Friction Factor Ratio Research Articles

Experimental Investigation on Heat Transfer and Friction Factor in Open Matrix Subchannels

Abstract Matrix cooling has opened new possibilities for enhancing the convective heat transfer coefficients without compromising upon the structural rigidity and the life of the gas turbine blade at elevated temperatures. However, the dense structure of the matrix significantly increases the flow resistance and imposes the limitation to its usage. Recently, a matrix with a gap on the sidewalls called open matrix has been proposed by few researchers to reduce the associated pressure penalties. This detailed experimental investigation aims to study the open matrix channel flow and presents the effects of varying sidewall gaps on heat transfer characteristics and friction factor in the open matrixes having rib angle 45 deg for three different subchannel aspect ratios 1.2, 0.8, and 0.4. Liquid crystal thermography has been utilized to discern the detailed heat transfer characteristics. The results have been evaluated in terms of augmentation Nusselt number, friction factor ratio, and overall thermal performance factor over the Reynolds numbers 5800–14,000. The closed matrixes provided the highest augmentation in Nusselt number, and the gaps on the sidewall have shown an overall reduction in augmentation Nusselt number in most cases. However, the suitable sidewall gaps show the effective reduction in pressure penalties for the smaller subchannel aspect ratios. The highest augmentation Nusselt number among the open matrixes has been found as 3.83 with a reduced friction factor ratio for the matrix with a 4-mm gap in subchannel aspect ratio = 0.8 (i.e., 4 subchannels) at Re = 8100.

Experimental study on heat transfer, friction factor, entropy and exergy efficiency analyses of a corrugated plate heat exchanger using Ni/water nanofluids

In the present study, the heat transfer, entropy, friction factor, exergy efficiency, pumping power, and performance index ratio of nickel/water nanofluids flow in a corrugated plate heat exchanger are investigated experimentally. The nickel nanoparticles were synthesized using the chemical precipitation method and characterized by various techniques. The stable water based nickel nanofluids were prepared with particle volume concentrations of 0.1%, 0.3%, and 0.6%. The experiments were conducted at nanofluids Reynolds numbers ranged from 300 to 1000. The properties of nickel nanofluid are evaluated experimentally as well. The thermal conductivity and viscosity enhancements are 33.92%, and 67.45% at a temperature of 60 °C compared to the base fluid data. The increase of nanoparticle loadings and Reynolds number leads to an augmentation of the overall heat transfer coefficient, heat transfer coefficient, and Nusselt number. The overall heat transfer coefficient, convective heat transfer, and Nusselt number enhanced by 38.60%, 57.35%, and 42.68% at 0.6 vol % of nanofluid and a Reynolds number of 707, respectively compared to water data. The thermal entropy generation is decreased by 15.70%, while frictional entropy generation and pumping power are increased by 68.29% and 61.77%, respectively at 0.6 vol % of nanofluid and a Reynolds number of 707 against water data. The exergy efficiency was enhanced by 42.27% at 0.6 vol % of nanofluid and a Reynolds number of 303 compared to water data. The performance index ratio is decreased with the use of nanofluids due to the increase of viscosity, friction factor, pressure drop, and pumping power.

A comprehensive review of parabolic trough solar collectors equipped with turbulators and numerical evaluation of hydrothermal performance of a novel model

Absorber tube in parabolic trough concentrating systems is located at the location of the focal line and a fluid passes through it, the temperature of which increases due to receiving heat from sunlight. The more heat the fluid can absorb from the concentrated solar energy, the better the performance of the system. Since turbulators can be used in the absorber tube for this purpose, a lot of experimental and numerical research have been done on the performance of parabolic trough collectors equipped with various turbulators. In this study, the most important findings of these studies are presented and then, Nusselt number ratio, mean friction factor ratio, and thermal–hydraulic performance evaluation criterion are used to compare the hydrothermal performance of the systems. After reviewing previous researches and identifying advantages and disadvantages of each turbulator, a novel parabolic trough collector equipped with a turbulator is introduced and its hydrothermal performance is evaluated through simulation. The outcomes revealed that the ribbed absorber tube and the concentric rod insert are the most optimum turbulators. In addition, the parabolic trough collector equipped with a combination of corrugated channel and obstacle has a much better hydrothermal performance than the collectors using each of these turbulators separately.

