Uniform Heat Research Articles

Thermophoretic particle deposition effect on a squeezed flow of radiative Jeffrey fluid past a sensor surface with uniform heat source/sink and chemical reaction

Abstract This anticipated model investigates the time-dependent, and incompressible 2D magnetized Jeffrey liquid flowing on a sensor surface placed between two infinite parallel plates with the existence of a uniform heat source/sink. The lower plate remains fixed while the upper plate is subject to squeezing. For the heat and mass transmission processes, the consequences of radiative heat flux, chemical reaction, and thermophoretic particle deposition are applied and analyzed. The envisioned model is supported by prescribed heat and mass flux conditions. The uniqueness of the proposed model is the analysis of the unsteady squeezed flow of Jeffrey liquid over a sensor surface, accounting for radiative heat flux, thermophoretic particle deposition, and variable thermal conductivity. The model possesses applications in microfluidic sensors, biomedical devices, thermal management systems, and inkjet printing. The equations comprising the model are subject to similarity transformations. The bvp4c package is utilized to analyze the dynamic flow system. The connotation of arising parameters with the associated profiles is depicted through graphs and tables. It is examined that fluid velocity, temperature, and concentration profiles are dwindling functions of squeezed parameter. It is also witnessed that the concentration of liquid drops with an enhancement of thermophoretic and chemical reaction parameters. The validation of the truthfulness of the envisioned model is an added feature of this study.

Numerical Assessment of the Thermal Performance of Microchannels with Slip and Viscous Dissipation Effects

Microchannels are widely used across various industries, including pharmaceuticals and biochemistry, automotive and aerospace, energy production, and many others, although they were originally developed for the computing and electronics sectors. The performance of microchannels is strongly affected by factors such as rarefaction and viscous dissipation. In the present paper, a numerical analysis of the performance of microchannels featuring rectangular, trapezoidal and double-trapezoidal cross-sections in the slip flow regime is presented. The fully developed laminar forced convection of a Newtonian fluid with constant properties is considered. The non-dimensional forms of governing equations are solved by setting slip velocity and uniform heat flux as boundary conditions. Model accuracy was established using the available scientific literature. The numerical results indicated that viscous dissipation effects led to a decrease in the average Nusselt number across all the microchannels examined in this study. The degree of reduction is influenced by the cross-section, aspect ratio and Knudsen number. The highest reductions in the average Nusselt number values were observed under continuum flow conditions for all the microchannels investigated.

Analytical generalized thermal resistance model for conductive heat transfer in pebble beds based on heat flux weighted temperature difference

A novel model for inter-particle contact thermal resistance based on analytical solutions is proposed. By applying the concept of heat flux weighted temperature difference in thermal resistance modeling for the first time, this model offers greater physical significance than traditional thermal resistance models. It effectively describes the dissipation in the heat transfer process and the influence of particle radius on thermal resistance, making it a generalized thermal resistance model suitable for multi-dimensional systems. The impact of applying different levels of uniform heat flux boundary conditions on thermal resistance is analyzed from the perspective of energy dissipation, revealing that a more uniform heat flux input results in lower thermal resistance. The effects of contact radius and particle size on the dimensionless generalized thermal resistance of inter-particle contact were studied, showing that the dimensionless resistance increases with larger particle contact radius and smaller particle size. Using the thermal discrete element method, the thermal resistance model with uniform heat flux density boundary conditions was applied to calculate the effective thermal conductivity of the pebble bed. Considering the distribution of contact radius, differences in effective thermal conductivity at various heights of the pebble bed due to different contact radii were examined and compared with the traditional fixed-coefficient contact resistance model. It was found that the difference between the two models decreases as the contact radius decreases. Finally, multiple sets of fixed contact radii were established under three different particle sizes, revealing that as the contact radius increases, the deviation between the new generalized resistance model and the traditional fixed-coefficient model rises from 8.18 % to 14.64 % for different particle radii.

