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At least 91 records · Page 5

Two-dimensional model of a Space Station Freedom thermal energy storage canister

The Solar Dynamic Power Module being developed for Space Station Freedom uses a eutectic mixture of LiF-CaF2 phase change salt contained in toroidal canisters for thermal energy storage. Results are presented from heat transfer analyses of the phase-change salt containment canister. A 2-D, axisymmetric finite-difference computer program which models the canister walls, salt, void, and heat engine working fluid coolant was developed. Analyses included effects of conduction in canister walls and solid salt, conduction and free convection in liquid salt, conduction and radiation across salt vapor filled void regions, and forced convection in the heat engine working fluid. Void shape, location, and growth or shrinkage (due to density difference between the solid and liquid salt phases) were prescribed based on engineering judgement. The salt phase change process was modeled using the enthalpy method. Discussion of results focuses on the role of free-convection in the liquid salt on canister heat transfer performance. This role is shown to be important for interpreting the relationship between groundbased canister performance (in 1-g) and expected on-orbit performance (in micro-g). Attention is also focused on the influence of void heat transfer on canister wall temperature distributions. The large thermal resistance of void regions is shown to accentuate canister hot spots and temperature gradients.

Kerslake, Thomas W.↗

Two-dimensional model of a Space Station Freedom thermal energy storage canister

The Solar Dynamic Power Module being developed for Space Station Freedom uses a eutectic mixture of LiF-CaF2 phase change salt contained in toroidal canisters for thermal energy storage. Results are presented from heat transfer analyses of the phase change salt containment canister. A 2-D, axisymmetric finite difference computer program which models the canister walls, salt, void, and heat engine working fluid coolant was developed. Analyses included effects of conduction in canister walls and solid salt, conduction and free convection in liquid salt, conduction and radiation across salt vapor filled void regions and forced convection in the heat engine working fluid. Void shape, location, growth or shrinkage (due to density difference between the solid and liquid salt phases) were prescribed based on engineering judgement. The salt phase change process was modeled using the enthalpy method. Discussion of results focuses on the role of free-convection in the liquid salt on canister heat transfer performance. This role is shown to be important for interpreting the relationship between ground based canister performance (in l-g) and expected on-orbit performance (in micro-g). Attention is also focused on the influence of void heat transfer on canister wall temperature distributions. The large thermal resistance of void regions is shown to accentuate canister hot spots and temperature gradients.

Kerslake, Thomas W.↗

Enhanced Boiling on Micro-Configured Composite Surfaces Under Microgravity Conditions

In order to accommodate the growing thermal management needs of future space platforms, several two-phase active thermal control systems (ATCSs) have evolved and were included in the designs of space stations. Compared to the pumped single-phase liquid loops used in the conventional Space Transportation System and Spacelab, ATCSs offer significant benefits that may be realized by adopting a two-phase fluid-loop system. Alternately, dynamic power systems (DPSs), based on the Rankine cycle, seem inevitably to be required to supply the electrical power requirements of expanding space activities. Boiling heat transfer is one of the key technologies for both ATCSs and DPSs. Nucleate boiling near critical heat flux (CHF) can transport very large thermal loads with much smaller device size and much lower pumping power. However, boiling performance deteriorates in a reduced gravity environment and operation in the CHF regime is precarious because any slight overload will cause the heat transfer to suddenly move to the film boiling regime, which in turn, will result in burnout of the heat transfer surfaces. New materials, such as micro-configured metal-graphite composites, can provide a solution for boiling enhancement. It has been shown experimentally that this type of material manifests outstanding boiling heat transfer performance and their CHF is also extended to higher values. Due to the high thermal conductivity of graphite fiber (up to 1,200 W/m-K in the fiber direction), the composite surfaces are non-isothermal during the boiling process. The composite surfaces are believed to have a much wider safe operating region (a more uniform boiling curve in the CHF regime) because non-isothermal surfaces have been found to be less sensitive to variations of wall superheat in the CHF regime. The thermocapillary forces formed by the temperature difference between the fiber tips and the metal matrix play a more important role than the buoyancy in the bubble detachment, for the bubble detachment manifests itself by a necking process which should not be weakened by reduced gravity. In addition, the composite surfaces introduce no extra pressure drop, no fouling and do not impose significant primary or maintenance costs. All of these suggest that this type of composite is an ideal material for the challenge of accounting for both reliability and economy of the relevant components applied in the ATCSs, the DPSs and other devices in future space missions. The aim of the proposed work is to experimentally investigate high nucleate pool boiling performance on a micro-configured metal-graphite composite surface and to determine the mechanisms of the nucleate boiling heat transfer both experimentally and theoretically. Freon-113 and water will be used as the test liquids to investigate wettability effects on boiling characteristics. The Cu-Gr and Al-Gr composites with various volume fractions of graphite fibers will be tested to obtain the heat transfer characteristic data in the nucleate boiling region and in the CHF regime. In the experiments, the bubble emission and coalescence processes will be recorded by a video camera with a magnifying borescope probe immersed in the working fluid. The temperature profile in the thermal boundary layer on the composite surfaces will be measured by a group of micro thermocouples consisting of four ultra fine micro thermocouples. This instrument was developed and successfully used to measure the temperature profile of evaporating liquid thin layers by the proposers in a study performed at the NASA/Lewis Research Center. A two tier model to explain the nucleate boiling process and the performance enhancement on the composite surfaces has been suggested by the authors. According to the model, the thicknesses of the microlayer and the macrolayer underneath the bubbles and mushrooms, can be estimated by the geometry of the composite surface. The experimental results will be compared to the predictions from the model, and in turn, to revise and improve it.