Experimental investigation and ANN modelling on thermo-hydraulic efficacy of cross-flow three-fluid plate-fin heat exchanger

Compact cross-flow three-fluid heat exchanger with plain rectangular fins is experimentally investigated for both thermal and hydraulic efficacy under steady-state condition. The elaborative investigation is conducted for all the four viable flow arrangements of cross-flow configuration which comprises the effect of Colburn factor and effectiveness ratio of central and adjacent fluids, and friction factor with Reynolds number. It is learnt that thermal efficacy is sentient to the operating conditions, type of flow arrangement and variation in flow rate. The comparison of the efficacy between the plain duct (without fin core) and with fin heat exchanger core is presented to analyse the impact of fins in enthalpy exchange. The regression correlation is developed to estimate the thermal and hydraulic performance which are accurate within ±16% and ±5.8% respectively. The investigation is further assisted with the ANN modelling for the prediction of the thermo-hydraulic efficacy with two input (Reynolds number and flow arrangement type) and four output performance parameters (Colburn factor, friction factor and effectiveness ratios). The fraction of 77% and 23% of data is considered for training and testing the neural network respectively. It is learnt that ANN predictions are more promising and accurate than regression predictions and the magnitude of the value of an absolute fraction of variance equals unity.

Measurements of Heat Transfer and Fluid Flow in A Rectangular Duct with Different Types of Rib-Turbulators.(Dept.M)

Experiments are conducted to study the heat transfer and friction in a rectangular duct roughened by arrays of alternate ribs (square-, triangle-. and circle-shaped ribs). The Reynolds number Re based on duct hydraulic diameter rages from 12.000 to 60.000. whereas the rib pitch-to-height ratio (P/h) varies from 6 to 18. To understand the mechanism of heat transfer enhancement the measurements of streamwise mean velocities are also conducted in the square-ribbed duct. The results show that the flow of air through the ribbed duct becomes periodically fully developed after the third rib from the duct inlet. The data indicate also that the triangular type ribs have a substantially higher heat transfer performance than any other ribs in the studied range. The experimental results show that the heat transfer enhancement factors are greater than the friction factor ratios associated with the use of rib-turbulators in the rectangular ducts. Also, the rib conductivity affects significantly on the heat transfer enhancement factor. Correlations for friction and heat transfer in square-ribbed ducts are developed to account for rib spacing to height ratio and flow Reynolds number.

Efek vortex generators terhadap peningkatan perpindahan panas pada aliran melewati heated tubes

In this decade, improving the rate of heat transfer has become a big challenge. The high thermal resistance of the gas side of the heat exchanger has an impact on the low rate of heat transfer. Therefore, an experimental study was carried out aimed at looking at conditions of hot temperature and decreased air flow pressure through a heated tube in a rectangular channel using artificial surfaces, namely the concave delta winglet and delta winglet vortex generators. Concave delta winglet vortex generators (CDW VGs) are installed in-line and staggered with one, and two pairs are arranged in common-flow-down (CFD) in the direction of flow with an angle of attack of 15o. The experimental results show that the best thermal performance is observed in the use of two rows CDW VGs staggered, where the value of performance evaluation criteria (PEC) is 28.88% higher than the use of CDW VGs in-line, DW VGs staggered and DW VGs in-line at the same Reynolds number. At the same Reynolds number, the Nusselt number ratio and the friction factor ratio increased 45.25% and 152.05% respectively, occurring in two rows of CDW VGs staggered compared to other vortex generators.Keywords: vortex generators, heat transfer, Nusselt number, friction factor, PEC

