Aligned Tube Research Articles

Heat transfer characteristic of particle flow around the out-wall of different geometries

In this study, large-scale simulations were carried out for different tube banks to explore the effect of geometrical factors. In addition, the heat transfer experiment of dense particles was carried out to validate the heat transfer model used in discrete element method. The stagnation zone and void zone with nearly triangular shape are found in staggered tubes. The stagnation zone with rectangular shape is formed between vertical adjacent tubes of the aligned tube, and the width of stagnation zone is one third of the tube diameter. A triangular particle blockade zone is formed in the rectangular stagnation zone. The heat transfer rate of staggered tubes is increased by 26% compared with that of the aligned tubes. The staggered elliptical-like combined tubes bank with chamfers significantly increase the heat transfer rate by 54.2% with the same heat transfer coefficient, compared with the staggered circular tubes bank. The local heat transfer performance can be enhanced by the addition of chamfers at the junction area of tubes. When penetration thermal resistance is dominant compared with the contact thermal resistance, the circular tube has higher heat transfer coefficient compared with elliptical-like combined tube with chamfers. The thermal resistance models for different tubes are developed.

Heat transfer of granular flow around aligned tube bank in moving bed: Experimental study and theoretical prediction by thermal resistance model

Gravity-driven granular flow has been the heat transfer mediums in moving bed heat exchangers, which play vital roles in industrial heat saving and solar energy utilization. However, the heat transfer mechanism of granular flow is still worth of investigating around the tube bank. In this work, the aligned tubes were arranged in the moving bed, and the heat transfer of metallurgical slag was experimentally tested. It was found that, the heat transfer coefficients are significantly sensitive to the flow rate in the slow granular flow. The smooth flow with particle mixing can improve the heat transfer, while the local particle lagging will worsen the heat transfer around aligned tubes. To predict heat transfer coefficients of granular flow, the contact thermal resistance and the penetration thermal resistance are built with empirical factors (χ, a and η). In the near-wall region, x represents the sensitivity of the contact thermal resistance to particle sizes. Meanwhile, the contact time can be modified by a and η for the penetration thermal resistance in the funnel flow structure. The values of a and η are affected by the granular flow pattern, which tend to decrease in the smooth flow with strong particle mixing. Verified with the present experimental results and the previous literature data, the thermal resistance model has great potentials to explain the heat transfer around the aligned tube bank.

Thermal and flow characteristics of a channel formed by aligned round tube bank fins stamped with curve delta-winglet vortex generators

The primary purpose of present study is to reveal the roles played by CDVGs in vectoring the airflow and breeding longitudinal vortices for enhancing heat transfer. The thermal-hydraulic characteristics of a finned aligned round tube heat exchanger with stamped CDVGs were numerically studied by using the custom code with SIMPLE algorithm in a nonorthogonal curvilinear coordinate system. Four geometric parameters including vortex generator height, radial position, peripheral position and fin pitch, were programmed to ascertain parametric effects on fin side thermal performance, and the regression formulas of Nusselt number and resistance coefficient in the fin side passage with Reynolds numbers and four geometric parameters were secured. The findings suggest that the mean Nusselt number, resistance coefficient and secondary flow strength for the novel fin with CDVGs are all prevail over that in the reference plain fin under a certain Reynolds number. The body fitted CDVGs are ideally situated for finned round tube exchanger in aligned arrangement. The action of CDVGs can not only efficiently lessen the size of recirculation area behind tube but also produce strong longitudinal vortices, accordingly heighten evidently the fin side heat transfer ability in the recirculation zone. Using the studied optimum geometric parameters can make the thermal property factor up to 1.35 under the same pumping power constraint in comparison with the reference plain fin geometry when Reynolds number equals to 3000. This study can be a real application in compact heat exchanger with finned round tubes when heat transfer augmentation is under consideration.