Zhang, Nengli↗

The share flight experiment - An advanced heat pipe radiator for Space Station

This paper reports on the design and thermal vacuum certification testing of the Space Station Heat Pipe Advanced Radiator Element (SHARE) Shuttle flight experiment, with primary emphasis on the heat pipe radiator system. The main objective of the SHARE experiment is to demonstrate suitable 0 g heat transfer performance of a 50 ft-long high-capacity monogroove heat pipe radiator element being developed for possible Space Station application. All of the flight certification tests were achieved, including a maximum heat rejection of 2 kW and thawing of a frozen heat pipe; and uninterrupted operation under cycling environmental and evaporator heat loads.

Alario, J. P.↗

Multiscale Porous High-temperature Heat Exchanger Using Ceramic Co-extrusion

In this project, our MIT, Purdue, and GE team aims to design, model, fabricate, and test a novel high temperature, compact, and durable ceramic heat exchanger to be operated under high temperature and pressure conditions for aerospace applications. Our approach is grounded in introducing multiscale porosity, i.e., centimeter-scale channels embedded with micrometer-scale channels, into the ceramic heat exchanger to significantly improve its heat transfer performance and mechanical strength while maintaining minimal pressure losses. We first developed high-fidelity thermal-fluid-mechanical model capable of precisely capturing the heat transfer rate, temperature profile, pressure drop, and mechanical stress throughout the entire heat exchanger design. Guided by our model, we identified the optimal design parameters for the SiC heat exchanger body and manifolds. Then, we established a completed fabrication procedure to create multiscale features in the ceramic heat exchanger, including co-extrusion, lamination, burnout, and sintering. We fabricated multiple heat exchanger bodies consisting of 6 × 6 and 3 × 3 centimeter-scale channels where each individual centimeter-scale channel comprises 625 crack-free microchannels with 90 μm × 90 μm opening. Owing to the multiscale features, our fabricated heat exchanger bodies exhibited desirable mechanical strength with 156 MPa flexural strength under 1300 Celsius degree. Despite the demonstrated highly tailorable microscopic features and superior mechanical strength, we identified delamination due to the complex interaction among ceramic, polymer, and gas species can be a critical challenge to create fully defect-free heat exchanger, which requires further fundamental investigations in future works. To test the heat exchanger performance, we constructed a high-temperature and high-pressure experimental apparatus that can be safely operated under 400 Celsius degree and 4 bar. With insights gained from mechanistic modeling, material development, and detailed characterization, a cost model was finally developed to understand the market potential of the developed technology, where a cost of $43,000 Celsius degree/kW was envisioned. This project developed a transformative approach to high-performance heat exchanger design. The thermal-fluid-mechanical design approach developed in this project can serve as a generic tool to guide the design of various heat-exchangers operated under high-temperature and high-pressure conditions. The material fabrication approach established in this project can be a useful guide for ceramic processing at extreme length scales.

