Heat Transfer Enhancement Research Articles

Enhancement of Heat Transfer rate using Axially Interrupted Rectangular Fins in Double Pipe Heat Exchanger

The current investigates the thermo-fluid behavior of a double pipe heat exchanger (DPHE) featuring axially interrupted rectangular fins (AIRF) on the annulus part. The inner tube under this study with AIRF represents an interruption of straight longitudinal fins. This modification introduces periodic breaks along the tube's surface, effectively disrupting the boundary layer of the fluid flow. Consequently, it enables a non-continuous fluid passage along the length of the tube, potentially enhancing heat transfer. The experimentation employs standard liquid water, for investigations conducted under varying cold water mass flow rate 0.136 Kg/s to with 0.374 Kg/s keeping hot water at constant flow rate of 0.34 Kg/s with a fin split interval of four different lengths 7mm,27mm,55mm,100mm. A comprehensive investigation of the AIRF arrangements is carried out in contrast to the plain pipe arrangement, concentrating on fluid flow parameters such as Nusselt number (Nu), friction factor, heat transfer rate, and overall performance factor. The findings reveal that heat transfer rates in an annulus equipped with 7mm AIRF exceed those of a plain pipe by 59.31% under similar fluid flow conditions. The Nusselt number shows 1.5 times increase in the 0.007 m AIRF arrangement compared to the plain pipe. Thermal performance factor for 7mm interrupted length of AIRF outperforms other models.

Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows

This study presents a detailed investigation of the temporal evolution of the Nusselt number (Nu) in uniformly accelerated and decelerated turbulent pipe flows under a constant heat flux using direct numerical simulations. The influence of different acceleration and deceleration rates on heat transfer is systematically studied, addressing a gap in the previous research. The simulations confirm several key experimental findings, including the presence of three distinct phases in the Nusselt number temporal response—delay, recovery, and quasi-steady phases—as well as the characteristics of thermal structures in unsteady pipe flow. In accelerated flows, the delay in the turbulence response to changes in velocity results in reduced heat transfer, with average Nu values up to 48% lower than those for steady-flow conditions at the same mean Reynolds number. Conversely, decelerated flows exhibit enhanced heat transfer, with average Nu exceeding steady values by up to 42% due to the onset of secondary instabilities that amplify turbulence. To characterize the Nu response across the full range of acceleration and deceleration rates, a new model based on a hyperbolic tangent function is proposed, which provides a more accurate description of the heat transfer response than previous models. The results suggest the potential to design unsteady periodic cycles, combining slow acceleration and rapid deceleration, to enhance heat transfer compared to steady flows.

Side-heated Rayleigh–Bénard convection

Unlike in solids, heat transfer in fluids can be greatly enhanced due to the presence of convection. Under gravity, an unevenly distributed temperature field results in differences in buoyancy, driving fluid motion that is seen in Rayleigh–Bénard convection (RBC). In RBC, the overall heat flux is found to have a power-law dependence on the imposed temperature difference, with enhanced heat transfer much beyond thermal conduction. In a bounded domain of fluid such as a cube, how RBC responds to thermal perturbations from the vertical sidewall is not clear. Will sidewall heating or cooling modify flow circulation and heat transfer? We address these questions experimentally by adding heat to one side of the RBC. Through careful flow, temperature and heat flux measurements, the effects of adding side heating to RBC are examined and analysed, where a further enhancement of flow circulation and heat transfer is observed. Our results also point to a direct and simple control of the classical RBC system, allowing further manipulation and control of thermal convection through sidewall conditions.

Twisted-tape inserts of rectangular and triangular sections in turbulent flow of CMC/CuO non-Newtonian nanofluid into an oval tube