Numerical Study of the Influence of Tube Arrangement on the Flow Distribution Inside the Heat Exchanger in the PCCS

Passive containment cooling system(PCCS) is widely applied in a new generation of nuclear power plants. The initial heat exchanger is the most improtant heat transfer device in the PCCS. Past studies show that the flow distribution has a great influence on the heat transfer performance of a heat exchanger. And a lot of work has been done on improving the flow distribution uniformity of the heat exchanger such as the geometry modification, proper choice of the geometry parameters. However, little work has been done on the tube arrangement. For a heat exchanger applied in the industry, the number of tubes are huge, and it is unrealistic to arrange all the tubes in a row on the one side of the heat exchanger. Therefore, more work should be paid on the influence of the tube arrangement on the flow distribution in the heat exchanger. The present study numerically investigated the effect of the tube arrangement on the flow distribution in a Central-type parallel heat exchanger. Six different kinds of tube arrangement have been investigated on the flow distribution and the pressure loss characteristics of the heat exchanger. The obtained results show that the tube arrangement has a great influence on the flow distribution and the staggered tube arrangement provides a better flow distribution than the aligned tube arrangement.

Heat Transfer Characteristics and Energy Efficiency Analysis of Finned Tube Heat Exchangers

Flow and heat transfer characteristics of the integral finned tube heat exchanger are studied by the numerical simulation method in the present paper. The energy efficiency levels of two types of finned tube heat exchangers (aligned finned tube and staggered finned tube) are evaluated by PEC method. The heat transfer intensity of different finned tube heat exchangers was evaluated by the field synergy principle. When the tube spacing ratio (S1/S2=1) is small, the field synergy of staggered finned tube is similar to the aligned finned tube, and the PEC index is less than 1; when the spacing ratio (S1/S2=3) is large, the field synergy of the staggered finned tube get much stronger than the aligned finned tube, and the PEC index is larger than 1 as the Re≥8×104. Considering both the change of heat transfer intensity and the increase of resistance, it is recommended to evaluate the energy efficiency level of finned tube heat exchanger by PEC method.

Fouling and thermal-hydraulic characteristics of aligned elliptical tube and honeycomb circular tube in flue gas heat exchangers

In this paper, aiming at resolving the contradictions of heat transfer enhancement, resistance reduction and soot-blowing effect of common heat transfer surfaces, aligned elliptical tube bundle (AETB) and honeycomb tube bundle (HCTB) were proposed for the high dust content conditions, and the fouling characteristics and thermal-hydraulic performance before and after fouling were investigated. Firstly, the thermal-hydraulic performance of aligned circular tube bundle (ACTB), AETB, conventional staggered circular tube bundle (SCTB) and HCTB in the clean state were compared, and advantages of AETB and HCTB were verified. Secondly, based on the ash fouling model and prediction method established by the author’s group, fouling distribution and morphology of AETB and HCTB were obtained, and ash fouling and thermal-hydraulic characteristics were examined by parameterization. Finally, in the range of geometry parameters studied in this paper, the correlations of the asymptotic value of fouling thermal resistance Rf∗ in fouling state, Nusselt number Nu and friction factor f in clean state were developed. Results show that the relative deviations between the predicted results and the numerical values is within 4%, which indicates that the proposed correlation is of sufficient accuracy for engineering purposes, and can accurately predict the thermal-hydraulic characteristics of flue gas heat exchanger. The results of this paper can provide a reference for development and engineering application of the heat-transfer surface for the efficient recovery of industrial flue gas waste heat.

An aligned nanofiber nerve conduit that inhibits painful traumatic neuroma formation through regulation of the RhoA/ROCK signaling pathway.

Traumatic neuromas represent a prevalent source of neuropathic pain. As of yet, there has been no single treatment method that can guarantee permanent relief of symptoms. Although nerve-capping techniques have shown promise, their exact mechanisms remain elusive. The authors' aim was to examine the role of the RhoA/ROCK signaling pathway in the prevention of neuroma formation after neurectomy utilizing a nerve-capping technique. An aligned nanofiber tube was fabricated to cap the sciatic nerve in Sprague Dawley rats. The rats (n = 60) were randomly divided into the aligned SF/P (LLA-CL) capping group (capping group, n = 20), the capping and Y-27632 (ROCK pathway inhibitor) intervention group (intervention group, n = 20), and the no-capping group (control group, n = 20). The authors undertook a comprehensive assessment of the capping group, examining the animals' behavior, the extent of neuroma development, histology, gene and protein expression, and ultrastructural changes associated with the RhoA/ROCK signaling pathway. These findings were compared with those in the intervention and control groups. The inciting injury resulted in the expression of the RhoA/ROCK signaling pathway, as well as its further upregulation in peripheral neurons. Axon outgrowth was significantly increased when RhoA/ROCK signaling pathway was suppressed. The average autotomy score in the capping group was observed to be much lower than that of the intervention and control groups. At 30 days postneurectomy, the capping group displayed no obvious neuroma formation, while a bulbous neuroma was found in the nerve stumps of both the control and intervention groups. Quantitative real-time polymerase chain reaction and the Western blot analysis demonstrated that the expression of myelin-associated glycoprotein was substantially upregulated in the capping group; in contrast, the expression of NF-200 was significantly downregulated. The expression of myosin light chain was notably lower in the intervention group, but there was no significant difference when compared with the control group (p > 0.05). The RhoA/ROCK signaling pathway has emerged as a critical player in the process of traumatic neuroma formation after neurectomy. It is possible that the nerve-capping technique could generate a "regenerative brake" based on the regulation of the RhoA/ROCK signaling pathway in this event. These findings may provide concrete evidence that could help develop new strategies for the management of painful neuromas.

