Annular Pipe Research Articles

Experimental investigation of the effects of metal foam porous rings on non-Newtonian fluid flow in a double pipe heat exchanger

In this study, we experimentally investigate the effects of metal foam porous rings on heat transfer, pressure drop, and the heat transfer performance ratio of two non-Newtonian fluids in a double-pipe heat exchanger. Enhancing the heat transfer rate is crucial for reducing the size and cost of heat exchangers. We considered various parameters in the experiment, including the power-law index (0.91 and 0.85), porous ring thickness (4, 6, and 8 mm), and the number of porous rings (2, 4, 6). The flow is a turbulent regime, with the Reynolds number ranging from 4000 to 10,000. The test setup includes a test section with a length of 1.6 m and a diameter ratio of 0.6. Open-cell copper metal foam rings with a porosity of 0.92 are placed in the annular pipe, while the internal surface of the inner pipe is subjected to constant heat flux. The results show that, for non-Newtonian Carboxy Methyl Cellulose fluids with concentrations of 0.1% and 0.2%, the average heat transfer coefficients at Reynolds number 4000 increase by 22.0% and 32.0%, respectively. With porous rings, these coefficients increase by 80.3% and 92.7%. Additionally, the average friction factor increases by 19.2% and 35.5% without porous rings and by 320% and 280% with porous rings, respectively. Furthermore, increasing the number of porous rings from 2 to 6 increases the Nusselt number by approximately 16.8% and 17.1%, respectively. The maximum friction factor is 400% higher when using a 0.2% concentration of non-Newtonian fluid. Finally, the performance of the two non-Newtonian fluids improved by approximately 28% and 36.4%, respectively, compared to the base fluid.

Experimental Investigation of Spherical Particles Settling in Annulus Filled with Rising-Bubble-Containing Newtonian Fluids

During the drilling of ultra-deep wells, gas kick often occurs, influenced by the complex void pressure profile. The accurate description of particle settling behavior in the gas–liquid mixture is of great significance to effectively deal with gas kicks and ensure drilling safety. In this study, the gas–liquid two-phase annulus flow with different gas volume fractions is created through the transparent annular pipe, constant pressure air pump, and gas flowmeter. High-speed photography is used to record and analyze the sedimentation of particles in gas–liquid mixtures. This study is based on 288 tests. The main parameters in this experiment include the particle Reynolds number, the gas fraction, and liquid viscosity. The effects of wall and gas fraction on the drag coefficient were analyzed. The correlation of particle terminal settling velocity was established. The results obtained show a correlation with average absolute errors (AAE) of 10.7%. This study reveals the settling characteristics of particles in the annular gas–liquid mixed flow, provides an accurate terminal settling velocity prediction explicit formula, and provides guidance for the calculation of bottom hole pressure under the condition of gas kick.

Synergistic Exploration of Heat Transfer for Integration Magnetohydrodynamics of Nanofluids Peristaltic Transport within Annular Tubes

The problem of treating cancer is considered one of the most important daily challenges that affect the lives of people with cancer. This research deals with solving this problem theoretically. Through previous studies, it has been proven that gold nanoparticles are able to remove these cancer cells. The idea of this research is theoretically based on injecting a cancer patient with gold nanoparticles that are exposed to a magnetic field. When these particles penetrate cancerous cells and are exposed to a magnetic field, this causes their temperature to rise. The high temperature of the nanometer gold particles that penetrate the cells of the affected body leads to the explosion of the cancer cells. In this research, the various external forces that affect the flow movement of the nanofluid are studied and how its physical and thermal properties are affected by those external forces. The MHD peristaltic flow of a nanofluid in an annulus pipe as a result of the effect of the wall properties has been investigated. This has been achieved through slip and thermal conditions. Wave velocity leads to flow development. The inner annulus wall is rigid, while the outer wall of the artery moves under the influence of wave peristaltic movement. The nonlinear equations that describe the flow are solved under long-wavelength assumptions. The results were compared with other numerical methods, such as finite volume and finite element and the long wavelength method and proved to be accurate and effective. The expressions of pressure difference, velocity, stream function, wall shear stress, and temperature are analyzed. It is noted that the flow velocity increases with the Knudsen number, and the increased source heat suggests an increased temperature. The increasing amplitude ratio at most of the interface points between the artery wall and the catheter results in increased velocity. The streamlines are affected by the magnetic field, as increasing the influencing magnetic field leads to a decrease in flow lines. It is observed that this stress decreases when nanoparticles increase, in contrast to the effect of the magnetic field and also the occurrence of slipping. It was found that the mass of the wall cells relative to their area works to decrease the pressure difference, in contrast to the tension between those cells, which works to increase the pressure difference. Without slipping and with slipping , the temperature decreases with increasing in nanoparticle concentration . The temperature also increases with the amplitude ratio . This strongly affects the generated drag on the catheter wall, which is mainly responsible for the enhanced temperature on this wall.