Purpose This paper aims to study numerically the non-Newtonian solution of carboxymethyl cellulose in water along with copper oxide nanoparticles, which flow turbulently through twisted smooth and finned tubes. Design/methodology/approach The twisted-tape inserts of rectangular and triangular sections are investigated under constant wall heat flux and the nanoparticle concentration varies between 0% and 1.5%. Computational fluid dynamics simulation is first validated by experimental information from two test cases, showing that the numerical results are in good agreement with previous studies. Here, the impact of nanoparticle concentration, tube twist and fins shape on the heat transfer and pressure loss of the system is measured. It is accomplished using longitudinal rectangular and triangular fins in a wide range of prominent parameters. Findings The results show that first, both the Nusselt number and friction factor increase with the rise in the concentration of nanoparticles and twist of the tube. Second, the trend is repeated by adding fins, but it is more intense in the triangular cases. The tube twist increases the Nusselt number up to 9%, 20% and 46% corresponding to smooth tube, rectangular and triangular fins, respectively. The most twisted tube with triangular fins and the highest value of concentration acquires the largest performance evaluation criterion at 1.3, 30% more efficient than the plain tube with 0% nanoparticle concentration. Originality/value This study explores an innovative approach to enhancing heat transfer in a non-Newtonian nanofluid flowing through an oval tube. The use of twisted-tape inserts with rectangular and triangular sections in this specific configuration represents a novel method to improve fluid flow characteristics and heat transfer efficiency. This study stands out for its originality in combining non-Newtonian fluid dynamics, nanofluid properties and geometric considerations to optimize heat transfer performance. The results of this work can be dramatically considered in advanced heat exchange applications.

Thermohydraulic Performance and Flow Structures of Diamond Pyramid Arrays

Abstract Surface features are a common heat transfer enhancement method used in a myriad of applications including gas turbines and heat exchangers. One such style of surface features are diamond pyramids, which offer significant heat transfer augmentation for moderate increases in overall pressure losses. This study investigated a suite of additively manufactured pyramids in a variety of sizes and arrangements at relevant scale contained in test coupons. Designs were printed with low surface roughness relative to typical additive components (Ra < 5µm), and pyramids were printed within 100 µm of the design intent. Experimental and computational results indicate that the pressure penalty and heat transfer increased as the pyramids increased in size with aligned pyramids on both channel walls having higher values than staggered pyramids. It was found that implementing the pyramids onto a rough surface had a lesser impact on the friction factor than implementing on a smooth surface, but that the relative increase in heat transfer was the same regardless of the roughness of the endwall. The greatest enhancement to local heat transfer and pressure loss was offset from the location of minimum flow area due to local acceleration around the wake regions. The vortices formed in the wake of the pyramid structures enhanced the endwall heat transfer and shear stress. The performance of the pyramids investigated in this study follows a similar trend to prior studies investigating smooth rib geometries, though certain rib designs had higher heat transfer at lower pressure losses.

Investigation of activation energy of Maxwell fluid with Newtonian heat effect at the boundary layer flow on a cylinder embedded in porous medium

AbstractThis study aims to investigate the flow of Maxwell fluid over a cylinder, considering the combined effect of Magnetohydrodynamics (MHD) and a permeable medium on the equation of momentum, heat generation and radiation on the equation of energy, and activation energy on the mass equation. The objective is to analyze the impression of these physical phenomena on the fluid's behavior under specified boundary conditions, with a focus on the Newtonian heating effect. The significance of this research lies in its application to industrial processes, polymer extrusion and cooling of metallic sheets, where controlling fluid flow and energy transfer is crucial. The dimensional governing equations for momentum, energy, and concentration were changed into non‐dimensional forms via appropriate dimensionless quantities and similarity variables. The subsequent nonlinear ordinary differential equations were answered using the BPV4C inbuilt MATLAB solver. The key findings reveal that the concentration outline rises with a rise in activation energy and declines with a rise in the chemical reaction. Additionally, the Nusselt number profile displays an increasing trend with the Newtonian heating parameter, indicating enhanced heat transfer. Quantitative results demonstrate that the occurrence of a porous medium and MHD significantly impacts the velocity and temperature contours. The real‐time application of this study can be seen in the optimization and design of chemical reactors, heat exchangers, and cooling systems in engineering processes. The developed model delivers insights into controlling energy and mass transfer in processes involving stretching surfaces, which is essential for improving efficiency and product excellence in various industrial applications.

