Transverse Ribs Research Articles

Effect of Vehicle Load on the Fatigue Cracks of the Center-stay for a Steel Girder Deck in a Suspension Bridge

Steel deck systems are widely used in cable-stayed and suspension bridges because of their various advantages. However, the direct effect of vehicle loads often leads to fatigue cracks in steel decks, particularly at the intersections of the longitudinal and transverse ribs, which have been the focus of most studies. In the target bridge of this study, unlike the location where fatigue cracking generally occurs, cracks were detected in the vertical stiffener inside the stiffening girder just below the center-stay and that adjacent to the center-stay. A precise analysis was performed to determine the cause of fatigue cracking, and the analysis model was verified by comparing it with the results of an existing load test. This study examined the effects of heavy vehicle loads by adjusting the vehicle weight and changing the position of the vehicle. This study confirms that as the vehicle load increases, fatigue cracing may occur in the internal vertical stiffener of the center-stay stiffening girder, leading to subseuent cracs in the external center-stay.

Experimental investigation of heat transfer augmentation of impinging jet solar air heater with stepped transverse ribs

The current experimental investigation analyses the thermal and frictional attributes of an impinging jet solar air heater (IJSAH) with stepped transverse ribs, having varying pitch and size, affixed to the absorber plate. Two ribs of dimension 2 × 4 (R1) and 4 × 6 cm (R2) were tested. The pitch (p) between ribs was 2, 4, and 8 cm, with Reynolds number (Re) varying from 4913 to 13103. The jet hole diameter (Dj) considered were 3, 6 and 9 mm. The maximum Nusselt number (Nu) with the recommended R1 rib having p = 4 cm and Dj = 3 and 6 mm equalled 128.784 and 104.5004 at Re = 13103, respectively, which was 31.22 and 21.76 % higher than that generated by smooth IJSAH. The friction factor (f) generated by the ribbed IJSAH having Dj = 6 mm and p = 4 cm was 57.08 % lower than ribbed IJSAH with Dj = 3 mm. The peak thermohydraulic performance parameter (THPP) achieved was for R1 rib with p = 4 cm and Dj = 6 mm and equalled 1.75, which was 19.49 % higher than smooth IJSAH. The R1 rib with p = 4 cm at Re = 11465 demonstrated better thermal characteristics based on detailed investigation.

On the reliability of steel frame joints in earthquake zones exposed to low temperatures

The paper analyzes the existing construction solutions of steel frames with a box-section column and an I-beam crossbar in order to use them in earthquake zones, including areas with low temperatures. Such solutions will allow the structure to accept the seismic inertial forces, while maintaining its bearing capacity throughout the entire period of operation. In order to solve this problem, the study proposes to use steel frame joints, which can be used both for the entire frame of the building and on individual floors, thereby creating a “flexible story” effect. The authors studied articles, books and patents issued in Russia, the United States, Japan, China and Iran, analyzed the factors that reduce the reliability and performance characteristics of the joints. The main factor consists in a welded joint, which is used to attach the crossbars to the columns, transverse ribs in the column body, and to form the box section of the column from sheets, angles or channels. The reliability of the welded joint is reduced even more under conditions of seismic zones with low temperatures in Russia. However, units without welded joints require special cast parts or structures, thereby reducing their availability. In this regard, the task consists in developing new original construction solutions for joints that meet the requirements of reliability and availability.

The effect of Scheuermann's kyphosis on rib cage morphology: A skeletal study

BackgroundEvolutionary changes in human rib cage morphology rendered it prone to pathologies like Scheuermann's kyphosis (SK). However, the impact of SK on rib cage morphology is unclear. PurposeThis study aimed to examine differences in rib cage morphology (e.g., ribs and sternum) between SK patients and a control group. MethodsMeasurements of the vertebral body, transverse process angle, sternum, and rib size were taken from the skeletons of SK patients (76) and a control group (96). Statistical tests were carried out to examine differences between the study and control groups and between the right and left sides. Correlations were obtained to examine the associations between the extent of the kyphosis (kyphosis angle) and rib cage variables. ResultsThe SK group yielded significantly longer and flatter ribs than the control group in both sexes. However, males had the largest differences in the 9th rib and females in the upper ribs (5-7). Inconsistency in symmetry results was found between the sexes. In summary, SK patients had a larger anteroposterior diameter in relation to the transverse diameter than the control group. Discussion and ConclusionsSK affects the morphology of the entire thorax and changes rib proportions similarly in males and females. These changes might have a role in bipedal stability and locomotion efficiency. Moreover, understanding the unique anatomy of SK patients is essential when performing an anterior release and anterior fusion operative approach. Finally, it provides insights into respiratory complications and poor prognosis related to individuals suffering from severe hyperkyphosis.