Numerical simulation of the flow and heat-transfer characteristics of an aligned external three-dimensional rectangular-finned tube bank

Finned-tube heat exchangers are commonly used for air conditioning, refrigeration, and utility boilers to enhance the energy efficiency of heat transfer. Compared with the 2D continuous finned tube, the 3D discrete finned tube heat exchangers have more outstanding performance on enhancement of heat-transfer. Especially, the 3D rectangular fin is believed to have better heat-transfer performance compared with common 3D fins.In this study, the flow and heat-transfer characteristics of an aligned external rectangular-finned tube bank with six rows of tubes were numerically investigated. The performances of an external rectangular-finned tube bank and a smooth tube bank were firstly compared. This was followed by an analysis of the effects of the geometric parameters (transverse tube pitch, longitudinal tube pitch, fin height, fin width, and fin pitch in the axial direction) and the Reynolds number on the flow and heat-transfer characteristics of an aligned external three-dimensional rectangular-finned tube bank.The results indicated that the heat transferability and friction loss of the aligned external three-dimensional rectangular-finned tube bank were higher than those of the smooth tube bank, while the comprehensive performance of external rectangular finned tube bank was not always superior. In addition, increasing the longitudinal tube pitch, fin height and fin width or decreasing the transverse tube pitch and fin pitch in the axial direction caused the heat-transfer capability and flow loss of the external rectangular-finned tube bank to increase, which can provide theoretical guidance for the design of a 3D finned-tube heat exchanger. The correlations of the Nusselt number (Nu) and the friction factor (f) for the six-row tube bank were presented, which can be helpful to engineering applications of heat exchanger for clean gas situations.

Numerical modeling and multi-objective optimization of a novel cross-flow heat exchanger with rotated aligned tube bank

A novel cross-flow heat exchanger with a rotated aligned tube bank is designed and utilized in a cement plant. The heat exchanger is numerically modeled with various tube pitches in order to obtain correlations of the shell-side average Nusselt number and friction factor. Then, a multi-objective optimization approach is performed based on the genetic algorithm. The goal of this study is to maximize the heat transfer rate and minimize the pressure drop. Pareto optimal solutions are obtained, which indicate that the increase in the heat transfer rate leads to an increase in pressure drop, and vice versa. In addition, heat exchanger effectiveness, total cost, and the ratio of the heat transfer rate to the fan/pumping power demonstrate different variations with the two objective functions. Several selection criteria are discussed to determine the optimal design and to help designers select an appropriate solution based on actual requirements. Two multi-objective optimization design schemes are compared to the original design under the same heat transfer rate. Results show that pressure drop decreases by 67.9% and 69.7%, respectively, and total annual cost decreases by 2.4% and 16.3%, respectively.

Experimental and numerical studies on the air-side flow and heat transfer characteristics of a novel heat exchanger

