Friction Factor Research Articles

Parametric study on thermal performance augmentation of TiO2/water nanofluids flowing a tube contained with dual counter twisted-tapes

The study of compound heat transfer enhancement technique using dual counter twisted tapes (DCTs) together with TiO2/water nanofluids was carried out. The dual twisted tapes in form of counter-swirl tape arrangement were utilized at three twist ratios (y/w = 1.5, 2.0 and 2.5). TiO2/water nanofluids having three different volume concentrations (φ = 0.05, 0.10 and 0.15 %) were employed as the testing fluids. The results indicated that heat transfer rate, friction factor and thermal enhancement index rose with decreasing tape twisted ratio and elevating nanofluid concentration. The TiO2/water nanofluids applied in the present work offered higher Nu than pure water (the base fluid) by 7.3–10.0 %. The application of DCT with the smallest y/w of 1.5 and TiO2/water nanofluids with the largest φ of 0.15 vol% led to the highest thermal enhancement index (TEI) of 1.53, under the same pumping power criteria. Additionally, the k-nearest neighbor (k-NN) and artificial neural network (ANN) were developed to predict the thermal enhancement index (TEI). It was found that the k-NN and ANN models provided maximum R2 values of 0.919 and 0.992 f, respectively.

Heat transfer scrutiny in EMHD ternary hybrid nanofluid flow between convergent/divergent channels with stretchable walls

ABSTRACT The main interest of the existing work is the numerical and analytical exploration of heat transference on MHD Jeffery-Hamel flowing of a ternary hybrid nanofluid with an external magnetized force and electrical field (EMHD). The two walls of the system are also taken to be stretchable (shrinkable). Mixture base fluid (ethylene glycol-water 50%–50%) hybrid nanofluid containing MoS2, Al2O3, and TiO2 as the nanoparticles are contemplated. The modeled partial differential equations were converted to nonlinearly ordinary differential equations by applying the similarity transformations and resolved analytically by utilizing the Duan – Rach Approach (DRA). The present results in particular cases are compared to results obtained by the HAM (homotopy analysis methodology)-based Mathematica BVPh 2.0 code and by the Runge-Kutta Fehlberg 4th–5th order (RKF-45) for validation. The effect of varied factors on non-dimensional rapidity, temperature profiles, frictional force factor, and Nusselt quantity has been examined and explained via tabular and graphical outcomes. Certainly, new modeling and reliable analytic treatment via the DRA approach for the ternary hybrid nanofluid is a sizable accomplishment of the current analysis.

Evaluation of nanoparticle shape factor on a laminar forced convective heat transfer characteristics of various nanofluids flow in a tube using single-phase numerical model

Nanotechnology is advantageous in improving thermophysical properties and enhancing heat transfer rate compared with conventional fluids due to their superior thermophysical properties. These properties vary with many parameters such as concentration and shape. In this study, the effect of nanoparticles shape is numerically explored on heat transfer performance under a laminar flow regime (Re=500 and 2000) through the smooth tube. Heat transfer enhancement capability of the nanoparticle shapes with targeted reference to average Nusselt number, average Darcy friction factor, pumping power, and performance evaluation criterion have been investigated. Three types of nanofluids (Fe3O4/water, Al2O3/water, and GO/water) with various nanoparticle shapes (brick, cylindrical, platelet, and spherical) and different nanoparticle volume fractions (φ=1.0, 2.0, 3.0, and 4.0%) have been used as heat transfer fluid in analyzes. Numerical results show that heat transfer performance was greatly influenced by changing nanoparticle shapes. The highest average Nusselt number was obtained for GO/water nanofluid with platelet nanoparticle shape and φ=4.0%. Compared to water, Fe3O4/water, and Al2O3/water, the average Nusselt number in GO/water increased by 64.34%, 54.02%, and 43.41%, respectively. The highest performance evaluaton criterionwas obtained for the GO-water nanofluid with platelet nanoparticle shape at Re=2000. On the other hand, it is found that the Fe3O4/water nanofluid with platelets nanoparticle shape causes the highest pumping power compared with other analyzed nanofluids.