Experimental investigation of the performance attributes of a double pipe heat exchanger equipped with baffles of conventional or flower layouts

In industrial heat management, the design of baffles within heat exchangers is crucial. They guide fluid flow and enhance turbulence, optimizing heat transfer. Yet, their configuration must be carefully considered to balance thermal efficiency with energy expenditure and pressure management. This research conducts practical tests on the hydrothermal attributes of a counter-flow double-pipe heat exchanger. It evaluates two baffle layouts: segmental and flower, considering baffle cut-off ratio (16.7 %≤δ ≤ 50 %), pitch ratio (8.3 %≤λ ≤ 22.2 %), flower-design relative angle (30°≤γ ≤ 90°), and operating conditions of annulus-side (2660 ≤ Rean ≤ 13110, 5.21 ≤ Pran ≤ 7.48). The findings assure that installing the baffles results in notable increases in both Nu¯an and fan. Besides, lowering baffle cut-off and pitch ratios, and increasing the relative angle of flower baffles lead to additional increases. Moreover, raising the annulus-fluid temperature reduces Nu¯an with a negligible effect on fan. Increasing Rean leads to a reduced fan and greater Nu¯an. Compared with no baffles, the maximum recorded increases in the Nu¯an and fan are 147.4 % and 60.2 %, respectively, realized by incorporating flower layout. On average, the flower baffles boost the Nu¯an by 20.8 % more than those using conventional baffles, with an average increase of 4.3 % in the fan. To judge the benefit of utilizing baffles, the Hydrothermal Performance Index (HTPI) is calculated, and its highest value is recorded as 2.23, attained by running the annular pipe at the lowest flow rate and temperature, with inserting flower baffles (δ = 16.7 %, λ = 8.3 %, γ = 90°). Finally, correlations for Nu¯an, HTPI, and fan prediction are suggested.

Experimental study of pipeline pressure loss laws with large-size gangue slurry during the process of industrial-grade annular pipe transportation

Gangue grouting and backfilling mining technology is one of the key techniques to achieve solid waste disposal and rock movement control in coal mines. The pipeline conveying performance of gangue slurry determines the success or failure of backfilling engineering directly. Due to the high cost of crushing small-sized gangue, research on pipeline transportation of large-sized gangue slurry has been gradually highlighted. In this study, the gangue slurry ratio optimization test and industrial-grade pipeline transportation experiments were conducted, and the optimal ratio of gangue slurry with different large particle size grading was obtained. Additionally, the rheological parameter changes of gangue slurry in pipeline transportation were analyzed, and the changes in slurry mass concentration, slurry flow velocity, and particle size matching of pressure loss in the straight and bent pipe sections of the transportation pipeline were studied. The results show that the optimal ratio for the 0–5 mm particle size gangue slurry is the mass concentration of 65 % and a mass proportion of 0.3: 2: 1 for 2–5 mm, 0.15–2 mm, and 0–0.15 mm particle size gangue; the optimal ratio for the 0–2 mm particle size gangue slurry gangue is the mass concentration of 60 % and a mass proportion of 2:1 for 0.15–2 mm and 0–0.15 mm particle size gangue. Both the mass concentration, flow velocity, and particle size grading of the gangue slurry have a significant impact on the pressure loss during pipeline transportation. The mass concentration of the gangue slurry has the most significant impact on the pressure loss in the straight pipe section, while the flow velocity has the highest impact on the pressure loss in the bent pipe section. The research results provide a theoretical basis for the design of pipeline transportation parameters for gangue grouting and backfilling projects.