A Universal Target Plate Design Scheme for Stellarators: theoretical basis and its application to heat load control

Abstract This study introduces a novel divertor target design scheme for stellarators, grounded in mathematical treatments and tailored to control toroidal heat load distributions. Initially, a differential equation characterizing toroidally uniform heat load distribution has been established in a two-dimensional (2D) slab configuration, and its analytic solution has been obtained. Subsequently, a numerical scheme has been developed to adapt the analytic solution into the 3D surface shape of stellarator target. The effectiveness of this design scheme has been validated through simulations of the Chinese First Quasi-axisymmetric Stellarator (CFQS) using a suite of codes including HINT, FLARE and EMC3-EIRENE, where a toroidally uniform heat load distribution has been achieved with an island configuration. Further, the effects of input parameters on the target shape and heat load distribution have been studied. The robustness of the designed target has been investigated by simulation results with varying magnetic island configurations, confirming that the toroidal uniformity of heat load distribution is insensitive to changes in island configurations. Moreover, the designed target has been assessed with gas puffing of neon, which shows that neon injections effectively reduce the heat loads without altering the toroidal uniformity of heat load distributions. The proposed scheme highlights the importance of theoretical and mathematical foundations of target design, offering an advantageous alternative/complement to the traditional numerical schemes.

Numerical study on fluid flow and heat transfer characteristics of supercritical CO2 in horizontal tube under various non-uniform heating conditions

Supercritical CO2 (sCO2) is deemed the potential working medium for thermodynamic cycles in the next generation of power machinery. In this paper, the flow and heat transfer characteristics of highly buoyant turbulent sCO2 in horizontal tubes are numerical studied under the non-uniform heating conditions. The tube with a typical internal diameter of 10 mm is selected with mass flux equaling to 300 kg/(m2·s), effective heat fluxes ranging from 20 to 60 kW/m2, and pressure equaling to 8 MPa. The results confirmed that the heat transfer of sCO2 inside the horizontal tube in the circumferential or axial non-uniform heating conditions is greatly deteriorated by 13 %-68 % compared to the uniform heating. The overall heat transfer performance of semi-circumferential axial non-uniform heating is about 2.5 % higher than that of bottom semi-circumferential uniform heating, while the axial temperature difference of the bottom surface exceeds 150 K. Screening three representative heating positions, the bottom heating has the best temperature uniformity. The corresponding turbulent streamlines featured by unique helical structures can substantially improve the circumferential and radial heat transfer over 10 %, enhancing the heat transfer performance of the smooth tube close to that of rifled tubes. Based on the numerical data, viable correlations were developed for calculating the axial local Nusselt number of forced convection heat transfer of sCO2 in horizontal tubes considering the effects of cross-sectional vorticity, secondary flow intensity, and buoyancy-natural convection, and the prediction values are in good agreement with experimental data.

Methyl ricinoleate droplet impact on a high temperature stainless steel surface: Dynamic behavior and heat transfer

The rapid and uniform heating of the feedstock plays a key role in pyrolysis processes. Dispersing methyl ricinoleate (MR) into spray droplets can improve the heating speed and uniformity in the pyrolysis process, which is of great benefit to the yield of the target product. This article describes the results and mechanisms of single MR droplet impacting on a heated stainless steel surface at different temperatures (385 ∼ 520 °C). Two non-contact measurement techniques, including a high-speed camera and a thermal infrared imager, were used to record the dynamic behavior and heating effects of the MR droplet on the heated surface at different temperatures, respectively. Four representative impingement states were observed during droplet impact: adhesion rebound, adhesion rebound with breakup, bouncing, and bouncing with breakup. As a result, a comprehensive map was created, based on a dimensionless analysis, describing the relationships between the typical states. Regarding the quantitative analysis, the maximum spreading factor and the dimensionless droplet residence time were linearly related to the 0.336 and 0.389 powers of the Weber number, respectively. By calculating the average heat flux of a droplet, it was found that it is related to the stainless steel surface temperature, the droplet saturation temperature, and the Reynolds number. The transient temperature at the surface of the MR droplet was measured to quantify the effectiveness of the heating. This study could provide a theoretical basis for the regulation and optimization of MR pyrolysis conditions.