42 ENGINEERING↗

A comprehensive modeling of falling film evaporators subject to vapor flow, pass arrangements, and refrigerants

Improving the heat transfer performance of falling film evaporators is a crucial step for improving the energy efficiency of the heat pump or refrigeration systems. This study conducts a numerical investigation for the practical-scale falling film evaporator based on the epsilon–NTU method with an updated heat transfer correlation. The algorithm was validated with lab-scale and real-scale falling film evaporator experimental results, and the prediction reaches a mean absolute deviation of 12.5%. Here, the parametric study encompasses eight refrigerants: R-134a, R-410A, R-600a, R-717, R-1270, R-152a, R-1234yf, and R-1234ze(E). The results indicate that vaporization enthalpy of refrigerant is a key property in selecting an appropriate working fluid because it helps minimize severe heat transfer degradation caused by dry-out. Additionally, the vapor-flow–induced heat transfer degradation can be predicted using the critical Weber number. Furthermore, the trade-off between extending the tube length and increasing the number of tubes for heat transfer improvement is discussed. Finally, different two-pass arrangements show deviations of less than 4 %.

Dry-out↗

Thermal and Well Flow Performance of Closed-Loop Geothermal in the Wattenberg Area: Preprint

Closed-loop geothermal systems provide an alternative to resource-constrained hydrothermal systems and stimulation-intensive enhanced geothermal systems. In this work, we apply the slender-body theory (SBT) model, to simulate the well flow and heat transfer performance of U-loop well designs drilled in the Wattenberg area of the Denver-Julesburg Basin. Three U-loop well patterns are investigated including a single, double, and multi-lateral design. The subsurface within area is characterized by deep, hot (> 200degreesC) igneous/metamorphic basement rock underlying multiple sedimentary formations. The lateral section(s) of the U-loop lies within a target depth of 6 km where temperatures are estimated to approach 300degreesC. As a base case, conduction-only heat transfer is investigated through simulations with the SBT model within U-loops with open-hole laterals that exchange heat directly with the hot dry rock using water as a working fluid. The utilization of supercritical CO2 as a heat transfer fluid is also considered. For each scenario, the system performance in terms of annual heat production and temperature profile over a 20-year project lifetime are assessed. Also, the levelized costs of heat and electricity (LCOH and LCOE) are determined using a top-down technoeconomic analysis model. The results show that the performance and cost optimized U-loop design is one having an injection-production well spacing of 1,000 meters with ten 50-meter-spaced laterals that traverse a subsurface system with a temperature gradient of 60degreesC/km. By injecting 20 degreesC-water at a rate of 60 kg/s through this loop, an average heat production of 19 MWth can be achieved, resulting in an LCOE and LCOH of $136/MWh and $1.53/GJ, respectively, over a 20-year project life.

closed-loop geothermal↗

Thermal and Well Flow Performance of Closed-Loop Geothermal in the Wattenberg Area

Closed-loop geothermal systems provide an alternative to resource-constrained hydrothermal systems and stimulation-intensive enhanced geothermal systems. In this work, we apply the slender-body theory (SBT) model, to simulate the well flow and heat transfer performance of U-loop well designs in the Wattenberg area of the Denver-Julesburg Basin. Three U-loop well patterns are investigated, including a single-, double-, and multi-lateral design. The subsurface within the area of interest is characterized by deep, hot (> 200 degrees C) igneous/metamorphic basement rock underlying multiple sedimentary formations. The lateral section(s) of the U-loop lie(s) within a target depth of 6 km, where temperatures are estimated to approach 300 degrees C. As a base case, conduction-only heat transfer is investigated through simulations with the SBT model within U-loops with open-hole laterals that exchange heat directly with the hot, dry rock using water as a working fluid. The utilization of supercritical CO2 as a heat transfer fluid is also considered. For each scenario, the system performance in terms of annual heat production and temperature profile over a 20-year project lifetime are assessed. Also, the levelized costs of heat and electricity (LCOH and LCOE) are determined using a top-down techno-economic analysis model. The results show that the performance- and cost-optimized U-loop design is one having an injection-production well spacing of 1,000 meters with ten 50-meter-spaced laterals that traverse a subsurface system with a temperature gradient of 60 degrees C/km. By injecting 20 degrees C-water at a rate of 60 kg/s through this loop, an average heat production of 19 MWth (i.e., 2.2 MWe net plant output) can be achieved, resulting in an LCOE and LCOH of $136/MWhe and $1.53/GJ, respectively, over a 20-year project life.