Effects of wick structure and installation angles on the heat transfer characteristics of concentric annular heat pipes: Experimental investigation

Thermal protection of the infrared sensor is critical in the temperature measurement of the turbine disk. One of the infrared sensors' most critical thermal protection structures is the Concentric Annular Heat Pipe (CAHP) due to its excellent heat transfer capability. In this study, specific CAHPs are designed with circumferential uniform wick (CUW) and circumferential grid wick (CGW) configurations according to the temperature measurement scenario of the turbine disk chamber. The effects of wick structure on the CAHP's startup characteristics and heat transfer performance are examined through experiments. Results show that, compared to CUW, CGW has a shorter startup time and smaller thermal resistance, but the critical heat flux is lower. Results also that, the circumferential temperature distribution at the evaporator of CUW is more uniform than CGW. An increase in the number of grids can enhance temperature uniformity. When the evaporator is positioned below the condenser, the thermal resistance of the heat pipe is lower, so this configuration is more suitable in engineering applications.

Improving sensible heat storage in a vertical annular pipe subject to variable inlet boundary condition using TiO2/water nanofluid: Numerical study

A computational fluid dynamics (CFD) analysis is conducted to investigate the thermal performance of unsteady free convection of TiO2/water nanofluids. The study process within a coaxial heat exchanger system. The model is based on the mixture Buongiorno approach. Due to the axisymmetric conditions, the study is carried out in two dimensions, and the conservation equations are reformulated in dimensionless form. The obtained PDE system is Discretized using the finite element method. The TiO2 concentration heterogeneity, resulting from thermophoresis and Brownian motion is considered. The presentation of the results encompassed isotherms, nanoparticle volume fraction distributions, and streamlines. The validation of the model shows a good agreement with the experimental results. The impact of the mass fraction’s nanoparticles ( 0.01 ≤ ϕ ≤ 0.04 ) and the Rayleigh number ( 10 3 ≤ Ra ≤ 10 8 ) on the heat transfer performance are analyzed. The parametric study shows that an increase in the Rayleigh number has no effect on heat transfer enhancement. Unlike for Ra = 10 6 where an increase in Nusselt number is observed. It was found also that the effect of nanofluid concentration on the Nusselt number was more noticeable in high Rayleigh cases due to the convection-driven heat transfer.

Simulation of heat transfer in Poiseuille pipe flow via generalized finite difference method with a space stepping algorithm

The aim of this paper is to propose an efficient numerical scheme to deal with heat transfer problems in pipe flow with a large length/diameter ratio. The generalized finite difference method (GFDM) is combined with a space stepping algorithm (SSA) for the solution. The SSA divides the solution domain into a number of overlapping sections in the length direction of the pipe. Due to the large Peclet number, the heat transport process is dominated by advection, which allows an approximate boundary condition to be applied at the downstream cross section. The problem is then solved section by section. Using the uniform distributed points, the solution matrix for each section does not change, and only the right hand side needs to be refreshed for the changing boundary conditions. This leads to a highly efficient scheme for problems with a large pipe length. To show the accuracy of the numerical scheme, a problem with available analytical solution is studied. Then the method is applied to problems of single pipe with different pipe wall temperature and flow Reynolds number, and concentric annular pipe. Numerical results confirm the stability and efficiency of the GFDM-SSA. The method can be applied to many real world transient heat transfer problems in which the pipe is heated or cooled along its length with arbitrary wall temperature for heat exchange and other purposes.