Enhancing Thermal–Hydraulic Performance in Nuclear Reactor Subchannels with Al2O3 Nanofluids: A CFD Analysis

In this paper, the performance of aluminum-based nanofluids with a possible application in pressurized water reactors is numerically investigated. A 605 mm long 4-rod array square (2 × 2) subchannel geometry with a uniform heat flux of 50 kW/m2 has been used in CFD simulation. This analysis has been carried out using the RNG k-epsilon turbulence model with standard wall function in ANSYS FLUENT 2022R1. The impact of various flow conditions and nanofluid concentrations has been examined. The effects of variable velocities on nanofluid performance have been studied using different Reynolds numbers of 20,000, 40,000, 60,000, and 80,000. The analysis was conducted with Al2O3/water nanofluid concentrations of 1%, 2%, 3%, and 4%. A comparison of the Nusselt number based on five different correlations was conducted, and deviations from each correlation were then presented. The homogeneous single-phase mixer approach has been adopted to model nanofluid characteristics. The result shows a gradual enhancement in the heat transfer coefficient with increasing volume concentrations and Reynolds numbers. A maximum heat transfer coefficient has been calculated for nanofluid at maximum volume concentrations (ϕ = 4%) and highest velocities (Re = 80,000). Compared to the base fluid, heat transfer was enhanced by a factor of 1.09 using 4% Al2O3. The Nusselt number was calculated with a minimal error of 3.62% when compared to the Presser correlation and the maximum deviation has been found from the Dittus–Boelter correlation (13.77%). Overall, the findings suggest that aluminum-based nanofluids could offer enhanced heat transfer capabilities in pressurized water reactors.

Numerical Simulation and Experimental Analysis for Microwave Sintering Process of Lithium Hydride (LiH)

Dense lithium hydride (LiH) is widely used in neutron shielding applications for thermonuclear reactors and space systems due to its unique properties. However, traditional sintering methods often lead to cracking in LiH products. This study investigates the densification sintering of LiH using microwave technology. A multiphysics model was established based on the measured dielectric properties of LiH at different temperatures, allowing for a detailed analysis of the electromagnetic and thermal field distributions during the microwave heating of cylindrical LiH samples. The results indicate that the electric field distribution within the LiH is relatively uniform, with resistive losses concentrated primarily in the LiH region of the microwave cavity. LiH rapidly absorbs microwave energy, reaching the sintering temperature of 520 °C in just 415 s. Additionally, the temperature difference between the low- and high-temperature regions during the sintering process remains below 5 °C, demonstrating excellent uniform heating characteristics. The microwave sintering process enhances interface migration within the LiH samples, resulting in dense metallurgical bonding between grains. In summary, this research provides valuable insights and theoretical support for the rapid densification of LiH materials, highlighting the potential of microwave technology in improving material properties.

On the intensification of thermal drift

Consider the flow through a channel with grooved edges on one (or both) side(s). If heating is applied to the boundaries, thermal drift is the flow generated by the interaction of the groove and heating patterns. It is known that, if one side of a channel is smooth while the other is grooved, the application of heating forms a so-called ‘thermal drift engine’. Two thermal drift engines are activated if both surfaces are grooved, and these may reinforce or oppose each other. Carefully choosing these engines can lead to an intensification of the thermal drift. The interplay of two drift engines is explored using a horizontal slot with grooves that have a sinusoidal profile with a prescribed wavenumber $\alpha $ . It is shown that the strength of the flow decreases proportional to $\alpha $ as $\alpha \to 0$ and proportional to ${\alpha ^{ - 1}}$ as $\alpha \to \infty $ . We determine the value of $\alpha $ corresponding to the strongest flow and characterize how the conclusions should be modified if a uniform heating component is added to the heating pattern.