Condensation heat transfer performance of R290 in a plate heat exchanger for electric vehicle heat pumps

In the continuous improvement of electric vehicles driving range, a heat pump system with low-global warming potential (GWP) refrigerant is a promising solution. In the present work, the condensation heat transfer coefficient (HTC) and frictional pressure drop (FPD) were experimentally evaluated in an offset strip fins embedded plate heat exchanger (PHE), using an eco-friendly, low-GWP refrigerant R290 as the working fluid. A Modified Wilson Plot Method was used to predict the heat transfer of the coolant side (water/ethylene glycol; 50/50 %). The main focus of the present study revolves around the R290-to-coolant condensation experiment, wherein we analyzed the influence of mass flux (G = 20–50 kg m−2 s−1), heat flux (q = 3–12 kW m−2), and saturation temperature (Tsat = 40–55 °C) on HTC and FPD within the PHE while variable mean vapor quality (xm). According to the results, all experimental conditions were fall in the forced-convection condensation regime. The results state that HTC increases with a rise in q, G, and xm, but decreases with a surge in Tsat. Conversely, FPD increases with a rise in G and xm, and decreases with a escalation in Tsat, while q has no significant impact. Correlations were developed to predict the Nusselt number and friction factor values of R290 with mean absolute errors of 10.6 % and 11.2 %, respectively. These correlations are compared to previous research findings, signifying their efficacy in predicting the heat transfer characteristics of R290 within PHEs.

Numerical investigation of flow boiling characteristics of R134A in a smooth horizontal tube

Three-dimensional transient simulations using ANSYS Fluentʼs mixture multiphase model was conducted to investigate the impact of heat flux, mass flux, and saturation temperature variations on pressure drop behaviour and heat transfer characteristics during flow boiling of R134a refrigerant in smooth horizontal tubes of different diameters. The simulations employ an implicit numerical method to solve the governing equations, with relevant source terms for mass and energy transfer, incorporating the continuum surface force (CSF) and shear stress transport (SST) κ-ω models to account for surface tension and flow turbulence respectively. The results are presented in both dimensional (heat transfer coefficient and pressure drop) and non-dimensional (Nusselt number and two-phase frictional factor) forms. The Nusselt number shows a direct relationship with the Reynolds number, while the two-phase friction factor exhibits different behaviour. At higher vapor quality, mass flux significantly affects heat transfer performance and pressure drop. Heat flux plays a crucial role in heat transfer, but its impact on pressure drop is negligible. Higher saturation temperatures enhance heat transfer while reducing pressure gradients. The obtained results demonstrate good agreement with existing correlations, with mean absolute deviations (MAD) as low as 1.2 % for the heat transfer coefficient and 23.7 % for the pressure drop behaviour. This highlights the model's accuracy in predicting flow boiling behaviour of R134a in smooth horizontal channels, providing valuable insights for thermal analysis. The findings contribute to the understanding of flow boiling processes and aid in designing and optimizing efficient heat exchangers for various engineering applications.

Numerical study of the effect of helical fuel rod geometry on single-phase flow and heat transfer characteristics

Helical fuel is a promising nuclear fuel proposed to improve the core power density and safety margin. In this study, the effect of helical fuel rod geometry on single-phase flow and heat transfer characteristics in helical fuel annuli has been investigated. The volumetric energy source is applied to the fuel pin, and coupled walls are used at the coolant-cladding and cladding-fuel interfaces. The numerical method with SST k-ω turbulence model has been validated with the results of bare annulus. The flow field, fuel central temperature, friction factor, and the circumferential distribution of swirl intensity, heat flux and wall temperature are obtained based on the numerical simulation. The increase in R2/R1 will result in broadening transverse flow region, reducing the gradient of surface heat flux and wall temperature, lowering the maximum wall temperature, but increasing the fuel central temperature and has no significant effect on the friction resistance. The decrease of helical pitch increases the swirl intensity and friction factor, but worsens the heat transfer at the blade roots.