Effects of ultrasonication time on stability, dynamic viscosity, and pumping power management of MWCNT-water nanofluid: an experimental study

It is known that ultrasonication has a certain effect on thermophysical properties and heat transfer of nanofluids. The present study is the continuation of the authors’ previous research on the effects of ultrasonication on the thermophysical properties of Multi-Walled Carbon Nanotubes (MWCNTs)-water nanofluid. Investigating the effects of ultrasonication time on samples’ stability, rheological properties, and pumping power of a water-based nanofluid containing MWCNTs nanoparticle is the main objective of the present study. The two-step method has been employed to prepared the samples. Moreover, a probe-type ultrasonic device has been used, and different ultrasonication times have been applied. The samples’ stability is investigated in different periods. The results revealed that prolonging the ultrasonication time to 60 min leads to improving the samples’ stability while prolonging ultrasonication time to higher than 60 min resulted in deteriorating the stability. As for dynamic viscosity, it is observed that increasing ultrasonication time to 60 min leads to decreasing the dynamic viscosity of the samples. As for pumping power, it is observed that the maximum increase in fanning friction factor ratio is less than 3%, which shows that adding MWCNTs to water does not impose a considerable penalty in the required energy for pumping power.

Three-dimensional simulation and experimental validation of solar air heater having sinusoidal rib

ABSTRACT A new geometry of roughness in the sinusoidal form has been investigated computationally using Computational Fluid Dynamics (CFD) software for examining the influence of roughness on heat transfer and fluid friction in solar air heater and results obtained have been compared with experimental results. The simulated results for smooth solar air heater are compared with Dittus-Boelter equation for heat transfer and Blasius equation for fluid friction. The deviation of simulated results are found to be 7.55% and 16.91%, respectively. In order to validate the simulated results experimental test rig was fabricated and experiments were carried out for the same set of parameters used in the simulation. The experimental results indicate that for the roughened absorber plate having a sinusoidal rib, the variation in heat transfer is within 9% from that of simulated results and for fluid friction, deviation is within 4%. The optimal value of thermohydraulic performance (THP) is obtained 2.05 for roughness pitch (P) = 10 mm and Reynolds number (Re) = 4000, where enhancement ratio of Nusselt number (Nur/Nus) and friction factor (ƒr/ƒs) are 2.48 and 1.76, respectively. The experimental value of THP is found to be within 6.77% of the value indicated by CFD analysis. The results are also compared with the triangular and square rib and found that the optimal THP of the proposed rib is 20.06% and 33.31% more.

On determining the power-law fluid friction factor in a partially porous channel using the lattice Boltzmann method

In the present work, the power-law fluid flow in a channel partially filled with a porous medium is numerically investigated using the lattice Boltzmann method (LBM). The porous domain, placed in the lower half of the channel, is represented according to a heterogeneous approach by a matrix of solid square disconnected blocks. The apparent viscosity of the power-law fluid is computed by locally varying the LBM relaxation factor. The results show the influence of geometry (porosity, number of obstacles, and hydraulic diameter), inertia (Reynolds number), and fluid properties (power-law index) over the partially porous-to-impermeable channel friction factor ratio. In general, the higher the porosity and the lower the number of obstacles, Reynolds number, and power-law index, the lower the friction factor. Finally, a correlation for the friction factor ratio as a function of the free region hydraulic diameter, permeability, and power-law index is presented for a specific channel configuration.