Numerical Assessment of MHD Tri-Hybrid Nanoparticles by Tangent Hyperbolic Model with Chemical Reaction: Thermodynamic Analysis

This paper investigates the influence of magneto-tangent hyperbolic nanofluid on the flow of a tri-hybrid nanoliquid consisting of [Formula: see text], and [Formula: see text] particles suspended in [Formula: see text]. The entropy production is encountered in this analysis. The fluid flows over a stretch sheet is considered. In addition, the energy equation also assumes the existence of a uniform heat source or sink and thermal radiation. Furthermore, the concentration equation emphasizes the chemical reaction. The current proposed model yields a set of nonlinear governing equations. The modeled formulation is transformed into a dimensionless system through the application of a suitable alteration. The complex nonlinear equation system was solved using the bvp4c through numerical methods. The main motive of this exploration is to emphasize the rate of heat and mass transfer in a flow of [Formula: see text], and [Formula: see text]-based hybrid nanofluid across a stretch sheet. The graphical study illustrates that Weissenberg number and magnetic field enhancement result in decreasing the velocity. But thermal layer, entropy production, and Bejan number are enhanced with larger values of Weissenberg number and magnetic field. This study focuses on different profiles with various flow parameters. Furthermore, we have compared the tri-hybrid nanofluid with the hybrid and mono nanofluid in all the figures and tabular format. Additionally, we have compared tri-hybrid, hybrid, and mono nanofluid using graphs for velocity, temperature, concentration, entropy production, and Bejan number.

Combinatorial approach to predict synergistic ablation behavior of carbon fiber phenolic composites under aerodynamic loading

The study conducts a comprehensive analysis across 1-D, 2-D, and 2-D axisymmetric geometries, investigating temperature profiles, surface recession patterns, pyrolysis gas flow dynamics, and density fluctuations within the composite material. The findings highlight the effectiveness of the FEA technique in modeling complex multi-physical interactions associated with ablation phenomena. The carbon-phenolic composites, characterized by low thermal conductivity, high specific heat capacity, and substantial char yield, are shown to be particularly well-suited as ablative materials. The char layer formed during ablation acts as an additional insulating barrier, enhancing thermal protection. In a specific case study, a 2 cm thick composite laminate was subjected to an intense heat flux of 200 W/cm2 for 180 s. The results demonstrate that the Thermal Protection System (TPS) effectively maintains the back face temperature below 350 K for the initial 60 s under uniform heat flux conditions. However, beyond this period, the back face temperature gradually increases, reaching 1698 K at the end of the 180-s simulation. These insights into the material’s thermal performance under severe heat exposure conditions provide valuable guidance for applications requiring effective heat management and thermal protection.

Simulation Analysis of 3-D Airflow and Temperature Uniformity of Paddy in a Laboratory Drying Oven

This study analyzed the effects of airflow characteristics on the temperature distribution and drying uniformity of paddy during convective drying. Simulations of the drying process with varying airflow inlet and outlet positions were conducted using COMSOL Multiphysics 6.1 software. The determination coefficient (R2) between the simulated data and experimental values of Sample1 (S1), Sample2 (S2), and Sample3 (S3) was calculated, and its average values were 0.964, 0.963, 0.963, and 0.967, respectively. This study demonstrates that the airflow direction and outlet location have a significant impact on the temperature uniformity of the paddy. The vortex structure generated by the obstruction of the sidewalls and paddy influences both the airflow and temperature distribution within the drying chamber. When the outlet was on the left side and the inlet airflow was in a vertical orientation (VO), the temperature distribution of the paddy exhibited higher temperatures in the edge regions and lower temperatures in the center, with a maximum temperature difference of around 16 °C. The time required for the temperature to reach equilibrium with the outlet positioned on the left was 28.6% shorter than with the outlets positioned in the center or on both sides. Moreover, the temperature uniformity of the three paddy samples was better under this condition. The developed model accurately reflected the paddy drying process. It could also be used to analyze the optimal heating uniformity, providing a technical basis for the design of grain dryers.