Numerical investigation of different transverse Rib shapes on thermal convection in a channel filled with nanofluid

With the growing interest in energy optimization, corrugated surfaces are arguably an excellent choice, finding applications in areas as diverse as heat exchangers, automobiles, building energy efficiency, and chemical reactors. However, due to the poor thermal properties of conventional fluids, heat transfer is limited. The introduction of nanoparticles into fluids is a promising solution to improve their thermal performance. This paper does a detailed numerical analysis of how different factors affect the forced convection heat transfer in a two-dimensional ribed channel. The shape of the ribs is one of the factors that are looked at, along with some new parameters like e/H, which is the ratio of rib height to channel height, and L2/P, which is the test section to the pitch between the ribs. The aim is to determine the optimum geometry that maximizes the Nusselt number while minimizing the pressure drop. The study also examines the effects of nanoparticle type and concentration on heat transfer and fluid flow characteristics. To this end, the continuity, momentum, and energy equations were solved with the finite volume method using the SIMPLE scheme with the k-ε turbulence model at different Reynolds numbers ranging from 4000 – 14,000. The results indicate that triangular ribs with ratios e/H = 0.15 and L2/P = 4 increase the Nusselt number by 63.3 % while reducing the pressure drop by 22 % compared with the other cases. The improvement in heat transfer in the water-SiO2 case was the greatest compared with the other nanofluids tested. Particle size fraction and Reynolds number increased the Nusselt number in ribbed channels by 20.7 % compared with water.

DEM evaluation of the mobilization of mechanisms governing the geogrid-aggregate interaction

Pullout tests of geogrids embedded in a single clean aggregate type were conducted and subsequently simulated to investigate the geogrid-aggregate interaction mechanisms. The Discrete Element Method (DEM) model, which was carefully calibrated and validated against the experimental results, was adopted for the simulations. The three-dimensional deformation behavior of geogrids and the shear behavior of aggregates with complex particle shapes were successfully predicted. Analysis of the particle displacement distribution and contact force distribution allowed determination of the particle-scale interaction mechanisms of the geogrid-aggregate system. In particular, the mobilization of pullout resistance components was tracked based on the contact identification method and the influence of geogrid stiffness on the mobilization of pullout resistance components could be evaluated. The results indicate that the activation of the different geogrid resistance components that develop during pullout are not synchronized. During the pullout process, DEM predictions indicate that the frictional resistance of the geogrid is activated first, peaking rapidly and being followed by the development of passive resistance of the transverse ribs. Also, an increased geogrid stiffness was found to enhance the passive resistance of the transverse ribs but to influence only negligibly the frictional resistance.

Fatigue performance of innovative open-rib orthotropic steel deck for super-long suspension bridge

This paper presents experimental and numerical studies on the fatigue performance of an innovative orthotropic steel deck (OSD) with open-ribs, apple-shaped cut-outs, and additional transverse ribs, which is employed by the Zhangjinggao Yangtze River Bridge. This bridge is set to become the world's longest suspension bridge upon completion. A full-scale section of the OSD was fabricated and subjected to fatigue loading with a total cycle of 12.3 million times. The interested cracking-prone fatigue details include rib-to-deck and rib-to-crossbeam welded joints, along with the apple-shaped cut-outs of the crossbeam. Experimental results indicated that fatigue cracks initiated separately beneath the deck plate, on the flange of the rib, and at the rib-to-crossbeam welded joint, with equivalent stress amplitudes of 159 MPa, 148 MPa, and 99 MPa at 2 million cycles, respectively. In addition, detailed finite element model of the OSD was developed using ABAQUS and validated against the experimental results. The effects of the geometry dimensions and structural details of the bridge deck, longitudinal ribs, crossbeams and transverse ribs that influence the fatigue performance of this OSD were analyzed and discussed. Parametric analyses revealed that increasing the thickness of the deck plate, the thickness or the height of the longitudinal rib, and the number of transverse ribs can effectively reduce the stress amplitudes at corresponding fatigue details, which therefore improves their fatigue performance. This study provides useful references for the fatigue evaluation and design of OSDs with open-ribs and apple-shaped cut-outs.