Experimental investigation on solar thermal air heater with a combination of roughness elements for heat transfer improvement

This work attempts to determine the influence of the integration of a combination of roughness elements on the heat dissipation and frictional losses occurring within the airflow channel pathways of a counterflow double-pass solar thermal air heater. The investigation considers three configurations, namely (1) circular rings with a relative width ratio of 4 (Case A), (2) circular rings with a relative width ratio of 6 (Case B), and (3) combination of circular rings and ribs (Case C). All three configurations were studied at different operating conditions of the Reynolds number (in the range of 4000 to 10,000) and relative roughness height (0.026 and 0.043). During the experiments, the operating parameters considered as constants for comparison were heat input (1000 W m−2), aspect ratio (20), and hydraulic diameter (0.048). The resultant observations of the three configurations were also compared with that of the smooth-plate absorber configuration. The observations revealed that with an increase in relative roughness height, there was only a marginal improvement in Nusselt number. The experimental findings reported that Case C resulted in maximum improvement in Nusselt number with a penalty of increase in friction factor among the different configurations. For Case C, the calculated maximum value of the Nusselt number ratio and friction factor ratio obtained corresponding to relative roughness height of 0.043 was 3.19 and 1.46, respectively. The maximum enhancement obtained in the thermohydraulic performance parameter for Case C configuration corresponding to the relative roughness height of 0.026 and 0.043 was 2.91 and 3.01, respectively.

Thermal-fluidic correlations for turbulent flow in a serpentine heat exchanger with novel wing-shaped turbulators

Turbulent flow structures and heat transfer in a 180-deg sharp turning two-pass internal coolant passage of a serpentine heat exchanger are explored experimentally. The coolant passage has a square cross-section with novel wing-shaped turbulators mounted on two sidewalls. The bulk Reynolds number (Re) and pitch ratio (Pi/DH) are varied from 5,000 to 20,000 and 0.6 to ∞, respectively. It is observed from the Particle Image Velocimetry measurements that there are wing-induced Fujiwhara co-rotating vortices. This unique flow feature leads to an averaged Nusselt number ratio (Nu¯/Nuo) up to 5.5 higher than the highest value of 4.4 reported previously based on the Infrared Thermography results. In addition, the elimination of wake vortices by the present wing-shaped turbulators results in the 61.5% to 66.8% reduction of friction factor ratio (f¯/fo) compared with the louvered channel. From the thermal-fluidic regression analysis for Pi/DH = ∞ and 0.7, the dimensionless spanwise-averaged mean transverse velocity and cross-sectionally averaged vorticity magnitude have the high correlation coefficient (R ≥ 0.7) with the spanwise-averaged local Nusselt number ratio in both the first and second pass. From the standpoint of thermal performance factor (TPF), Pi/DH = 0.7 is preferable to other values of Pi/DH since it provides the TPF value of 1.68 higher than the previous reported value of 1.41 for 15 ≤ f¯/fo ≤ 80. Finally, empirical correlations of Nu¯/Nuo and f¯/fo versus Re and Pi/DH are proposed.

Effects of Boot-Shaped Rib on Heat Transfer Characteristics of Internal Cooling Turbine Blades

Abstract Gas turbine engine has been widely applied to many heavy industries, such as marine propulsion and aerospace fields. Increasing turbine inlet temperature is one of the major ways to improve the thermal efficiency of gas turbines. Internal cooling for gas turbine cooling system is one of the most commonly used approaches to reduce the temperature of blades by casting various kinds of ribs in serpentine passages to enhance the heat transfer between the coolant and hot surface of gas turbine blades. This paper presents an investigation of the boot-shaped rib design to increase the heat transfer performances in the internal cooling turbine blades for gas turbine engines. By varying the design parameter configuration, the airflow is taken with higher momentum, and the minor vortex being at the front rib is relatively removed. The object of this investigation is increasing the reattachment airflow to the heated wall and reducing the vortex occurring near the rib for improving the performances of heat transfer using three-dimensional (3D) Reynolds-averaged Navier–Stokes (RANS) with the SST model. A parametric study of the boot-shaped rib design was performed using various geometric parameters related to the heel-angle, toe-angle, slope-height, and rib-width to find their effect on the Nusselt number, temperature on the ribbed wall, friction factor ratio of the channel, and thermal performance factor. The numerical results showed that the heat transfer performances are significantly increased with the heel-angle, toe-angle, slope-height, while that remained relatively constant with the rib width.