Numerical simulation of two-phase gas-liquid flowthrough horizontal annulus pipe

Chemical, petroleum and nuclear systems are only a few of the industrial processes that utilize gas-liquid flow in annular closed channels. However, concentric horizontal annuli flow patterns have received little attention. The ability to precisely characterize two-phase flow patterns using computational techniques is crucial for the production, transportation, and optimization of designs. This current research aims to establish the accuracy of the computational fluid dynamics (CFD) model in predicting the gas-liquid flow pattern in the concentric annulus pipe and validating the flow pattern of liquid holdup with experimental results from the literature. The simulations were done on a test section of a 12.8 m length pipe with a hydraulic diameter of 0.0168 m using air and water as the working fluids. The volume of fluid (VOF) model in Ansys Fluent based on the Eulerian- Eulerian approach in conjunction with the realizable k-ε turbulence model was used to model the gas-liquid flow pattern, i.e. dispersed bubble, elongated bubble, and slug in a horizontal annulus. A comparison of the model with the experimental high-speed video images shows a reasonable agreement for the flow pattern and liquid holdup data.

An integrated system combining MDBHE (multi-casing DBHE) and heat pump achieves heating and cooling for medium-deep geothermal energy utilization

Due to its convenient application in utilizing the medium-deep geothermal energy, the deep borehole heat exchanger has received extensive attention. Here we initiated an integrated system by coupling the multi-casing deep borehole heat exchanger (MDBHE) and heat pump to realize heat extraction and heating in the whole well in winter, and heat storage and cooling in the well upper part in summer. In the MDBHE, an annular pipe was used to store heat. Through the analysis of the simulation results of the influence of several variables on the system performance, it is found that the increase of heat storage temperature, annular pipe length and formation thermal conductivity raised the heat storage rate of the system, but the geothermal gradient is opposite. Benefiting from heat storage, the heat extraction rates in winter is also improved. Meanwhile, the heat pump elevated the heating rate by 15.9% in winter, and the cooling rate of the heat pump were respectively 19.3%, 21.5% and 23.7% less than the heat storage rate of the MDBHE based on the heat storage temperature of 40, 45 and 50 °C. Therefore, the integrated system can simultaneously satisfy the requirements of summer cooling and winter heating and maintain the formation heat balance, so that the urban heat island effect is mitigated.

Pipe to annular flow conversion: Numerical study

Large Eddy Simulation (LES) of turbulent flow at the entrance to an annular pipe section has been performed. The flow over a single circular rod, coaxially immersed in a circular pipe is considered. The Reynolds number, based on mean velocity and hydraulic diameter of the annular section, is ReDh=40530. The study aims to gain insights into the turbulence characteristics of the primary and secondary separation bubbles, developing on a side surface of the rod. Key findings include tiny toroidal vortices in the primary bubble's front, forming a vortex train with intermittently shed vortex structures. Large-scale helical stripes have been reproduced at the entrance to the annular section. Tilting of the axially-oriented streaks was observed close to the rod surface. It resulted in a slight anisotropy of the normal Reynolds stresses. The LES data could refine classic Reynolds-averaged Navier-Stokes-based turbulence models.

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes – ERRATUM

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes – ERRATUM

Annular expansion for enhanced orientation and mechanical properties of extruded amorphous PPESK/PES pipes

AbstractWith the discovery of deeper oil fields, conventional metal pumping pipes have been proven to be ineffective in meeting the requirements for deep well oil production due to their high weights and limited corrosion resistance. Therefore, in this study, a composite of Poly(phthalazinone ether sulfone ketone) (PPESK) and polyethersulfone (PES) was used to fabricate nonmetal pipes. To enhance the mechanical properties of the PPESK/PES pipes, a self‐designed annular expansion pipe extruder head was used. The circumferential burst stress and axial tensile strength of the PPESK/PES pipes subjected to 30° expansion were 73.0% and 48.9% higher than those of the unexpanded sample, respectively. When annular expansion was integrated into the extrusion of PPESK/PES/carbon fiber pipes, the axial tensile strength and circumferential burst stress were 45.9% and 88.8% higher than those of the unexpanded sample, respectively. Results of polarized infrared testing and metallographic microscopic examinations demonstrated that molecular chains present a regular orientation at a certain angle to the extrusion direction, under the effect of annular expansion extrusion. These findings highlight the efficiency of annular expansion in promoting the large‐scale production of pipes.