closed-loop geothermal↗

Simulations of Heat Transfer Using Tight-Fitting Twisted Tape Inserts for First Wall Cooling in Molten Salt Breeder Blankets

One of the major components in fusion energy systems is the fusion blanket, which has a vacuum vessel to contain the plasma. As part of the fusion blanket/vacuum vessel, the first wall and plasma-facing components require sufficient cooling to prevent material degradation during operation from the superheated plasma. Most fusion blanket concepts involve first wall and divertor coolant channels with heat transfer enhancements (HTEs) that are intended to withstand the incident high heat fluxes of 1 to 5 MW/m 2 . Twisted tape inserts are a proposed HTE that have been investigated previously for first wall cooling and monoblock divertor cooling channels and in other nonfusion heat transfer components. By inserting twisted tapes into straight pipes, the amount of turbulence in the system can be increased at lower Reynolds numbers by swirling the flow. This results in better heat transfer characteristics with marginal increases in frictional pressure losses. In particular, simulations of high-Prandtl-number fluids such as the proposed molten salt FLiBe in twisted tapes, which is prototypic to liquid immersion blankets, have not been previously explored. Here, in this study, we simulate various Prandtl numbers in pipes with twisted tape inserts using large eddy simulations to determine the effects of increasing Prandtl numbers on heat transfer performance. The quantities of particular interest are the Nusselt number and the friction factor, which were recovered using data reduction techniques to determine impacts on heat transfer and pressure losses. This work serves as a starting point for determining the feasibility of twisted tape inserts for liquid immersion blanket concepts.

LES↗

Space shuttle orbital maneuvering engine platelet injector program

A platelet face injector for the Orbit Maneuvering Engine (OME) on the space shuttle was evaluated as a means of obtaining additional design margin and lower cost. The program was conducted in three phases. The first phase evaluated single injection elements, or unielements; it involved visual flow studies, mixing experiments using propellant simulants, and hot firings to assess combustion efficiency, chamber wall compatibility, and injector face temperatures. In the second phase, subscale units producing 600 lbf thrust were used to further evaluate the orifice patterns chosen on the basis of unielement testing. In addition to combustion efficiency, chamber and injector heat transfer, the subscale testing provided a preliminary indication of injector stability. Full scale testing of the selected patterns at 6,000 lbf thrust was performed in the third phase. Performance, heat transfer, and combustion stability were evaluated over the anticipated range of OMS operating conditions. The effects on combustion stability of acoustic cavity configuration, including cavity depth, open area, inlet contour, and other parameters, were investigated.

Source record↗

Heat Transfer and Pressure Loss of Additively Manufactured Internal Cooling Channels With Various Shapes

Abstract Additive manufacturing (AM) provides the ability to fabricate highly customized internal cooling passages that are relevant to gas turbine components. This experimental study examines the pressure loss and heat transfer performance of a range of fundamental channel shapes that were produced using direct metal laser sintering. Circular, hexagonal, pentagonal, elliptical, diamond, square, rectangular, trapezoidal, and triangular channel cross sections were investigated. To maintain the same convective surface area between shapes, the wetted perimeters of the channel cross sections were kept constant. Parallel computational fluid dynamic simulations were performed to understand the relationships in cooling performance between several channel shapes. Several characteristic length scales were evaluated to scale the pressure loss and heat transfer measurements. Among the channel shapes investigated, the diamond channel showed the lowest Nusselt number and friction factor. The pentagon exhibited a similar Nusselt number as the circular channel despite having a lower friction factor. There was no difference in scaling the friction factor or Nusselt number results of the different channel shapes between using the square root of cross-sectional area compared to hydraulic diameter as the characteristic length scale

Engineering↗

Experimental investigation on nucleate boiling heat transfer of low GWP refrigerants over metal-foam enhanced tube bundles

The objective of this work is to develop an enhanced tube bundle to improve the nucleate boiling heat transfer for the application of flooded evaporators. The enhanced tube bundle was made by deploying metal foam around the outer surface of aluminum tubes, which provide higher heat transfer area and nucleation site density. The pool boiling experiments for horizontal tube bundles were conducted in a pressure vessel at difference heat fluxes. The heat transfer performance of bare aluminum tube bundle was compared against the metal-foam enhanced tube bundle using low GWP refrigerant, R-1234yf. The experimental results showed that the heat transfer coefficient of the metal-foam enhanced tube bundle was at least two times higher than that of the bare tube bundle, and the enhancement ratio depended on the heat flux condition.