Numerical Investigations on the Enhancement of Convective Heat Transfer in Fast-Firing Brick Kilns

In order to reduce CO2 emissions in the brick manufacturing process, the effectiveness of the energy-intensive firing process needs to be improved. This can be achieved by enhancing the heat transfer in order to reduce firing times. As a result, current development of tunnel kilns is oriented toward fast firing as a long-term goal. However, a struggling building sector and complicated challenges, such as different requirements for product quality, have impeded developments in this direction. This creates potential for the further development of oven designs, such as improved airflow through the kiln. In this article, numerical flow simulations are used to investigate two different reconstruction measures and compare them to the initial setup. In the first measure, the kiln height is reduced, while in the second measure, the kiln cars are adjusted to alternate the height of the bricks so that every other pair of bricks is elevated, creating a staggered arrangement. Both measures are investigated to determine the effect on the heating rate compared to the initial configuration. A transient grid independence study is performed, ensuring numerical convergence and the setup is validated by experimental results from measurements on the initial kiln configuration. The simulations show that lowering the kiln height improves the heat transfer rate by 40%, while the staggered arrangement of the bricks triples it. This leads to an average brick temperature after two hours which is around 130 °C higher compared to the initial kiln configuration. Therefore, the firing time can be significantly reduced. However, the average pressure loss coefficient rises by 70% to 90%, respectively, in the staggered configuration.

Heat transfer enhancement for electro-thermo-convection of FENE-P viscoelastic fluid in a square cavity

This study numerically investigates the heat transfer enhancement for viscoelastic electro-thermo-convection in a two-dimensional differentially heated cavity with injection from below. The flow motion is assumed to be incompressible, which is driven by the Coulomb force and the thermal buoyant force. The polymers are described by the FENE-P model which exhibits typical shear-thinning and elastic properties. Based on the extensibility parameter (L), the cases are divided into several scenarios, corresponding to weak elasticity with strong shear-thinning, moderate elasticity with moderate shear-thinning, and strong elasticity with weak shear-thinning, respectively. We find that the competition between the shear-thinning and elasticity dominates the flow state and heat transport. The shear-thinning effect tends to facilitate heat transfer, while its elastic properties tend to decrease it. In the scenario of weak elasticity with strong shear-thinning (L2=10), the polymer additives significantly improve the heat transfer enhancement (HTE) of the electric field as the polymer viscosity ratio (β) decreases or Weissenberg number (Wi) increases, where the maximum HTE reaches around 92.1%. The amount of HTE first increases rapidly with Wi but then remains almost constant once a critical Wi is exceeded. However, the HTE significantly decreases in the scenario of strong elasticity with weak shear-thinning (300≤L≤1000) since the elasticity dominates over the shear-thinning. These heat transfer performances are then corroborated with the boundary layer and kinetic energy budget analysis.

Unveiling the fundamentals of flow boiling heat transfer enhancement on structured surfaces.

Micro- and nanostructured surfaces offer the potential to enhance two-phase heat transfer. However, the mechanisms behind these enhancements are not well-understood due to insufficient diagnostic methods, leading to reliance on trial-and-error surface development. We introduce in situ boroscopy to investigate microscale bubble dynamics during flow boiling nucleation and subsequent flow regime development. This method was applied in saturated flow boiling experiments within chemically etched aluminum and copper tubes. Although the surfaces have self-similar surface structures, our findings revealed varied heat transfer coefficient enhancements, with increases of up to 391% on aluminum and 41% on copper. Using boroscopy, we identified key mechanisms of heat transfer enhancement. We further used mercury porosimetry to determine the impact of pore size distribution on thermal performance. The boroscopy technique introduced here not only elucidates the underlying processes of flow boiling heat transfer enhancement but also has potential applications for the study of other two-phase phenomena.

Hybrid Nanofluid Flow in Microchannel With Fins: Thermal-Hydraulic, Entropy Generation and Energy Management Analysis

This study aims to numerically analyze the thermal-hydraulic performances and total entropy generation of mono-nanofluid and hybrid nanofluid in microchannel heat sinks (MCHS) with fins for laminar flow regime. Besides, the performance evaluation plots (PEPs) are plotted to explore the possibilities of energy saving for mono-nanofluid and hybrid nanofluid flow in MCHS with different fin configurations. The two-phase model is adopted to model the flow of nanofluid in the MCHS. The fin height, fin number, and nanoparticles loading are varied to investigate their effect on the heat transfer, flow characteristic, and entropy generation in the MCHS. It is discovered that 1.0% Al2O3–Cu hybrid nanofluid gives the least total entropy generation if compared to water and Al2O3 mono-nanofluid owing to the significant heat transfer enhancement it offered. The MCHS with 5 fins and a fin height of 0.8 mm configuration is found to be the optimal design for heat removal in this study. Moreover, the plotted PEPs show that the use of Al2O3–Cu hybrid nanofluid and Al2O3 nanofluid (with the concentration range of 0.1%–1.0%) in the MCHS can save energy at either constant pressure drop or flow rate.