Thermohydraulic analysis of hybrid smooth and spirally corrugated tubes

A novel hybrid smooth and spirally corrugated tube is introduced in this article, which is the combination of smooth part and corrugated part. With the help of the finite volume method, a better understanding of the mechanism for heat transfer enhancement can be obtained. A qualitative and quantitative analysis about the effect of geometrical parameters on heat transfer, pressure loss and Performance Evaluation Criteria (PEC) is given, with pitch ratio p/D ranging from 3.50 to 4.50, and corrugation depth ratio e/D from the range of 0.09–0.22 at Reynolds numbers of 10,000–35,000. The results of heat transfer coefficient and turbulent kinetic energy confirm the superiority of the case with p/D = 3.75 in heat transfer enhancement, while the maximum augmentation is found to be 258%. To evaluate the pressure loss of the hybrid smooth and spirally corrugated tube, the friction factor ratio is calculated with the comparison of smooth tube. Results show that tube of the case with p/D = 4.5 generates less pressure loss, which is 1%–8% larger than smooth tube. As an indication for the comprehensive performance under the same pumping power, the highest value of PEC index is achieved by the case with p/D = 4.5, which is about 1.10 times that of the lowest value. With the corrugation depth ratio e/D = 0.09, the hybrid smooth and spirally corrugated tube has better thermal and hydraulic performance.

Experiments and Stress-Blended Eddy Simulations of turbulent flow over edge-rounded dimples

Experiments and numerical simulations have been conducted to reveal the detailed turbulent flow and heat transfer characteristics over the surfaces with spherical dimples with different edge schemes, including the sharp edge, the fully rounded edge and the upstream rounded edge. The dimples have the same depth-to-diameter ratio of hd/d = 0.2. Steady-state heat transfer experiments were carried out for the turbulent flow over the three dimpled surfaces within the Reynolds number range of 10,000 ≤ ReDh ≤ 60,000, and the globally averaged heat transfer enhancements and friction factor ratios were obtained. Furthermore, transient liquid crystal thermography technique was used to obtain the local heat transfer characteristics on the dimpled surfaces. In addition, numerical simulations were carried out with a newly developed hybrid RANS-LES method of Stress-Blended Eddy Simulation (SBES) and the local heat transfer enhancement, detailed flow structure and turbulence statistics data were obtained and analyzed. The experimental results show that the best thermal performance is achieved by the dimples with upstream rounded edge, indicating an increase of about 11.4% in total heat transfer enhancement and an increase of about 5.2% in pressure loss when compared to the conventional dimples with sharp edge. The numerical results show that the flow over the dimpled surfaces can be divided into five zones: the mainstream zone, the recirculation zone, the Kelvin–Helmholtz vortex zone, the upwash zone and the rear separation zone, and each zone has its unique flow features. It is also found that the lowest pressure is achieved by the dimple with fully rounded edge, which is due to the absence of flow separation behind the rear edge of the dimple. The upstream-edge-rounded dimples show the reduced recirculation flow in the recirculation zone, the enhanced impingement and upwash flow in the upwash zone near the rear edge. These cause the stronger production of turbulent kinetic energy behind the rear edge, which are responsible for the higher thermal performance.

Experimental Study on Flow Resistance Characteristic of Corrugated Low Finned Tubes

The heat transfer enhancement techniques have been developed to the third generation. The most popular and successful enhancement techniques are the artificial roughness surface and helically corrugated tube. Corrugated low finned tube is a kind of helically corrugated tube with trapezoidal shape groove. In this paper, the flow resistance characteristic of corrugated low finned tubes was studied experimentally. The results showed that all the enhanced tubes had a larger friction factor than the smooth tube due to the turbulence augmentation and rotational flow produced by helical rib. Moreover, the friction factor ratios slightly increased with the raise of Reynolds number and rib height presents more significant effect on flow resistance. Finally, all the experimental data were fitted as the function of Reynolds number, Prandtl number, tube pitch and rib height. The research results can provide a foundation for designing heat exchangers using this enhancement technique.

