged with the axis ratio at constant Rayleigh number. The agreement between the experimental and numerical heat transfer density is qualitative. [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]