Encapsulation of mRNA in lipid nanoparticles by membrane micromixing

Messenger RNA encapsulated in lipid nanoparticles (mRNA-LNPs) are successfully used worldwide for vaccination against COVID-19. mRNA-LNPs are manufactured by mixing an ethanolic phase (containing an ionizable lipid, a phospholipid, a PEGylated lipid and cholesterol) and an aqueous phase (citrate buffer at pH 4.5 containing mRNA). The characteristics of the mRNA-LNPs obtained (size, internal structure, mRNA functional delivery in vivo, etc) depend on several parameters and among them are the mixing conditions of the ethanolic and aqueous phases. While the impact of these parameters is well-recognized for small scale preparations (some microliters), their effect at a larger scale is less well-known. The purpose of this study is to investigate the production of some hundreds of millilitres of mRNA-LNP suspension using a ceramic membrane (SPG Technology) as a new mixing device. Summarily, in this technique, the ethanolic phase permeates through the membrane pores and mixes with the aqueous phase flowing in a small annular pipe between the tubular membrane and an inside rod. First, empty LNPs were prepared to determine the effect of membrane pore size, flow rate, and the ratio between the ethanolic and aqueous phase volumes. The experimental conditions tested did not change the characteristics of the LNPs obtained. Second, mRNA-LNPs were prepared and the suspensions obtained were then submitted to buffer exchange/concentration/ sterile filtration dialysis. The resulting mRNA-LNPs had a particle size of 103 ± 5 nm, a polydispersity index of 0.15 ± 0.005, and encapsulation efficiency of 96 ± 0.0 %. mRNA-LNPs with similar characteristics were obtained using ethanol ratios of 1/4 (20 % ethanol in the final preparation) and 1/6 (14 % ethanol). Overall, membrane micromixing using a ceramic membrane was shown to be a suitable technology for the preparation of mRNA-LNP suspensions.

Cross-sectional temperature field of a solar collector’s absorber in the case of annular pipe

In households, solar collectors are finding ever increasing use for hot water preparation. Although the design of solar collectors is relatively simple, the authors over many years concentrate attention on modelling the cross-sectional temperature field of the solar collector’s absorber [1-7]. In solving the cross-sectional temperature field for an annular pipe [1], the periodical cross-sectional domain is divided into three sub-domains where the first sub-domain is the plate between pipes, the second – a pipe’s wall, and the third – the liquid; as a result, the temperature field expressions have been obtained for all the three sub-domains. In works [2, 3] the temperature fields obtained were simplified. To define its variations in time, the temperature field was found by solving the Laplace equation under non-stationary time-dependent conditions [4]. The obtained results evidence that the non stationary conditions might not be taken into account in long- lasting sunny weather, while such non-stationarity changes considerably the temperature field when it is short-term (e.g. in cloudy weather). The temperature has also been found for a square-pipe absorber [7] as more technological in design. In the present work, the final temperature field model is proposed for the absorber of a round-pipe collector. As distinguished from [1], in this work the temperature of liquid is assumed to be constant over the entire pipe cross-section. Such an assumption significantly simplifies the calculation while not changing the physical essence.

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models incorporate a finite local slip length and constant shear stress along the slits, and thus go beyond the assumption of perfect slip employed commonly for superhydrophobic surfaces. Thereby, they provide the possibility to assess the influence of both the viscosity of the air or other fluid that is modelled to fill the slits as well as the influence of the micro-geometry of these slits. First, expressions for tubes and annular pipes with superhydrophobic or slippery walls are provided. Second, these solutions are combined to a tube-within-a circular-pipe scenario, where one fluid domain provides a slip to the other. This scenario is interesting as an application to achieve stable fluid–fluid interfaces. With respect to modelling, it illustrates the specification of the local slip length depending on a linked flow field. The comparison of the analytically calculated solutions with numerical simulations shows excellent agreement. The results of this paper thus represent an important instrument for the design and optimization of slippage along surfaces in circular geometries.