Fluorocarbon‐based Solvent‐Bath Annealing for High‐Performance Perovskite Photovoltaics

AbstractThermal annealing is a critical process in producing high‐quality perovskite films for high‐performance perovskite solar cells. Conventional TA presents challenges such as delayed heat transfer, leading to unwanted crystal growth and hindering processing scalability. Solvent‐bath annealing is an attractive approach that can improve heat transfer and promote perovskite crystallization by immersing the as‐deposited precursor film in a liquid medium. In this study, fluorocarbon‐based solvents are developed as novel solvent baths for uniform heat flow through omnidirectional annealing. In addition, the previously neglected solvent‐to‐solvent interaction between fluorocarbon and solvents for perovskite precursor is investigated by comparing two fluorocarbon solvents. By increasing the solvent‐solvent interaction, higher quality perovskite films with increased crystallinity, improved perovskite transition, and reduced film defects are achieved. As a result, the perovskite solar cells exhibited an increased power conversion efficiency with excellent reproducibility. These findings suggest that the selection of suitable solvent bath is promising for further improving perovskite quality and device performance.

Tailoring coil geometry for achieving uniform heating through coil shape topology optimization for induction heating-based metal wire additive manufacturing

Tailoring coil geometry for achieving uniform heating through coil shape topology optimization for induction heating-based metal wire additive manufacturing

Modular high frequency resonant inverters in constant power mode

ABSTRACT In this paper, a modular resonant inverter is proposed for high frequency industrial heating applications. To maintain a uniform heating profile, the inverter is operated in constant power mode. A hybrid voltage and frequency control is proposed. Voltage control is used for active power tracking while frequency control is used to minimise circulating current due to reactive power and to achieve soft switching for the inverter switches. Analytical and test results are shown to verify the proposed approach.

Optimizing Flow and Heat Transfer With Guiding Pin Fins in a Wedge-Shaped Cooling Channel for Gas Turbine Blade Trailing Edge

Abstract In this study, an innovative guiding pin-fin array optimization has been developed through three-dimensional numerical simulations to enhance the cooling efficiency of gas turbine blade trailing edge. The guiding pin-fin array is optimized using the Kriging surrogate model and Genetic Algorithm (GA), aiming to significantly improve the heat transfer rates and uniformity within the wedge-shaped channel. The design parameter chosen for optimization is the deflection angle of each guiding pin fin, and the optimization process is conducted in two rounds. The first-round optimization yields a first-optimized guiding pin-fin array, which exhibits superior overall heat transfer performance and reasonable pressure loss compared to conventional circular, oblong, and parallel pin-fin arrays. For the first-optimized guiding pin-fin (1st-OGP) channel at the Reynolds number of Re = 50,000, the total Nusselt number and pressure loss are 44.1% higher and 9.9% lower than those of the baseline circular pin-fin array (CP), respectively. An experimental validation using the transient liquid crystal (TLC) thermography method is carried out and proves the effectiveness of the optimization process. However, it is noted that the first-optimized guiding pin-fin exhibits even lower heat transfer at a low Reynolds number of Re = 10,000, particularly in the channel middle region, which is mainly due to the incapable turning flow control in the root region of the wedged channel. To address this issue and further improve the heat transfer performance at low Reynolds numbers, a second-round optimization is performed by specifically adjusting the deflection angle of the selected guiding pin fins near the root region of the wedged channel. This secondary optimization demonstrates significant heat transfer improvements over the whole studied Reynolds number range with a reasonably reduced consumption of computational resources. The total Nusselt number and pressure loss are 69.3% higher and 11.9% lower than those of the baseline circular pin-fin array, respectively, at Re = 50,000. The optimization process proposed in this paper produces a high-performance cooling structure design with elaborate guiding pin-fin arrangements in the wedge-shaped channel, which indicates high heat transfer enhancement and relatively lower pressure loss in the wedged channel for the turbine blade trailing edge.