Dynamic response and damage of pile-geogrid composite reinforced high-speed railway subgrade under seismic actions

In this study, the dynamic response and damage mode of a pile-geogrid composite reinforced high-speed railway subgrade under seismic action were investigated based on a unidirectional shaking table test. Various seismic waves were applied to the subgrade, allowing for an analysis of acceleration, dynamic soil pressure, displacement, and strain responses. The displacement field of the subgrade was visualized using particle image velocimetry (PIV). The study shows that changes in peak ground acceleration (PGA) amplification factors become evident with height due to the presence of geogrid layers. The increase in peak ground motion causes a redistribution of dynamic soil pressures inside the subgrade. The transverse and longitudinal ribs of the geogrids provide an “anchoring effect”. The peak strain of the piles in the center is greater than that of the piles on the sides. The direction of soil particle displacement is closely related to the damage patterns observed in the subgrade. Damage begins to occur once the peak ground motion exceeds 0.4 g, characterized by collapse at the bottom of the subgrade.

Lumbarization and sacralization: Domains of their co-occurrence with other costal-vertebral transformations are not identical.

This study evaluates whether sacralization of a lumbar vertebra and lumbarization of a sacral vertebra are a paired duality but with opposite expressions; the former is associated with 23 presacral vertebrae (PSV) and the latter with 25 PSV. Are sacralization and lumbarization local phenomena, involving only vertebra (V) 24 and V25, or are they associated with other costal-vertebral transformations? Study sample is of skeletonized humans, 431 females and 1405 males, who were 20-49 years of age-at-death and who died in the United States in the 20th and 21st centuries. Data collected are numbers of PSV and sacral vertebrae, presence of rib of V7, position of diaphragmatic vertebra, and transverse process and rib lengths of V5-V9, V18-V19, and V21-V22. Females and males differ significantly in numbers of PSV. Both sexes show significant differences among individuals with 23 PSV, 24 PSV, and 25 PSV: (1) individuals with 23 PSV have the shortest ribs, whereas those with 25 PSV have the longest ribs, of V18 and V19; and (2) individuals with 23 PSV have the highest frequency of 6 sacral vertebrae, whereas those with 25 PSV have the highest frequency of 5 sacral vertebrae. Individuals with 23 PSV and 25 PSV show posterior and anterior homeotic transformation, respectively, of the thoracic-lumbar and lumbar-sacral boundaries, but only individuals with 25 PSV show transformation of the sacral-coccygeal boundary. As co-occurring costal-vertebral transformations differ between sacralization and lumbarization, inferentially the set of genes that influences these vertebrae also differs.

Large-scale direct shear testing for assessing interfacial parameters of natural and recycled sand with geosynthetic reinforcements

The demand for infrastructure projects is being driven by urbanization, which led to scarcity of natural sand (NS), which prompts exploration of alternative sustainable construction materials due to environmental concerns. Recycled sand (RS), processed from construction and demolition waste (C&DW), is an alternative material in infrastructure applications. Investigating interfacial shear behaviour between geosynthetic reinforcements with RS as a sustainable alternative material is crucial for infrastructure projects. This study presents the comprehensive large-scale direct shear testing (LSDST) on RS, NS, and its interfaces with ten types of geosynthetic reinforcements (i.e., polypropylene geogrids (GRD1 – GRD3), polyester geogrids (GRD4 – GRD6), and geotextiles (GT1 – GT4). LSDST were carried out using self-fabricated direct shear testing equipment of size equal to 500 mm x 500 mm x 300 mm (L x B x H). The findings indicate that the RS and NS exhibit similar shear strength parameters, sand-GRD interface demonstrates greater resistance compared to the sand-GT interface. RS and NS-GRD4 - GRD6 interfaces with transverse ribs and rough texture and NS-GRD1 interface with triangular apertures, exhibit significant shear strength parameters than the unstabilized case due to the mobilization of passive thrust. Interfacial shear coefficients for NS and RS range from 0.94 – 1.27 and 0.80 – 1.15 for GRD interfaces, and 0.89 – 1.06 and 0.86 – 0.99 for GT interfaces, respectively. Therefore, the RS can be a sustainable alternative for NS.