Thermohydraulic analysis of nanofluid flow in tubular heat exchangers with multi-blade turbulators: The adverse effects

Based on the significance of heat transfer in tubular flows, various methods of heat transfer enhancement have been developed by scholars. The use of turbulator inserts like twisted tapes is widely discussed and suggested by researchers, and many studies have concentrated on the positive influence of these devices. However, the question is whether these devices always positively impact heat transfer and fluid flow. In this study, efforts were made to find possible adverse impacts of using twisted tapes on the average Nusselt number (Nu), friction factor (f), flow behavior, and performance evaluation criterion (PEC) of water-titania nanofluid. Three-dimensional (3D) numerical methods were used to assess a combination of three different configurations of 156 cases with/without turbulators with different numbers of blades and pitch ratios (PR). Results suggest that at Reynolds number (Re) = 4000, 6000, and 8000, only 25 %, 25 %, and 22.9 % of the examined cases led to PEC values over 1. Based on the results, while twisted tapes raised the Nu by up to 65.1 %, the f can be increased by up to more than six times. Furthermore, streamlines and velocity magnitude contours were employed to discuss the fluid flow behavior in the presence of the turbulators. According to the findings, while with the best turbulator, the PEC value was increased by only 6.3 %, some of the turbulators reduced this parameter by up to 11.8 %, which is more severe. The worst performance was observed with the Case C (three-bladed) turbulator at a PR value of 11, which reduced the PEC by 11.8 %.

Heat transfer analysis of subcooled flow boiling in copper foam helical coiled heat exchanger – A pore-scale numerical study

High performance thermal energy systems are crucial in fulfilling the growing demand of thermal energy. Consequently, numerous heat transfer enhancements have been proposed. Some of the promising methods are boiling flow heat transfer, helical coiled tube and metal foam insert. Although the performance of each strategy has been extensively studied, based on our literature review, the effectiveness of combining these strategies has not been investigated. This missing information may impede further development of efficient heat transfer systems. This study is therefore performed to investigate subcooled flow boiling heat transfer in helical tube with copper foam insert. A high-resolution three-dimensional pore scale model that considers the shape, porosity and pore density of the metal foam is developed and validated against the published experimental results. Using the model, the effect of inlet temperature, mass flux, wall heat flux, porosity, pore density and half-filled metal foam are studied. The results suggest that operating parameters have mild effects on the heat transfer performance. In contrast, porosity and pore density show significant influence in heat transfer coefficient and pressure drop. It has also been found that total heat transfer surface area and base area are better in characterizing heat transfer in pore-scale level than porosity and pore density at pore-scale level. Moreover, implementing metal foam at outer half of the tube is observed to offer slightly better heat transfer than implementing it at the inner side by around 4.8%. Overall, this study indicates that helical metal foam tubes offer the best performance at mass flux of 200 kg/m2∙s with performance index of 0.72, while straight tubes with 0.90 porosity has the highest performance index of 0.66. Empirical correlations to relate dimensionless parameters to the Nusselt number and friction factor is generated. Finally, the model developed in this study can serve to provide guidelines for the upcoming studies in boiling in metal foam structure and assist in designing metal foam heat exchangers.

Employing uniform and non-uniform inner twisted elliptical tubes in a double-pipe heat exchanger

Turbulent hydrothermal characteristics in a double-pipe heat exchanger with an internal twisted elliptical tube (TET) are investigated. The impacts of aspect ratio (AR = 1.4–2), uniform twist pitch (p = 100 mm-400 mm), and non-uniform twist pitch (five cases) on flow stream characteristics and heat transfer of parallel and counter-flows are investigated numerically. Utilizing a TET with a non-uniform twist pitch as an innovative approach yields noteworthy results, particularly in contrast to the traditional use of TETs with uniform twist pitch, owing to the longitudinal asymmetry. The outcomes depict that the pressure drop and heat transfer augment as the uniform twist pitch declines and the AR rises. The counter-flow has a more significant average Nusselt number than the parallel-flow by about 2–4 % without increasing the friction factor. Still, in some cases of non-uniform twist pitch, the average Nusselt number of the parallel flow is even 4 % higher than the counter-flow. The case with p = 100–200–400 mm (three parts with various twist pitches) and parallel-flow exhibits the most significant performance evaluation criterion (PEC) among the non-uniform twist pitch. As the aspect ratio increases from AR = 1.4 to AR = 2, the PEC factor in the counter-flow mode increases; however, there is an out-of-trend point at AR = 2 for the parallel-flow mode. The PEC factor augments about 8.47 % and 6.16 % for the counter-flow and the parallel-flow modes, respectively. The growth of TET twist pitch by 300 % reduces PEC by about 13.3 % in the counter-flow. The most significant PEC value is 1.166, which belongs to the case with the counter-flow condition and p = 100 mm.