A novel heat exchanger involving rotated aligned tube banks is proposed and investigated experimentally and numerically. It is utilized within a waste heat recovery system in a cement plant, and has features of both staggered and aligned arrangements. Heat transfer and flow characteristics of the heat exchanger are analyzed. Experimental data of the rotated aligned arrangement are compared with that of the aligned arrangements, and correlations of Nusselt number as well as friction factor are obtained. A two-dimensional numerical study is conducted employing CFD simulation. A model of the entire heat exchanger is built and simulated. Boundary conditions are formulated by a given inlet temperature of 300°C and a constant tube wall temperature of 150°C, with inlet velocity ranging from 2m/s to 7m/s. Simulated results are compared with the experimental data, and good agreement is achieved with the correlation results for rotated aligned arrangement. Moreover, simulations of aligned and staggered tube banks are implemented in comparison with the rotated aligned tube bank. Numerical results indicates the superior heat transfer performance of the rotated aligned tube bank over the other two arrangements. Heat transfer coefficient is 37.5–78.8% higher than the aligned arrangement, and 32.7–66.7% higher than the staggered arrangement. It also has high level of turbulence intensity as well as large maximum air velocity within the tube bank, yet the pressure drop is high. Nusselt number has a fairly good agreement with the staggered arrangement, and friction factor lies between the aligned and staggered arrangements, for 6000<Re<10000.

Numerical optimization of location of ‘common flow up’ delta winglets for inline aligned finned tube heat exchanger

Heat transfer augmentation of a fin and tube heat exchanger by the winglet type vortex generator strongly depends on the location of the winglet w.r.t. tube centre. This study was aimed at optimizing the location of the ‘common flow up’ delta winglets for the maximum thermal compactness of a given inline aligned fin and tube heat exchanger. The winglets were erected with a conservative attack angle to avoid severe increase in the pressure drop. This work also attempts to first time model the contact resistance between the fins and the tube as a hypothetical conduction resistance. Beginning with the selection of all promising locations of the winglets, an optimal location was identified that allows maximum augmentation of the thermal performance on the fin side. This numerical study clearly shows that the optimally located ‘common flow up’ delta winglets have improved the average thermal performance of both the fins and the tubes at the same Reynolds number.

Thermal Analysis of NR Composite with MWCNTs Aligned in a Magnetic Field

We got the aligned carbon tube in the rubber matrix through magnetic field. TEM shows that Fe3O4is symmetrically coated on the outer surface of MWCNTs. Diffraction peaks corresponding to Fe3O4cubic crystal also appeared in the X-ray diffraction spectra. Thermal conductivity of composites increases by filling the appropriate content of carbon tube. If the magnetic field is larger and the direction time is longer, a greater thermal conductivity of composites can be obtained.

Effects of preferential concentration on collision and erosion between solid particles and tube bank in a duct flow

The impact and erosion on the stainless steel heat exchanger tubes located in the middle row of a 10×10 aligned tube bank caused by coal ash particles are investigated numerically by means of direct numerical simulations (DNS) to study the influence of preferential concentration on particle–tube interactions. The immersed boundary technique is applied to account for the coupling effect on the flow by the immersed tubes. A two-way coupled Lagrangian solver is developed for particle tracking. The experimentally validated particle–wall impact and erosion models are used to describe the collision between particles and tubes and the resulting erosion. The results demonstrate that the particles Stokes number has significant effects on particle dispersion patterns as well as collision and erosion characteristics. The global tube erosion of the first tube increases with the increment of the particle size, but the particles with an intermediate Stokes number of 1.6 cause the most erosion to the other downstream tubes with lower collision frequency, due to the preferential concentration. The maximum local tube erosion happens in the front side surface of each tube with certain angle region for all particles where more attention should be paid to prevent from erosion caused by coal ash particles.

Sheet resistance characterization of locally anisotropic transparent conductive films made of aligned metal-enriched single-walled carbon nanotubes.

One-dimensional conductive fillers such as single-walled carbon nanotubes (SWNTs) can be aggregated and aligned during transparent conductive film (TCF) formation by the vacuum filtration method. The potential error of analysing the average sheet resistance of these anisotropic films, using the four-point probe in-line method and the conversion formula developed assuming uniform isotropic material properties, was systematically investigated by finite element analysis and experiments. The finite element analysis of anisotropic stripe-patterned TCFs with alternating low (ρ1) and high (ρ2) resistivities revealed that the estimated average sheet resistance approached ρ1/t when the probes were parallel to the aligned nanotubes. The thickness of the film is t. It was more close to ρ2/t when the probes were perpendicular to the aligned tubes. Indeed, TCFs fabricated by the vacuum filtration method using metal-enriched SWNTs exhibited highly anisotropic local regions where tubes were aggregated and aligned. The local sheet resistances of randomly oriented, aligned, and perpendicular tube regions of the TCF at a transmittance of 89.9% were 5000, 2.4, and 12 300 Ω □(-1), respectively. Resistivities of the aggregated and aligned tube region (ρ1 = 1.2 × 10(-5) Ω cm) and the region between tubes (ρ2 = 6.2 × 10(-2) Ω cm) could be approximated with the aid of finite element analysis. This work demonstrates the potential error of characterizing the average sheet resistance of anisotropic TCFs using the four-point probe in-line method since surprisingly high or low values could be obtained depending on the measurement angle. On the other hand, a better control of aggregation and alignment of nanotubes would realize TCFs with a very small anisotropic resistivity and a high transparency.