Visualization of heat transfer characteristics using thermochromic liquid crystal temperature measurements in channels with inclined and transverse twisted-baffles

Channels with ribs/baffles are widely applied in thermal engineering applications such as heat exchangers, solar water/air heaters and gas turbine cooling. In the present work, inclined and transverse twisted-baffles (I-TBs/T-TBs) are developed for heat transfer enhancement in a channel. The effects of Reynolds number (Re = 4000, 8000, 12,000, 16,000 and 20,000) roughness pitch ratios (p/w = 4.0, 6.0, 8.0, 10.0 and 12.0) and baffle twist ratios (y/w = 2.0, 3.0, 4.0 and 5.0 corresponding to twisted-baffle loop numbers (N) of 5, 7, 8 and 9) were investigated using air (Prandtl number, Pr = 0.7) as a working fluid. Heat transfer behavior was examined using thermochromic liquid crystal temperature measurements. Typical transverse and inclined baffles were also tested for comparison. Heat transfer, flow friction and thermal performance are reported in terms of Nusselt numbers (Nu), Nusselt number ratios (Nu/Nus), friction factors (f), friction factor ratios (f/fs) and thermal performance indices (η). Experimental results reveal that under most conditions examined, I-TBs show better heat transfer, lower frictional losses and higher thermal performance than TBs, IBs and T-TBs. For I-TBs, maximum heat transfer and thermal performance are obtained at a moderate pitch ratio (p/w = 6.0). However, in cases of T-TBs, heat transfer and thermal performance monotonically increase with a decreasing pitch ratio. Friction losses caused by both I-TBs and T-TBs decrease considerably with increasing pitch ratio. For I-TBs, heat transfer and thermal performance monotonically increase with increasing twist ratios. However, for T-TBs, maximum heat transfer and thermal performance are obtained at y/w = 3.0. Over the present studied range, a channel with I-TBs having optimal geometry (p/w = 6.0 and y/w = 5.0) yields maximum thermal performance indices, as high as 1.98, which is greater than the maximum values yielded by channels with T-TBs, TBs, IBs, and smooth channels, by around 74.1%, 98%, 52.5% and 98.3%.

A COMMENT ON UNSTEADY–PERIODIC FLOW FRICTION FACTOR: AN ANALYSIS ON EXPERIMENTAL DATA GATHERED IN PULSATILE PIPE FLOWS

In 1940’s, Schultz- Grunow proposed that time-average value of friction factor, λ_u,ta was similar to its corresponding steady state value, λ for the presence of gradual and slow oscillations in pulsatile flows. A recent approach was available for low frequency pulsatile flows through narrow channels in transitional and turbulent regimes by Zhuang et al, in 2016 and 2017. In this analysis; extensive experimental data of λ_u,ta in fully laminar and turbulent sinusoidal flow are processed in the measured time-average Reynolds number range of 1390 ≤ Re_ta ≤ 60000 disregarding the transitional regime. The ranges of dimensionless frequency-Womersley number, √(ω') and oscillation amplitude, A_1 are 2.72 ≤ √(ω') ≤ 28 and 0.05 ≤ A_1≤ 0.96 respectively. A multiplication element is defined as Mel = Re_ta×√(ω^'). A modified friction multiplier, λ_(Mel ) which is similar to the conceptual parameter of Zhuang et al’s friction factor ratio C ( λ_Mel = λ_(u,ta)/λ ) is also referred. The correlation of λ_Mel = λ_Mel (Mel) is dependent on flow regime and the magnitude of Re_ta for the range of √(ω^') > 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of λ_Mel = 1 is observed for turbulent flow cases with Re_(ta ) ≥ 35000. In laminar regime the magnitude of Re_(ta ) is governing the fact. The magnitude of λ_Mel varies in 0.589 ≤ λ_Mel ≤ 28.125 for Re_(ta ) ≤ 5000 while λ_Mel = 1 is obtained for Re_(ta ) > 5000. The graphical representation of λ_Mel = λ_Mel (Mel) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.