Design and evaluation of an active vineyard heating system to simulate temperature increase in the context of climate change

The current study introduces an innovative direct and active heating system designed for precise temperature control in vineyards. This system serves as a valuable tool for investigating the influence of climate change on grapevine physiology and, consequently, the characteristics of the resulting wine. The research took place in an experimental vineyard located in Mendoza, Argentina, with V. vinifera cvs. trained to a vertical shoot positioning trellis system over two consecutive growing seasons. The system design utilized electric hot water tanks and polypropylene pipes attached to the foliage catch wires. Over two growing seasons, the system consistently elevated the ambient air temperatures within the canopy by 2.5 ± 0.12 °C compared to the control group. This temperature increase emulated the temperature projections for Mendoza as forecasted by the IPCC by the end of this century. The system displayed heating uniformity, as evidenced by the absence of both vertical and horizontal temperature gradients. Additionally, the significant variation in mean daytime and night-time temperatures between the control and heated treatments highlighted the effectiveness of the system in modifying temperature conditions on a diurnal basis. The heated treatment applied with this system proved to have an effective biological impact on the physiology of grapevines. In both seasons, plants under the heated treatment advanced their bud break and harvest dates. The study showed a significant growth enhancement in the heated treatment, with apical shoots extending significantly longer than those in the control treatment. Additionally, the total soluble solids content increased in the heating treatment, while yield decreased, for both experimental seasons. These results illustrate the robust performance of the system throughout the entire growth period, regardless of fluctuations in atmospheric conditions. This study establishes a new foundation for future research on grapevine responses to climate change. It also opens the door to the implementation of effective adaptation strategies in vineyards, promising a more resilient and adaptable future for grape cultivation.

Comparative analysis of buoyancy-driven hydromagnetic flow and heat transfer in a partially heated square enclosure using Cu-Fe3O4 and MoS2-Fe3O4 nanofluids

Purpose This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe3O4 and MoS2-Fe3O4. Design/methodology/approach The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios. Findings Results obtained show that the Cu-Fe3O4 hybrid nanofluid exhibits higher entropy generation than the MoS2-Fe3O4 hybrid nanofluid when comparing them at a Rayleigh number of 106 and a Darcy number of 10–1. The MoS2 hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 104are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS2 nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 105 and a Darcy number of 10–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature. Originality/value The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

Wind tunnel experiment of ventilation rate and airflow characteristics in natural ventilation induced by wind and buoyancy effects

In this paper, the investigation focused on natural ventilation induced by wind and buoyancy effects through a wind tunnel experiment. A scaled-down model of a single-zone building featuring two opposing openings at varying heights was subjected to uniform heating from a source on the interior floor. Wind pressure coefficient differences were measured in a sealed model to assess the wind’s driving force. Indoor and outdoor temperatures were recorded to ascertain the buoyancy-driven driving force. The ventilation rate was assessed using the tracer gas constant emission method, while airflow characteristics were quantified through particle image velocimetry (PIV). The comparison between predicted and measured ventilation rates revealed generally good accuracy in cases where wind assists buoyancy. However, errors were evident in cases of opposing wind and buoyancy due to neglecting the effect of wind turbulence. The airflow in cases of opposing wind and buoyancy effects demonstrates the most dynamic changes, as illustrated through flow visualizations and transient temperature fluctuations at the openings.

Enhancement of turbulent heat transfer by using CuO nano-particle and twisted tape

AbstractA computational model is developed to investigate the convective heat transfer properties and the fluid flow characteristics of cupric oxide - water nano-fluid in a horizontal circular pipe aiming to provide insights into optimizing heat transfer in such systems. A twisted tape with varied twist ratios is inserted. This quantitative investigation used five Reynolds number from 4,000 to 12,000 under a uniform heat flux scenario of 25,000 W m−2. All experiments were performed as a single-phase fluid with cupric oxide values of 0, 0.4, 1, and 2% by volume. By reducing the twist ratio and increasing volume concentration, the average heat transfer coefficient of cupric oxide-water nano-fluid was improved. For a twist ratio of 4D, the maximum heat transfer improvement was 228% greater than the plain pipe. The presence of twisted tape with modest step ratios causes the friction factor to grow.