Dynamical steady Carreau fluid with heat generation and porosity effect in a suspension of hybrid solid and dust particles

Hybrid nanofluid is a superior working fluid that is considered as appropriate for variety of applications, including machine cutting, engine applications, automobile cooling, photovoltaic thermal management, electronic component thermal management, and solar collectors. With the motivation these application, magneto hydrodynamic Carreau fluid is explored in this study when graphene and titanium hybrid nanoparticles with heat generation and porosity are taken into account. Titanium alloy nanoparticles combined with base water are used to simulate the process. Titanium is utilized in the military and aerospace because it is strong and lightweight. It is also employed in biology as an anti-microbial, anti-biotic, and anti-fungal agent. The ensuing collection of governing equations (P.D.E.) is changed into an assortment of O.D.E. with the use of an appropriate similarity transformation. This O.D.E. is then solved by implementing the Runge-Kutta shooting method. Graphs have been used to study variation behavior accurately. Local Nusselt number and Friction factor were examined for different kinds of physical factors. We concluded after the debate that, the influence of porosity or heat generating parameter improves temperature profile. When porosity effect is applied, velocity profile is reduced, and temperature profile is increased by amplifying porosity effect.

Effects of non-uniform wavy ribs on flow and heat transfer characteristics of turbine blade cooling channel

Aiming at the problem of reduced heat transfer performance and uneven distribution along the ribbed channel in aero-engine turbine blades, the influence mechanism of rib height, rib angle and fillet radius on the flow and heat transfer characteristics of wavy rib cooling channel under different inlet Reynolds numbers is analyzed by experimental and numerical methods. The research illustrates that the non-uniform change of the rib height has the most profound influence on the heat transfer performance of the ribbed channel. Schemes featuring larger initial and final rib heights demonstrate superior heat transfer performance and uniformity, with the friction factor primarily determined by the maximum rib height. The optimal rib height variation scheme shows a 22.6 % increase in overall Nu/Nu0, with only a 6 % reduction in heat transfer evenness. The non-uniform variation of rib angle and fillet radius mainly affects the local heat transfer and friction factor. Increasing Reynolds number, the distribution of friction factor of the large rib height scheme changes more drastically. At a large Reynolds number (Re = 40000), the enhanced heat transfer in the middle and rear sections of the channel due to the larger rib angle and fillet radius comes at the cost of increased pressure loss.

CFD investigation of flow hydrodynamics and optimization in an industrial‐scale annular lance with swirl flow

AbstractSwirling flow has been applied in various fields due to its ability to enhance mass, heat, and momentum transfer performance. However, the generation of swirling flow occurs at the price of augmenting the pressure drop, and enhancing the friction and shear intensity of the jet with respect to the reactor wall. In the present work, the impact of geometrical configurations of the swirler on the hydrodynamics of the fluid in an industrial‐scale annular lance is investigated via the computational fluid dynamics method, with the discussion of the friction coefficient of the lance walls. It shows that the axial flow injected from the central lance is transformed into a weak swirl flow upon the introduction of swirl flow generated in the casing pipe. Within the mixing region, the interaction between axial and swirl flows results in elevated turbulent kinetic energy. Notably, under varying geometrical configuration conditions, the pressure drop between the inlet of the central pipe and the outlet is maximized. Additionally, the highest friction factor appears at a height of 1.35 m along the middle shell, with a value of 96.67.

A Note on the Moody Diagram

In this work, we underscore the significance of selecting an appropriate scaling to derive dimensionless quantities that accurately reflect their dimensional counterparts, thereby enhancing the comprehension of the underlying physics. For the loss of head in a pipe flow, we argue that employing inertial force (or kinetic energy) to non-dimensionalized pressure force (or mechanical energy loss) lacks physical justification. As a result, an anomalous trend emerges for the classical friction factor: it decreases as the dimensionless flow rate (Reynolds number) increases, contrary to the behavior observed in the corresponding dimensional quantities. Conversely, by non-dimensionalizing the pressure force with the viscous force, a novel friction factor arises. In laminar flow, it is constant, while in turbulent flow, it is a monotonically increasing function of the Reynolds number, mirroring the behavior observed in the dimensional problem.