Optimizing of heat transfer and flow characteristics within a roughened solar air heater duct with compound turbulators

AbstractThermal systems for solar air heating have been widely used in both industrial and residential contexts, and are essential for converting and recovering solar energy. Thermal performance in solar air heaters (SAHs) can be improved through the repetitive application of artificial roughness to the surfaces. This research work includes a numerical evaluation of SAH performance with artificial rough surfaces made up of combined transverse trapezoidal ribs and chamfered grooves. The ANSYS Fluent software version 2023 R1 was used to simulate SAH with varying relative roughness pitch (), relative roughness heights (), and Reynolds number (). The RNG model was chosen to forecast an enhancement in Nusselt number (), friction factor (), and thermohydraulic performance factor (TPF) for the proposed roughness. Out of multiple roughness parameters analyzed, it was determined that the compound turbulator with and , were the most effective. The TPF for this scenario was determined to be 2.12 at . Finally, a numerical based empirical correlations for and in terms of Re, , and were developed.

Performance enhancement of solar air heater with two-sided curvilinear transverse rib: Experimental and numerical investigation

Solar energy as prime energy source draws attention of world due to its availability and eco-friendliness. Low performance of solar air heater create curiosity for researchers to increase its performance. To enhance performance of solar air heater active and passive techniques used by researcher. Surface modification is one of the most prominent passive techniques to improve the performance. Present experimental and numerical investigation explore thermal characteristics of two-sided curvilinear rib roughened solar air heater. An indoor experiment was performed on two side curvilinear rib roughened absorber plate having constant heat flux of 1000 W/m2. Parallelly 2-dimensional numerical simulation was also performed to explore flow behavior and to complete investigation within optimum cost. ANSYS Fluent 2021.R was used for performing this simulation with K-ε RNG model with enhanced wall treatment. Velocity inlet and pressure outlet was selected as boundary condition. Main roughness and flow parameters were relative roughness height ( e/ D h = 0.21–0.042), relative roughness pitch ( p/ e = 7.14–35.71), and Reynolds number ( Re = 3800–18,000). Maximum value of Nusselt number improvement ratio and friction factor improvement ratio was 3.17 and 3.26 at roughness and flow parameter of ( e/ D h = 0.042, p/ e = 15, Re = 15,000) and ( e/ D h = 0.042, p/ e = 7.14, Re = 3800) respectively. Thermohydraulic performance parameter achieved its maximum value of 2.77 at e/ D h = 0.042, p/ e = 17.85, and Re = 18,000.

Experimental and numerical investigation on deck system of a 102 m simply supported prestressed UHPC box-girder highway bridge

To address two main challenges (excessive mid-span deflections and numerous cracks in the main girder) in long-span prestressed concrete (PC) box-girder bridges, this paper proposes a long-span simply-supported UHPC box-girder bridge. In comparison to conventional PC box-girder bridges with three-dimensional prestress, the proposed UHPC box-girder consists only one-dimensional (longitudinal) prestress, and the thickness of the bottom/top plate and web of the UHPC box-girder are relatively thin and are strengthened with dense diaphragms and stiffening ribs. The 4th Beijiang River Bridge adopts this type of bridge with a span of 102 m, which is the longest span simply supported prestressed UHPC box-girder highway bridge in the world. Considering the fact that the thickness of the top plate of the UHPC box-girder is relatively thin (only 20 cm) and the transverse prestress is removed from the top plate, thus, under the direct action of wheel loads, the risk of bridge deck cracking may correspondingly increase. To investigate the mechanical behavior of the deck system of UHPC box-girder bridges, a 1:2 scaled experimental specimen associated with the field bridge is tested. The mechanical behavior of the new deck system is investigated and discussed. It is found that because the support strength of the stiffening rib is significantly weaker than that of the web, the UHPC deck slab should still be regarded as a two-way slab rather than a one-way slab in the elastic stage. In addition, although the test load location is unfavorable to the UHPC deck slab and the first crack appears on the UHPC deck slab, this deck system finally suffers from bending failure of the transverse rib. Furthermore, finite element analysis is carried out to study the mechanical behavior of this new deck system. Parametric analysis considers some factors including the reinforcement ratio in the transverse rib, the height of the transverse rib, and the space between transverse ribs. The results provide a good reference for design and optimization in the new deck system of UHPC box-girder bridges.