Yang, Cheng-Min↗

Analysis of Laminar Convective Heat Transfer Over Structured Non-Wetting Surfaces

Structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow which, in turn, affects the convective heat transfer performance over the surfaces. In this work, an analytical model is developed for the interfacial Nusselt number, the overall Nusselt number and a thermal hydraulic performance factor for fluid flow in a cylinder patterned with structured non-wetting surfaces, for the two cases of uniform wall heat flux and uniform wall temperature. In addition, by considering the stability of the Cassie state of wettability and its transition to the Wenzel state for flow over superhydrophobic surfaces, the present model overcomes certain limitations of the previously reported studies in the literature. Based on the analytical formulations and the stability constraints, the present paper provides optimum design maps for tailoring structured non-wetting surfaces for maximizing convective heat transfer and the combined thermal-hydraulic performance in applications. Use of the design maps on example cases is also discussed. It is shown that the use of structured non-wetting surfaces is most effective for low Reynolds numbers and/or small cylinder radius.

42 ENGINEERING↗

Investigation of gaseous propellant combustion and associated injector/chamber design guidelines

Injector design criteria are provided for gaseous hydrogen-gaseous oxygen propellants. Design equations and procedures are presented which will allow an injector-chamber designer to a priori estimate of the performance, compatibility and stability characteristics of prototype injectors. The effects of chamber length, element geometry, thrust per element, mixture ratio, impingement angle, and element spacing were evaluated for four element concepts and their derivatives. The data from this series of tests were reduced to a single valued mixing function that describes the mixing potential of the various elements. Performance, heat transfer and stability data were generated for various mixture ratios, propellant temperatures, chamber pressures, contraction ratios, and chamber lengths. Applications of the models resulted in the design of procedures, whereby the performance and chamber heat flux can be calculated directly, and the injector stability estimated in conjunction with existing models.

Calhoon, D. F.↗

Conventional Rib Turbulators For SCO 2 Turbine Internal Cooling (Report)

This report documents experimental work in the NETL Heat Exchange and Experimental Testing (HEET) rig. The heat transfer performance of additively manufactured internal cooling features in supercritical CO 2 were characterized. It was demonstrated that the thermal performance factor of conventional angled rib turbulators remains independent of Reynolds number up to 3.1 x 10 5 indicating that these features may be employed to enhance heat transfer in sCO 2 turbine blades and vanes. This augmentation of heat transfer in the internal cooling passages decreases the required turbine coolant and improves the power cycle efficiency.

20 FOSSIL-FUELED POWER PLANTS↗

Enhancing Steam-Side Heat Transfer via Microdroplet Ejection using Inorganic Coatings

During condensation of water on a superhydrophobic nanostructured surfaces, droplets coalesce and jump (droplet ejection) due to the release of excess surface energy. Meticulously designed nanostructured surfaces or coatings capable of droplet ejection can enhance heat transfer performance by easy removal of droplets during condensation. In the present work, the capabilities of the Nelumbo droplet ejection coatings technology currently used in commercial heat exchangers are explored and optimized for materials and conditions relevant to steam condensers. Specifically, this includes (1) adapting and optimizing the procedures and chemistries to deposit droplet ejecting coatings on materials used in the steam condenser, (2) testing of the heat transfer, durability, and fouling of the fabricated coatings under a variety of steam condenser relevant conditions, and (3) modeling of the impact of droplet dynamics and interfacial properties on heat transfer in steam condensers. We experimentally demonstrated that at low supersaturation conditions (S~1.02), developed superhydrophobic nanostructured surface gives a 40% higher peak heat transfer flux and a 17% higher peak overall heat transfer coefficient (U) with droplet ejection mechanism compared to the dropwise condensation mechanism on the same nanostructured surface. Though the experimentally observed droplet ejection mechanism was short-lived (~3 min) due to the limitation of the chiller to maintain a constant supersaturation condition in fabricated steam condenser. And large variations in water inlet temperature (+ to - 2 degrees C) caused flooding of nanostructure (Wenzel state) at higher supersaturation (S > or = 1.12). This is an important finding because typical supersaturation levels in field operation are over 1.8 and as such, either the flooding potential for these materials should be improved or operation at lower supersaturation may be required to maximize heat transfer efficiency. If supersaturation conditions can be maintained reliably in the steam condenser in addition to droplet ejection mechanism during condensation, this could provide a potential 2% reduction in water flow rate which equates to a savings of over 3900 gallons of water per minute for a 500 MW steam turbine and over $0.3MM savings annually given a 0.02 cent marginal water withdrawal cost. It is also worth noting that these savings are based on improvement of droplet ejection coatings over coatings capable of performing consistent dropwise mechanism in in-field surface condensers. Savings due to the droplet ejections coatings when compared to bare substrates could be much higher. Additionally, the present work provides the importance of steam condenser operating conditions and insights into the challenges in modeling the condensing droplet dynamics on surfaces.