Experimental investigation and performance prediction of SAH using different arc rib roughness geometries – A comparative study

This study aims to investigate and compare the thermal performance of a solar air heater using a passive technique to enhance heat transfer between the absorber plate and the flowing fluid. The technique involves generating turbulence near the heat transferring surface through the use of artificial rib roughness. The study focuses on two different novel roughness geome-tries: full symmetrical arc rib roughness and half symmetrical arc rib roughness. By introducing additional gaps and varying the number of gaps in the roughness geometries, the study examines their effects on the solar air heaters thermal performance. The artificially roughened surface creates different turbulent zones, which are essential to the development of different types of turbulence in the vicinity of the heat transferring surface. The study finds that an optimal escalation in Nusselt number and friction factor by 2.36 and 3.45 times, respectively, occurs at certain gap numbers as 6 and ng as 5 for full symmetrical arc rib roughness. The maximum thermal-hydraulic performance parameter of 1.66 is attained at a Reynolds number of 6 000. The study also conducts correlation, mathematical modeling, and performance prediction under different operating circumstances.

Free convective heat flow from cold and heated conical shape bodies in Newtonian liquids

Investigation on the simulation effects of free convection flow from a cold and heated cone with a downward pointing tip in various stagnant fluids is presented in this study. Examining the steady-state isotherm patterns around the cone to determine heat transfer characteristics. Results are presented for friction factor and Nusselt number distributions Over the surface of the cone for distinct dimensionless quantities like Pr and Gr to deliver an extensive class of dimensionless numbers. The commercial program ANSYS CFX 16.0 was used to solve the regulating equations which governs the motion vis., momentum mass and energy were computed. The temperature as well as flow fields are coupled using the Boussinesq approximation in order to simplify the governing equations and capture natural convection. Heat transmission has a rather minimal influence on the local Nusselt number for low Grashof and Prandtl values, according to the findings. It gains strength as the Grashof and Prandtl numbers grow, because of the extreme curvature of the isotherms, the maximum value of the local Nusselt number may be found around the corner of the vertical cone in both cones. The current simulations closely match the numerical values provided in the printed matter.

Numerical assessment of solar air heater performance having a broken arc and broken S-shaped ribs as roughness

This research article aims to provide a detailed numerical study of the multifaceted impact of S-shaped and broken arc roughness on solar air heaters. Therefore, a strong comparison was made between the modified heaters and smooth heaters for Reynolds numbers ranging from 2 00022 000. Also, the impact of two parameters, i.e. pitch and gap was analyzed to optimize the performance of the heater. The gap varies from 0.3 mm to 0.9 mm in both types of ribs with a step size of 0.2 mm. Afterwards, the pitch distance between both types of roughness was varied from 15 mm to 25 mm in the step size of 5 mm. Notably, it has been observed that among all the considered configurations, the gap length of 0.9 mm and pitch length of 25 mm have shown significant improvements in heat transfer characteristics. The specific combination of the gap of 0.9 mm and pitch of 25 mm has demonstrated better heat transfer capabilities at the expense of an increased friction factor. Lastly, the thermal performance factor of the systems was analyzed and reported. It was reported that the pitch length of 25 mm and gap length of 0.9 mm have shown a maximum thermal performance factor value from 2.9 to 3.3, while the pitch length of 25 mm and gap length of 0.3 mm have depicted the lowest thermal performance factor value. In terms of the overall performance, i.e. the thermal performance factor, the combination with a gap of 0.9 mm and pitch of 25 mm has shown the best performance, while a gap of 0.3 mm and pitch of 25 mm has yielded the worst performance.

Thermal performance analysis of corrugated plate solar air heater integrated with vortex generator

This research investigates the impact of vortex generators integrated with a corrugated absorber plate of solar air heater on the enhancement of heat transfer and thermal-hydraulic performance utilizing a 3D numerical model for Reynolds numbers varying from 7,000 to 25,000. Three different types of vortex generators (rectangular, trapezoidal, and delta) are investigated separately. Vortex generators in two pairs with various angles of attack of 15º, 30º, 45º, and 60º are mounted on the entrance section's upper wall of the domain of computation. The current numerical models are validated by comparisons with experimentally published data. The velocity vectors, turbulent kinetic energy, friction factor, Nusselt number, and thermal-hydraulic performance parameters are examined for the considered current cases considered. The numerical results demonstrate a significant impact of vortex generators on friction loss and transmission of heat. The values of thermal-hydraulic performance for utilizing a corrugated absorber plate integrated with vortex generators are found to be considerably higher than those for using a corrugated absorber plate alone. The highest value of the thermal-hydraulic performance parameter is 0.91 in the case of rectangular vortex generators at Re of 7000 and an angle of attack of 30º.