Experimental studies on bond behaviour of steel rebar with different rib patterns in concrete

The bond between concrete and steel rebar is one of the most crucial parameters in the construction of reinforced concrete structures. The load-bearing capacity and serviceability of these structures depend heavily on bond strength. The rib pattern of the rebar plays a significant role in enhancing bond behaviour. The impact of different rebar patterns on bond studies in the concrete mix is found to be limited. In the study, six concrete mixes were prepared and tested. Three of these mixes incorporated fly ash in varied amounts to partially replace cement, while the other three mixes had no fly ash. Three different rib patterns of steel bars were embedded into these six grades of concrete. The pull-out tests were used to assess the bond strengths of various combinations in accordance with RILEM recommendations. The findings show that the ribs in rebars significantly increase mechanical interlocking whereas the presence of fly ash improves chemical adhesion in bond behaviour. Particularly, pattern 2 rebar (transverse rib thickness, 0.797 mm; transverse rib width, 2.06 mm; rib spacing (inner to inner), 6.428 mm; longitudinal rib thickness, 1.04 mm; longitudinal rib width, 2.312 mm; rib inclination angle, 66.39o; nominal diameter, 16 mm; length of transverse rib, 25 mm) exhibited notably superior bond strength, reaching a maximum of 17.21 MPa in M30 grade concrete in which 95 kg/m³ of fly ash was used as a replacement for cement.

Kinked again! From congenital brachial plexus palsy to adult neurogenic thoracic outlet syndrome: Case Report.

Neurogenic thoracic outlet syndrome (nTOS) is a chronic, focal lesion of the lower trunk of the brachial plexus or of the T1 and C8 anterior primary rami, often arising due to distortion of neural structures by a fibrous congenital band extending from a C7 transverse process or cervical rib. Accordingly, patients present with chronic weakness or atrophy of the hand, most prominently of the thenar eminence, which receives most innervation from the T1 root. We present clinical, electrophysiologic, and imaging findings in a case of nTOS presenting in an adult with a history most suggestive of congenital brachial plexus palsy (CBPP), another pathology sharing the mechanism of nerve compression or injury within the supracostoclavicular space. The patient had new right thenar eminence atrophy and a lifelong history of medial forearm sensory deficit and she improved after first rib resection. The convergence of two disorders in the same patient arising in different phases of life illustrates how anatomic or structural variation in this space can predispose to lower brachial plexus injury.

A two-way coupled fluid–structure interaction method for predicting the slamming loads and structural responses on a stiffened wedge

Ships navigating through rough seas are subjected to slamming loads from waves, which can lead to structural damage and maritime accidents. The wedge model is commonly employed to investigate slamming loads and structural responses. While a stiffened wedge closely resembles a real ship hull plate, incorporating it into fluid–structure interaction simulations presents challenges. This paper proposes a two-way coupled fluid–structure interaction method to examine slamming loads and structural responses of a free fall non-prismatic stiffened steel wedge. Hydrodynamic loads are determined through Reynolds-averaged Navier–Stokes computations using OpenFOAM, while structural responses are predicted using the finite element analysis (FEA) software Calculix. To achieve two-way coupling between computational fluid dynamics and FEA simulations, a coupling library for partitioned multi-physics simulations, preCICE, is introduced. The computed impact pressure and stress align well with available experimental data. Various free fall heights are investigated in the numerical simulations. The results indicate that elastic deformation mitigates impact pressure, while the presence of transverse ribs enhances the rigidity of the flexible plate. The duration of pressure and the peak slamming pressure exhibit an inverse correlation. Greater free fall heights result in shorter pressure duration times, and smaller free fall heights may reduce rise time. Three-dimensional effects cause pressure to decrease along the midpoint of the plate toward both sides. Additionally, structural stress in the central area exceeds that in the areas on both sides at the same height. In conclusion, the proposed two-way coupled model proves suitable for accurately and efficiently computing hydroelastic slamming on flexible wedges.