Heat dissipation analysis on the designed inner-outer circulation impingement double-layer microchannel heat sinks with chamfers in power electronic cooling system

This study discusses a new design which utilizes chamfers to further improve the thermal performance of inner-outer circulation impingement double-layer microchannel heat sinks by simulations and experiments manufactured with 3-Dimension printing. In contrast to former designed inner-outer circulation impingement double-layer microchannel heat sinks, inner-outer circulation impingement double-layer microchannel heat sinks with chamfer shows significant advantages in improving overall thermal performance in power electronic cooling. The results of simulation are in good agreement with those of experiment in five 3-Dimensional printing tests. It is demonstrated that the introduction of chamfers is effective in controlling the thermal gradient on substrate of heat sinks, and reducing the peak temperature on substrate of inner-outer circulation impingement double-layer microchannel heat sinks with chamfer as a result. The best performance is presented by a 0.2 mm chamfer located on the corner of the inner-outer circulation shaft in inner-outer circulation impingement double-layer microchannel heat sinks with chamfer. Experimental studies and numerical simulations both indicate that inner-outer circulation impingement double-layer microchannel heat sinks with a 2 mm chamfer significantly enhances heat transfer characteristics. In addition, the average Nusselt number for inner-outer circulation impingement double-layer microchannel heat sinks with a 2 mm chamfer is higher than that of other tests. Moreover, inner-outer circulation impingement double-layer microchannel heat sinks with a 2 mm chamfer performs better than other designs in terms of the overall heat transfer performance, which is significantly better than inner-outer circulation impingement double-layer microchannel heat sinks without chamfers.

Experimental study on heat transfer and resistance of round tube with tube sheet under ultrasonic action

AbstractEnergy is vital to the survival and development of human beings. In the era of ‘carbon neutrality’, all walks of life around the world are upgrading their technological capabilities to reduce carbon emissions. As a new type of active strengthening technology to improve the comprehensive performance of heat exchangers, ultrasonic technology has attracted the attention of more and more scholars. From the actual installation situation, a set of ultrasonic enhanced heat transfer test device with tube sheet round tube was built. After experimental research and data analysis, the influence of ultrasonic sound intensity, frequency, and position on heat transfer, flow resistance, and comprehensive performance of heat exchange tube under different working conditions and without ultrasonic wave is studied. The results show that the ultrasonic enhanced heat transfer and drag reduction capacity increases with the decrease of ultrasonic frequency, and under the action of ultrasonic waves of different frequencies, the critical sound intensity of its enhanced heat transfer and drag reduction performance is different. The drag reduction performance of the ultrasonic heat exchange tube is increased by 18.41%, the heat transfer performance is increased by 36.53%, and the overall performance is increased by 20.57%.

Dynamics of droplet adsorption by liquid film on a grooved surface

Abstract Understanding the dynamics of droplet adsorption by liquid film on a grooved surface is of great significance for the possible manipulation of dropwise condensation on the grooved surface. In this study, an improved phase-field lattice Boltzmann model is proposed to describe the process of droplet adsorption from the ridge to the liquid film within the channel. The results indicate that the leading edge of the droplet undergoes two accelerations during the adsorption process, obeying the power law of l/R = t^2.2 and l/R = t^0.9, respectively. The adsorption process between droplets with different sizes and the liquid film exhibits self-similarity characteristics including the same first peak velocity, the similar droplet displacement-time curve and the equal dimensionless spreading length of l/R=5.5. Decreasing the contact angle of the droplet from θe = 120° to θe = 60° accelerates the displacement of the leading edge and extends the spreading length. These findings may help reveal the mechanics of droplet adsorption by the liquid film on the grooved surface and thus manipulate the condensation behavior for the heat transfer enhancement.

