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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]

The heat transfer density rate from a row of rhombic tubes cooled by forced convection is maximized based on constructal design. A row of parallel rhombic tubes are placed in a fixed volume, the horizontal axis of the tubes is kept constant while the vertical axis of the tubes and the spacing between the tubes are changed to facilitate the heat flow from the tubes to the coolant. The tubes are kept at constant temperature and the incoming free‐stream flow is induced by constant pressure drop. For steady, two‐dimensional, incompressible, and laminar forced convection, the governing equations are solved numerically by finite volume method with SIMPLE algorithm. The dimensionless pressure drop (Bejan number, Be) ranging from 10 3 to 10 5, the range of the vertical axis of the tube is 0.2 ≤ B ≤ 2, and the working fluid is air (Pr = 0.71). The results show that the optimal spacing decreases and the maximum heat transfer density increases as the Bejan number increases for all vertical axes of the tube. Bejan number and the bluntness of the tube have a significant effect of the flow structure (separation and vortex formation) around the tubes at the optimal spacings. [ABSTRACT FROM AUTHOR]

Abstract: The numerical investigation of the natural convection in concave and convex parabolic enclosures with a nanofluid consisting of water and copper nanoparticles is carried out by using the finite volume method. The upper and lower walls of the enclosures are adiabatic while the sidewalls are isothermal at a cold temperature. An internal heat source of constant length (ε = 0.2) and negligible thickness is placed at various vertical positions along the center of the enclosure. It was found that the increase in the location of the heat source leads to a drop in the water and nanofluid flow circulation in both types of enclosures. For both considered Cases I and II, the average Nusselt number increases when the Rayleigh number and solid volume fraction increase. Moreover, it was concluded that Case I with δ = 0.8 is the optimum case for heat transfer enhancement for Ra = 103 and Ra = 104. Case II with δ = 0.5 is optimum for Ra = 105. Both cases are satisfied when the nanofluid is used with ϕ = 0.2. [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]

The effect of impinging uniform jet on flow and heat transfer over isothermal moving plate is investigated. The flow and temperature fields are studied numerically with different jet velocity ratio (jet to plate velocity ratio 0-5). The laminar flow field is analyzed numerically by solving the steady, two-dimensional incompressible Navier- Stokes and energy equations. A collocated (non-staggered) grid is used in the momentum equations, which discretized by finite volume method, SIMPLE algorithm is used to adjust the velocity field to satisfy the conservation of mass. The range of Reynolds number is (Re = 10 - 100). The results show that at high jet velocity ratio (V/U = 5) and Reynolds number (Re = 100), the rate of heat transfer from the plate is doubled. [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]

Heat transfer coefficients and pressure drop are studied experimentally for airflow over aligned round and flattened tube configurations. The Reynolds number is based on the outer diameter of the round tube or the outside transverse diameter of the flattened tube, which is used for various flows, ranging from 133 to 800 with a constant input heat flux. In the present work, a total of 30 samples of round and flattened tubes heat exchangers with three transverse pitches, 2.0, 3.0, and 4.5, were studied to investigate their thermal performance. The results indicate that the relative gain in the overall Nusselt number is about 32.5 to 60.6% in flattened tubes, while the reduction range in the friction factor is about 11 to 30.6%. Correlations are proposed for the overall Nusselt number, friction factor, and Colburn j–factor for both round and flattened tube banks. A higher value means that a deviation error of 9.9% in the round tube banks and 10.1% in the flattened tube banks are expected. In addition, the best value for thermal performance for the flattened tube bundle was found to be coincident with a smaller Reynolds number. [ABSTRACT FROM AUTHOR]

Heat transfer coefficients are studied experimentally for airflow over a four‐flat‐tube configuration with different inlet attack angles. The range of Re numbers was from 1668 to 3782. The heat fluxes are 13.2, 38.5, and 99.8 W/m². In this paper, 45 samples of a flat tube with inlet airflow angles (30°, 45°, and 90°) are set up to investigate its thermal performance. The design of experimental approach was used to conduct the heat transfer parametric study by designing 45 experiments, analyzing the empirical model, and optimizing heat transfer. The response was modeled using a general factorial design model based on experimental data. From analysis of variance (ANOVA), we obtained significant coefficients by performing the 5% test of level of significance. The results indicated that both the Nu and Re numbers increase for all heat flux cases and these decrease with increasing the air attack. Also shown are that the Colburn j‐factor decreases with increase of air velocity. It was found that the ANOVA results are appropriate to the collected experimental data, as the R² and R² ‐adjusted statistics are found to be 92.61% and 90.97%, respectively, for Nu number. In a similar manner, for Colburn j‐factor, the R² and R² ‐ adjusted statistic are 96.97% and 96.29%, respectively. [ABSTRACT FROM AUTHOR]