Analytical assessment of pullout capacity of reinforcements in unsaturated soils

The effective interaction mechanisms in the pullout resistance of reinforcements include skin friction mobilized at the soil-solid surface, soil-soil shear resistance, and compressive resistance created against transverse elements. The third component is obtained from passive lateral pressure (LPM) or bearing capacity (BCM) methods. An analytical solution is proposed to determine the pullout capacity of geocell, geogrid, and strengthened geogrids embedded in ordinary and unsaturated soils. For unsaturated soils, the effective stress approach was employed. The solution-predicted results were compared with those obtained from large-scale pullout tests reported in the literature. Results indicated that considering LPM for 2D and 3D reinforcements better agrees with experimental results. The mobilized frictional rib-soil interfaces and the soil-soil shear resistance components generally contribute more to the pullout capacity of the geocell and geogrid, respectively. For the extensibility represented by mpi and flexibility of geocell denoted by αpi, the values of mpi = 1, 0.7, and 0.3 for the first, second, and third row of geocell, αpi= 0.4 for the first row of geocell and 0.25 for the second and subsequent rows are suggested to be considered. Parametric studies showed that the optimum transverse rib spacing is over 50 times the equivalent rib thickness (Beq).

Diseño de estructuras hidráulicas en régimen supercrítico con sedimentos: un criterio matemático para calcular la rugosidad del fondo

In some channels with high gradients, heavy scouring and erosion, as well as overflow, is highly common to occur, thus it is required a water flow velocities regulation. An option for achieving this, is to significantly increase the channels’ s bottom roughness through the installation of rapid hydraulic structures. However, in sedimentary density fluids, the change of velocity generates the deposition of solids which could be consolidated by changing the geometric design of these structures. This study aims to estimate the degree of confidence expected when modifications take place to artificial roughness geometries in the bottom of the channel with turbulent flow and sediment flow. This modification requires to transverse ribs into ramps using an experimental mathematical analysis. The study allows us to conclude that the newly generated bottom roughness causes more stable water flows, and it is a way to reduce flow velocities.

Evaluation Method of Generatrix Straightness Coefficient and Application in AZ31 Magnesium Alloy Panel

Abstract An evaluation method of the generatrix straightness coefficient for magnesium alloy panel is proposed. The generatrix straightness coefficient and characterization parameter are defined. The reasonable process parameters for equal curvature grid panels were determined, and various specifications of magnesium alloy grid panels were processed. For the magnesium alloy grid panel, with an increase in the curvature radius of the panel, the deviation of generatrix straightness and generatrix straightness coefficient of each point is reduced. The deviation of generatrix straightness at the junction of the transverse is the smallest. The deviation of generatrix straightness at the center of the grid is the maximum. The deviation of generatrix straightness at the junction of transverse and longitudinal ribs was minimal. The maximum deviation of generatrix straightness is 0.097 mm, and the maximum generatrix straightness coefficient is 0.277%.

Numerical analysis of a solar air heater with offset transverse ribs placed near the absorber plate

Solar air heater (SAH) is used to convert readily available solar energy into useful thermal energy. Several studies have been conducted with different roughness elements on the absorber plate. However, study with ribs which are placed slightly above the heated plate, termed as offset transverse ribs, are still scant in the literature. Such study would explain the effect of flow between the ribs and the absorber plate on heat transfer augmentation in a SAH. With this objective a 2-D numerical study is performed here by solving steady RANS equations with RNG k−ɛ turbulence model. The effect of offset transverse ribs on heat transfer, pressure drop and thermal enhancement factor (TEF) is investigated. The geometrical parameters, such as, relative gap (α), relative height (β) and relative pitch (λ) are varied in the range of 0.0–0.045, 0.015 to 0.09, and 0.0333 to 0.1, respectively. The performance of SAH is evaluated on the basis of highest enhancement in relative Nusselt number (NuR/Nu) and thermal enhancement factor (TEF). A slight gap between the ribs and the absorber plate (α = 0.0075) is observed to yield better thermal performance than that for the attached ribs (α = 0). The maximum enhancement in NuR/Nu is found to be 1.52 for α = 0.0075. However, increasing the gap (i.e., α) prevents the flow reattachment with the absorber plate. Increase in rib height, on the other hand, is found to be more effective in heat transfer enhancement, but with a price of a significant enhancement in pressure drop. This leads to a reduction in the overall performance of SAH. Increment in pitch distance, however, reduces the enhancement in both Nusselt number and friction factor. By considering these three parameters, the highest TEF is found to be 1.042 for α=0.0075, β=0.030, and λ=0.0333 at Re equal to 13000. Finally, correlations for NuR and fR are derived as a function of the parameters investigated for helping the design of SAHs.