The Role of Heater Size and Location in Modulating Natural Convection Behavior in Cu-Water Nanofluid-Loaded Square Enclosures

Enhancing the energy efficiency of thermal systems reduces their consumption, lowers costs, and reduces undesired environmental impact, thus making these systems more sustainable. The current work introduces a passive method for heat transfer enhancement that is carried out using natural convection by nanofluid. This work introduces a computational study of the process of natural convection within a square cavity containing Cu/H2O nanofluid. The cavity wall on the left side undergoes partial isothermal heating, while the opposing side is fully cooled isothermally, with all other boundaries maintained adiabatic. A mathematical model formulated based on a 2-D model was used to provide the solution for the system of governing equations of mass, momentum, and energy conservation, employing the finite element technique. A commercial CFD package is utilized to perform the computational simulation. The present investigation delves into the impact of the Rayleigh number, nanoparticle concentration, heater length, and heater location on the flow field and heat transfer characteristics. The model outcomes were displayed for a wide range of the pertinent parameters as 103 ≤ Ra ≤ 106, 0.25 ≤ lh ≤ 1.0, 0.125 ≤ hc ≤ 0.875, and 0.02 ≤ ϕ ≤ 0.10. Also, correlation equations relating the average Nusselt number to these crucial parameters are derived. These equations are simple and can be applied in practice easily in many fields, such as electric and electronic equipment cooling and thermal management of heat sources. Also, these equations gather all the parameters that affect the heat transfer process. They are shedding light on the intricate interplay between these parameters in the natural convection heat transfer process.

Enhanced Efficiency of Latent Heat Energy Storage by Inclination

Latent heat storage (LHS) has emerged as a promising solution for addressing the challenges of large-scale and long-term energy storage, offering a clean and reusable system. Being in the developmental stage, and with only limited theoretical predictions being available, there is a need to enhance the efficiency of LHS systems. In this study, we use numerical simulations to study the melting process of a phase-change material (PCM) in a rectangular domain. A significant enhancement in the melt rate of the PCM is found by a simple inclination of the domain, with a 60% increase in melt rate compared to a standard square unit without inclination through enhanced heat transfer. We establish a theoretical relation for the optimal PCM melt rate, based on the inclination angle and the domain aspect ratio, outlining the optimal conditions for the PCM melt rate, which is solely dependent on the domain geometry. We further propose a heat-transfer model that predicts the optimal aspect ratio for achieving the maximum melt rate as a function of the Rayleigh and Prandtl numbers. Published by the American Physical Society 2024

Thermal and rheological behavior of aluminium-doped zinc oxide nanofluids: Experimental study and application of artificial neural network model

In this study, the influence of Al-doping concentration on the thermal and rheological characteristics of pristine zinc oxide (ZnO) nanofluids was investigated across a range of temperatures and nanoparticle concentrations. A multilayer perceptron (MLP) artificial neural network (ANN) with an optimized topology was employed to model the thermal conductivity and viscosity of nanofluids. The addition of 0.13 M of Al-doped zinc oxide nanoparticles at 1 % rate led to a remarkable 64 % increase in the thermal conductivity of the base fluid (50:50 ratio water + ethylene glycol mixture). Furthermore, incorporating 1 % of these Al-doped nanoparticles outperformed pure zinc oxide, resulting in a 44 % boost in thermal conductivity. The enhanced heat transfer capabilities of Al-doped zinc oxide were evident across different doping and nanoparticle concentrations. The viscosity of nanofluids increases with an increase in nanoparticle concentration and decreases with an increase in temperature. ZnO and Al-doped ZnO nanoparticles have been prepared and studied their structural, morphological and elemental properties using XRD, SEM and EDS respectively. The predicted thermal and rheological behaviours are in close agreement with the experimental values.

Heat transfer enhancement in vehicle cabin heating system with hybrid nanofluid: An experimental and artificial intelligence approach