Implantation of Completely Biological Engineered Grafts Following Decellularization into the Sheep Femoral Artery

The performance of completely biological, decellularized engineered allografts in a sheep model was evaluated to establish clinical potential of these unique arterial allografts. The 4-mm-diameter, 2-3-cm-long grafts were fabricated from fibrin gel remodeled into an aligned tissue tube in vitro by ovine dermal fibroblasts. Decellularization and subsequent storage had little effect on graft properties, with burst pressure exceeding 4000 mmHg and the same compliance as the ovine femoral artery. Grafts were implanted interpositionally in the femoral artery of six sheep (n=9), with contralateral sham controls (n=3). At 8 weeks (n=5) and 24 weeks (n=4), all grafts were patent and showed no evidence of dilatation or mineralization. Mid-graft lumen diameter was unchanged. Extensive recellularization occurred, with most cells expressing αSMA. Endothelialization was complete by 24 weeks with elastin deposition evident. These completely biological grafts possessed circumferential alignment/mechanical anisotropy characteristic of native arteries and were cultured only 5 weeks prior to decellularization and storage as "off-the-shelf" grafts.

Blood Outgrowth Endothelial Cells Alter Remodeling of Completely Biological Engineered Grafts Implanted into the Sheep Femoral Artery

Hemocompatibility of tissue-engineered vascular grafts remains a major hurdle to clinical utility for small-diameter grafts. Here we assessed the feasibility of using autologous blood outgrowth endothelial cells to create an endothelium via lumenal seeding on completely biological, decellularized engineered allografts prior to implantation in the sheep femoral artery. The 4-mm-diameter, 2- to 3-cm-long grafts were fabricated from fibrin gel remodeled into an aligned tissue tube in vitro by ovine dermal fibroblasts prior to decellularization. Decellularized grafts pre-seeded with blood outgrowth endothelial cells (n = 3) retained unprecedented (>95 %) monolayer coverage 1 h post-implantation and had greater endothelial coverage, smaller wall thickness, and more basement membrane after 9-week implantation, including a final week without anti-coagulation therapy, compared with contralateral non-seeded controls. These results support the use of autologous blood outgrowth endothelial cells as a viable source of endothelial cells for creating an endothelium with biological function on decellularized engineered allografts made from fibroblast-remodeled fibrin.

Letter to the Editor: Does PFNA II Avoid Lateral Cortex Impingement for Unstable Peritrochanteric Fractures?

To the Editor We read the article entitled “Does PFNA II Avoid Lateral Cortex Impingement for Unstable Peritrochanteric Fractures?” by Macheras et al. [3] with great interest. We commend the authors for confirming that the Proximal Femoral Nail Antirotation (PFNA)-II could avoid lateral cortex impingement; they concluded a flattened lateral surface and smaller mediolateral angle could decrease the pressure on the lateral trochanteric wall. Beginning in August 2009, we have used PFNA-II to treat more than 300 cases of pertrochanteric and intertrochanteric fractures (AO/OTA: 31A) [4]. In our opinion, the operative technical evolution in nail insertion may be more important than instrument modification. In cephalomedullary nailing, it is important to ensure the instrument insertion line (guide wire, reamer, and the nail) and the femoral canal line are coaxial. However, there are several reasons that make this unachievable in some patients [1, 2]. In addition to morphologic features of the fracture (some can be reduced only with the hip in abduction) and a stiff spine in geriatric patients, the soft tissue mass about the hip, operative drapes, or a laterally oriented operating trajectory of the side-standing surgeon can result in a shift of the ideal trochanteric tip entry point and gradual enlargement in a lateral direction. A laterally enlarged oval hole combined with the existing trochanteric fracture line will lead to more lateral placement of the intramedullary nail than intended. To avoid lateralization, we move the entry point slightly medial (approximately 5 mm) from the trochanteric tip, near the medial wall of the greater trochanter (Fig. 1). There are several advantages to medial reaming. First, it avoids the hard-crest bone of the head-neck fragment, preventing medial abutment and thus reduces the risk of varus reduction of the proximal head-neck fragment or a high helical blade position in the femoral head, both of which are undesirable. Second, it provides adequate space for nail insertion, preventing a wedge-opening effect between the head-neck fragment and the shaft fragment. Third, it provides a well-aligned tube after reaming (even with lateralization) for nail insertion, avoiding pressure on the trochanteric lateral cortex, and nail-cortex impingement or even lateral wall rupture.Fig. 1: Medial migration of the entry point (red point) from the exact tip of the greater trochanter produces an optimal aligned tube (blue area) after reaming.We thank the authors for sharing their experience. We agree with their conclusion that regardless of the implant choice and its specific technical characteristics, the technique of inserting is the key to ensuring a stable fixation and preventing major complications.