Numerical evaluation on the decaying swirling flow in a multi-lobed swirl generator

Accurate predictions of decaying swirling flow behavior in the multi-lobed swirl generator (MLSG) are essential for certain engineering applications. In this study, decaying swirling flow characteristics in an MLSG are examined using the Computational Fluid Dynamics (CFD) technique with a Reynolds stress turbulence model (RSM). The effects of different lobe numbers (n) and pitch length ratios (P/D) on swirl intensity, pressure drop, friction factor coefficient, and decay rate are observed with Reynolds number from 50,000 to 125,000. Combined with the pressure loss, the efficiency of swirl induction is evaluated by introducing a swirl effectiveness (SE) evaluation criterion. The initial swirl intensity is shown to first increases and then decreases as lobe number increases. The maximum value is obtained at lobe number n = 4. The pitch length ratios P/D corresponding to the optimal SE value obtained from different lobe also differ. The optimal SE value is achieved at n = 4 and P/D = 8. The friction factor ratio f s/f p decreases as pitch length ratio increases, but the decreasing trend decelerates over time. Correlations based on the numerical predictions of friction factor ratio f s/f p and decay rate β are presented accordingly.

Investigations of the turbulent thermal-hydraulic performance in circular heat exchanger tubes with multiple rectangular winglet vortex generators

This work explores the turbulent thermal-hydraulic performance in circular heat exchanger tubes with multiple rectangular winglet vortex generators. Numerical simulations demonstrate that multi-longitudinal vortices are induced, which enhances fluid mixing in the tubes. The effects of geometric parameters including the circumferential number of rectangular winglets (N = 4, 6, 8), height ratio (HR = 0.05, 0.1, 0.2), and pitch ratio (PR = 1.57, 3.14, 4.71), are examined experimentally. The results demonstrate that both the friction factor and Nusselt number increase with the height ratio and the number of rectangular winglets due to the better fluid mixing performance caused by multi-longitudinal vortices with higher turbulent kinetic energy. For the considered Reynolds numbers, the friction factor and Nusselt number ratios are in the range of 1.46–11.63 and 1.15–2.32, respectively. An increase in the number of rectangular winglets improves the thermal enhancement factor (TEF) for HR = 0.05, while the opposite trend is found for the other cases. The maximum TEF is up to 1.27. Moreover, correlations for the friction factor and Nusselt number are derived based on the experimental results for practical applications.

Discharge estimation in converging and diverging compound open channels by using adaptive neuro-fuzzy inference system

The computation of total flow in a flooded river is very crucial work in designing economical flood defense schemes and drainage systems. Further, under non-uniform flow conditions like in converging and diverging compound channel, the traditional methods provide poor results with high errors. The analytical methods require the system of nonlinear equations to be solved, which is very complex. So, mathematical models that prompt in taking care of a complex system of problems are solved here through an artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). By utilizing ANN and ANFIS, an attempt is made to predict the discharge in converging and diverging compound channels. In the analysis, the most influencing dimensionless parameters such as friction factor ratio, area ratio, hydraulic radius ratio, bed slope, width ratio, relative flow depth, angle of converging or diverging, relative longitudinal distance, and flow aspect ratio are taken into consideration for computation of discharge. Gamma test and M-test have been performed to achieve the best combinations of input parameters and training length respectively. The significant input parameters that influence the discharge are found to be friction factor ratio, hydraulic radius ratio, relative flow depth, and bed slope. A suitable performance is achieved by the ANFIS model as compared to ANN model with a high coefficient of determination of 0.86 and low root mean square error of 0.005 in predicting the discharge of non-prismatic compound channels taken under consideration.