Numerical investigation of fluid flow and heat transfer characteristics of MWCNT-Al 2 O 3/H 2 O hybrid nanofluid flowing through a novel semi-arc ribbed square duct

This study carried CFD analysis to study the fluid flow and heat transfer characteristics of MWCNT- Al 2 O 3 / H 2 O hybrid nanofluid flowing through square duct equipped with novel semi-arc ribs. The turbulent flow simulations are performed at varying Reynolds numbers ( Re ) between 3,000 and 18,000 and nanoparticle volume concentration ( φ ) range of 1–4% for different rib parameters, namely relative stream pitch ratio ( X pr ) range from 2.67 to 3.67, Rib height ratio ( R hr ) range from 0.05 to 0.20, number of ribs ( n ) range from 1 to 4. Different performance indicators, such as Nusselt number ( Nu ), friction factor ( f r ) , and thermal hydraulic performance (THP) was examined to evaluate the system performance. The RNG k ‐ ε model was engaged to simulate turbulent nanofluid flow within the channel under constant temperature condition (T = 300 K). The findings indicated that the development of vortex flow and increased turbulence due to the effects of arcs can improve the heat transfer enhancement. The THP, Nu and f r were found to be highest for R hr = 0.15 , X pr = 3.34 , φ = 4 % , and n = 3 , yields to the best THP at 1.94.

Numerical study of turbulent heat transfer and particle deposition in enhanced pipes with helical roughness

Large-eddy simulations of turbulent heat transfer and solid particle deposition in helically rib-roughened pipe flows have been performed for different Reynolds numbers Re and various particle diameters Dp. An Euler–Lagrange approach, using cyclic boundary conditions for the continuous and the dispersed phase, have been applied to achieve a fully developed turbulent flow. An adhesion and removal model have been added to the multiphase large-eddy simulations to take into account the physical effect of particle re-entrainment. The complex interactions between particle-laden turbulent flow and the structured pipe wall in multiple-started helically ribbed pipes are numerically investigated with regard to heat transfer, pressure loss, and particulate deposition. The results of the Nusselt numbers Nu, friction factors fd, and particle deposition rates Ṅd are presented for each geometry variant. For same Reynolds numbers Re, significant differences of those values have been observed for the differently structured pipes.

Numerical study of parabolic trough solar collector’s thermo-hydraulic performance using CuO and Al2O3 nanofluids

The current study aims to boost the thermal and hydraulic performance of a parabolic trough solar collector by modifying the absorber tube with a porous obstacle insertion. The research investigates how porous media and nanoparticles together influence the system's thermal performance, considering factors like outlet temperature, average Nusselt number, average friction factor, thermal performance factor, and thermal efficiency at different mass flow rates. To achieve better thermal performance, the base fluid, water, is substituted with Copper Oxide (CuO)-water and Aluminum Oxide (Al2O3)-water nanofluids at concentrations ranging from 3% to 7% by volume. The experiments are conducted at 800–1000 W.m-2 heat flux on the outside tube surface. The finite element method discretizes the governing equations for 3-D fluid flow simulations conducted in COMSOL Multiphysics 6.1 software. The simulation is carried out considering four altered rates of mass flow, ranging from 0.015 kg.s−1 to 0.060 kg.s−1. The findings show that at a Reynolds number of 1428 and a 7% volume concentration, the maximum thermal performance factor recorded is 1.97 and 1.99 for Al2O3 and CuO nanofluids, respectively. Additionally, the absorber tube achieves maximum thermal efficiency of up to 77.93% and 79.03%. Also, the augmentation in the average Nusselt number ratio is 26.27% and 36.74% when using Al2O3 and CuO nanofluids, respectively, with the tube height-to-diameter ratio (h/D) set at 0.42. The average friction factor ratio was reduced by 2.9% using CuO nanofluids compared to Al2O3 nanofluids. Thermal efficiency was enhanced by 7.2% using a porous obstacle insert in the parabolic trough solar collector system compared to a non-porous system.