In louvered fin-and-flat-tube aluminum heat exchangers, the interrupted surfaces of the louvered fin channel, through which air flows, enhance heat transfer by growing and degrading laminar boundary layers, while the large surface-to-cross-section flow area ratio of the flat tube further enhances heat transfer. Consequently, due to their relatively good heat transfer performance and compact design, louvered fin-and-flat-tube aluminum heat exchangers are often utilized for cabin heating systems. Considering previous studies involving louvered fin-and-flat-tube aluminum heat exchangers with conventional fluids and with mono-nanofluids, this is the first study employing Al2O3-TiO2/water hybrid nanofluid experimentally in this context, and utilizing a forward-looking ANN forecasting model for scenarios that cannot be experimentally conducted in such systems. Accordingly, the heat transfer enhancement in the louvered fin-and-flat-tube heat exchanger is experimentally investigated for both pure water alone and for different volume concentrations of Al2O3-TiO2/water hybrid nanofluid. Heat transfer rate, convection heat transfer coefficient, Nusselt number, effectiveness, overall heat transfer coefficient, pressure drop, and performance evaluation index were assessed for different inlet temperatures (50 °C, 60 °C, 70 °C) and volume flow rates (3.65 LPM, 5.65 LPM, 7.65 LPM) in the range 0–0.2 % volume concentration. The experimental results show that the highest heat transfer rate enhancement was 113.32 % using the hybrid nanofluid at φ = 0.2 % compared to pure water at a 50 °C inlet temperature and 7.65 LPM flow rate. It was further shown that even using only the hybrid nanofluid, the effectiveness can be increased up to 0.422 at a constant fan speed without the need to enlarge the heat exchanger size, at a flow rate of 7.65 LPM and an inlet temperature of 70 °C. It has also been found that the maximum values of the performance evaluation index calculated according to two different formulas are 2.260 and 2.049 at φ = 0.2 %. In the following part of the study, heat transfer rate, effectiveness, and pressure drop values in the instances of 0.3 % and 0.4 % volume concentrations were forecast using an artificial neural network model trained with the Levenberg-Marquardt algorithm using experimental data. With the proposed artificial neural network model, the forecast heat transfer rates were as expected, while the expected trend could not be achieved in terms of the effectiveness and pressure drop predictions. The study ultimately found that the utilization of a Al2O3-TiO2/water hybrid nanofluid in cabin heating systems, even at a relatively low concentration value of 0.2 %, is capable of achieving very high heat transfer enhancement in exchange for only a very minor pressure drop.

CFD analysis of rotation effect on flow patterns and heat transfer enhancement in a horizontal spiral tube heat exchanger

CFD analysis of rotation effect on flow patterns and heat transfer enhancement in a horizontal spiral tube heat exchanger

Start-up investigation and heat transfer enhancement analysis of a loop thermosyphon with biomimetic honeycomb-channel evaporator

Loop thermosyphon has the ability of heat transfer without external energy input, which has good application potential in many areas. Biomimetic flow channel is an effective way for heat transfer enhancement and resistance optimization, therefore it is a promising method to improve the performance of loop thermosyphon. While currently few studies have been conducted in this field. In this paper, the start-up stages, flow patterns and heat transfer performance of a loop thermosyphon with biomimetic honeycomb-channel evaporator are experimentally investigated, and compared with a loop thermosyphon with parallel-flow evaporator. The results show that the start-up of can be divided into three stages: stage dominated by heat conduction, stage dominated by boiling and stage transited to stable operation; For the steady-state performance, the heating power of the optimal point with the lowest thermal resistance increases from 90 W to 150 W with the increase of the filling ratio from 50% to 70%; Compared to loop thermosyphon with parallel-flow evaporator, loop thermosyphon with biomimetic honeycomb evaporator has lower thermal resistance. The decline of thermal resistance is 4.1%-21.6%, and is more significant under small heating power. This paper provides a simple and affordable method for heat transfer improvement of loop thermosyphon.

Incorporating numerical method for analyzing the conduction heat transfer during solidification loading nanoparticles

This study examines the freezing within a tank with a curved cold surface, integrating an innovative use of fins. The addition of fins and the careful introduction of nanomaterial knowingly enhance solidification efficiency, with potential applications in areas such as cryopreservation and thermal energy storage. To further optimize the solidification process, various types and concentrations of nano-powders were dispersed into the water, serving as heat transfer enhancers. The mathematical model was refined through specific assumptions, leading to the derivation of two principal equations. These equations were then effectively solved using the Galerkin method, offering a novel optimization approach for solidification. The enhancement in conductivity due to the modifications plays a key role in improving the productivity of the system. Furthermore, the addition of nanoparticles resulted in a notable extension of freezing time around 26.71%. The use of an adaptive grid method during grid generation, coupled with the successful verification of the final model, strengthens the reliability of the research. By increasing the parameter "m" (shape factor) from 4.8 to 8.6, the solidification time was reduced by approximately 6.96%, demonstrating a significant improvement in the system's efficiency.