Numerical study of solid particle erosion on the tubes near the side walls in a duct with flow past an aligned tube bank

AbstractComputational fluid dynamic (CFD) tool has been applied to investigate the erosion of duct walls and that of tubers (10 × 10 aligned tube bank in the duct) near side walls, which is caused by coal ash particle impaction. The flow field is obtained by using direct numerical simulation (DNS) method. The coupling between tubes and flows are made through the immersed boundary technique. Particles are tracked by using Lagrangian approach and further coupled with gas phase. Four coal ash particles are considered 6.2, 20, 80, and 200 μm. In the end, the erosion of the duct walls and that of the tubes near side walls has been well predicted and characterized. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Focused In Vivo Genetic Analysis of Implanted Engineered Myofascial Constructs

Successfully engineering functional muscle tissue either in vitro or in vivo to treat muscle defects rather than using the host muscle transfer would be revolutionary. Tissue engineering is on the cutting edge of biomedical research, bridging a gap between the clinic and the bench top. A new focus on skeletal muscle tissue engineering has led investigators to explore the application of satellite cells (autologous muscle precursor cells) as a vehicle for engineering tissues either in vitro or in vivo. However, few skeletal muscle tissue-engineering studies have reported on successful generation of living tissue substitutes for functional skeletal muscle replacement. Our model system combines a novel aligned collagen tube and autologous skeletal muscle satellite cells to create an engineered tissue repair for a surgically created ventral hernia as previously reported [SA Fann, L Terracio, W Yan, et al., A model of tissue-engineered ventral hernia repair, J Invest Surg. 2006;19(3):193–205]. Several key features we specifically observe are the significant persistence of transplanted skeletal muscle cell mass within the engineered repair, the integration of new tissue with adjacent native muscle, and the presence of significant neovascularization. In this study, we report on our experience investigating the genetic signals important to the integration of neoskeletal muscle tissue. The knowledge gained from our model system applies to the repair of severely injured extremities, maxillofacial reconstructions, and restorative procedures following tumor excision in other areas of the body.

Numerical analysis on heat transfer enhancement by longitudinal vortex based on field synergy principle

Three-dimensional numerical simulation results are presented for a fin-and-tube heat transfer surface with vortex generators. The effects of the Reynolds number (from 800 to 2 000) and the attack angle (30° and 45°) of a delta winglet vortex generator are examined. The numerical results are analyzed on the basis of the field synergy principle to explain the inherent mechanism of heat transfer enhancement by longitudinal vortex. The secondary flow generated by the vortex generators causes the reduction of the intersection angle between the velocity and fluid temperature gradients. In addition, the computational evaluations indicate that the heat transfer enhancement of delta winglet pairs for an aligned tube bank fin-and-tube surface is more significant than that for a staggered tube bank fin-and-tube surface. The heat transfer enhancement of the delta winglet pairs with an attack angle of 45° is larger than that with an angle of 30°. The delta winglet pair with an attack angle of 45° leads to an increase in pressure drop, while the delta winglet pair with the 30° angle results in a slight decrease. The heat transfer enhancement under identical pumping power condition for the attack angle of 30° is larger than that for the attack angle of 45° either for staggered or for aligned tube bank arrangement.