20 FOSSIL-FUELED POWER PLANTS↗

Optimization of Triply Periodic Minimal Surface Heat Exchanger to Achieve Compactness, High Efficiency, and Low-Pressure Drop

With advancements in additive manufacturing (AM) techniques, high-quality triply periodic minimal surface (TPMS) structures can now be produced. TPMS walled heat exchangers (HX) hold significant potential for industrial applications and are receiving increasing attention. This paper explores the impact of various TPMS design variables on flow and thermal performance to optimize TPMS heat exchangers for compactness, high efficiency, and low pressure drop. The design variables examined include the type of TPMS lattice, unit cell size, wall thickness, aspect ratio, TPMS orientation, and equivalent thickness. The study reveals that the flow and heat transfer performance of TPMS structures are significantly affected by these design variables. For the Gyroid, Diamond, and SplitP lattices, performance is nearly identical when the surface-to-volume ratio is kept constant. The average velocity of the fluid in the TPMS HX should be 0.3 m/s. The corresponding Re is between 300~800. Thin wall thickness, small equivalent thickness, and flat lattice configurations can significantly reduce pressure drop while maintaining the overall heat transfer coefficient. Additionally, the angle between the flow direction and TPMS orientation can increase pressure drop. Three aluminum heat exchangers were successfully printed using an AM machine, and testing results are comparable with theoretical prediction.

42 ENGINEERING↗

Performance evaluation of finned tube heat exchanger using curved wavy delta winglet vortex generators with circular perforations

Vortex generation is recognized as an effective passive approach to improve the heat transfer rate in fin and tube heat exchangers (FTHEs). The current study proposed innovative designs of curved wavy delta winglet vortex generators (CWDWVGs), both without and with circular perforations, to improve the heat transfer efficiency of FTHEs. There is potential to increase heat transfer performance further through various CWDWVG designs. Here, this study explores seven unique CWDWVG configurations, from 1-wave to 7-wave. A 3-D computational numerical model is utilized to evaluate the Thermo-hydraulic performance of FTHEs fitted with these different CWDWVG configurations across Reynolds numbers from 400 to 2000. This comparative analysis of the Thermo-hydraulic performance of FTHEs featuring four parallel circular tube layouts assesses configurations both with and without vortex generators (VGs) and various hole configurations. The evaluation of Thermo-hydraulic performance involves different parameters, including the London area goodness factor (LAGF), Colburn factor (j), friction factor (f), pressure drop (?P), and Nusselt number (Nu). Results demonstrate that the various CWDWVG configurations and the number of holes in them substantially affect the efficiency, as evaluated by the dimensionless Performance Evaluation Criteria (PEC). Notably, the 7-wave CWDWVGs surpassed other configurations, and integrating circular punched perforations further improved the thermal-hydraulic performance of FTHE. Specifically, the 7-wave CWDWVGs without holes demonstrated superior performance over other configurations, showing a significant increase in Nusselt number by 75.18% and 85.16% at Reynolds numbers of 2000 and 400, respectively, alongside an increase in pressure drop by 216.38% to 224.96%. Meanwhile, the 7-wave CWDWVGs with eight holes, in comparison to those without holes, exhibited a Nusselt number increase of 0.85%, a pressure drop decrease of 7.31%, and a reduction in the friction factor by 5.82%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