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A single‐row crossflow heat exchanger with concentric and eccentric circular fins is designed and shown in this paper using a constructal design approach. The transverse fins spacing, the spanwise fins spacing, and the fin‐tube eccentricity are varied inside a fixed volume. In addition to the concentric case (ε = 0), two tube‐fin eccentricities are considered with (ε = ±0.25). The (heat transfer/volume) heat density is to be optimized with respect to the transverse and the spanwise spacing. The height and the width of the heat exchanger occupation space in addition to the fin diameter are fixed as design constraints. The crossflow is motivated by constant pressure drop with two dimensionless pressure drop numbers (Bejan number) (Be = 103 and 105). Both the fins and the tubes are maintained at a constant temperature, and they are cooled by the cross air of ambient temperature. The ratio of the fin to tube diameter is kept at 0.5. Three‐dimensional equations for conservation of mass, conservation of momentum, and conservation of energy are solved using finite volume method for incompressible and steady flows. The heat density for concentric fins (ε = 0) and eccentric fins (ε = ±0.25) is maximized two times, one with respect to transverse spacing, and the other with respect to spanwise spacing at Bejan numbers (Be = 103 and 105). The highest double‐maximized heat density is attained at the fin eccentricity (ε = 0.25). The increase in the double maximized heat density when the fin eccentricity (ε = 0.25) is 7.65% for Be = 103, and it is 12% for Be = 105. [ABSTRACT FROM AUTHOR]

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]

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]

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 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]