Insights into the hydrodynamics in the annular pipe of industrial‐scale top‐blown smelting furnace

AbstractThe coaxial jet consisting of swirl jet and axial jet plays a critical role in the industrial processes but is rarely investigated; therefore, it is numerically explored by means of the computational fluid dynamics (CFD) approach in the present work. The force on the swirler, axial and tangential velocity at the annular pipe outlet, and the spatial distribution of swirl number (SN) are selected to evaluate the effect of geometrical parameters on the swirling performance. The results clarify that the velocity and their azimuthal components in the transverse cross‐section can be categorized into six segments based on high/low velocity values. The coaxial jets form a weak swirl with high axial, certain tangential, and low radial velocities. x‐ and y‐vorticity vary within −200 to 200 s−1. Coaxial jet mixing decays the SN. Based on the multi‐objective matrix analysis, swirler height has the largest effect on swirl performance followed by diameter, angle, and number based on analysis. Optimal parameters are 130° vane angle, 240 mm diameter, 10 vanes, and 250 mm height of the swirler.

Zalety materiałów kompozytowych stosowanych w otworowych narzędziach skrawających

One of the important reserves for the growth of oil and gas production is the acceleration of emergency recovery work in production and exploration wells at minimal cost. A significant amount of work in downhole conditions is performed using downhole destructive and cutting tools. Each oil and gas producing country annually uses more than 100 standard sizes, thousands of cutting tool sets: downhole, annular, combined, pilot, internal and external pipe cutters, as well as reamers for cutting side “windows” in production strings. Therefore, the need for them is growing significantly every year. The conducted experiments show that during the operation of cutting tools, the working abrasive-cutting part of the tool wears out and collapses, but the body, other elements and the connecting thread remain suitable for further operation. Therefore, the restoration of working bodies, consisting of crushed particles of used borehole cutting tools, is an urgent scientific and technical task for the oil and gas industry. When repairing oil and gas wells, as well as eliminating the most complex accidents, more than a hundred standard sizes of downhole cutting and destructive tools are used. Currently, an acute shortage of this equipment in oilfield facilities makes it necessary to reconsider the technologies for restoring downhole cutting and destructive tools and introduce them into production. The conducted studies show that there is not enough information about the thickness and height of the layers of the material applied to the damaged area of the cutting and destructive tool, as well as the information necessary for the optimal mode of its operation and its effectiveness after restoration. Composite materials are widely used in the preparation of cutting-chopping and destructive elements of oil-field tools and equipment used in the drilling, operation and repair of wells. In order to increase the cutting capacity of the cutting part of the tool, it is necessary to investigate the advantages of tungsten-carbide (TC) type composite materials compared to other materials and ensure their resistance to high temperatures. As a result of theoretical studies, the stress-deformation state of the contact areas of the composite elements, where the working areas of the cutting and destructive tools are reinforced, and the dependence of the productivity of the composite materials on the speed of transition to metal and the sizes of the composite grains were determined by using the finite element method (two-dimensional simplex elements).

The influence of corrugated pipes parameters on heat transfer characteristics

In order to investigate the influence mechanism of various corrugated structures on the heat transfer of continuous annular concave-convex corrugated pipes, this paper examines the influence of corrugation height (Ch = 1 mm, 1.5 mm, and 2 mm) and corrugation width (Cw = 1 mm, 1.5 mm, and 2 mm) on the flow pattern, turbulent kinetic energy, Nusselt number, friction coefficient, and performance evaluation factor. Then, the correlation equations for Nusselt number and friction coefficient are established with different corrugated structural parameters. The results show that with the increase of Ch, the vortex number, turbulent kinetic energy, and friction coefficient in the pipe increase while Nusselt number decreases. The maximum perfomance evaluation factor is 0.90 at Ch = 1 mm. However, with the increase of Cw, the vortex number and Nusselt number in the pipe increase, while turbulent kinetic energy and friction coefficient in the pipe do not change much. The maximum performance evaluation factor is 0.87 at Cw = 2 mm. Therefore, for this type of corrugated pipe, one should choose a small Ch and a large Cw.

Inner thermal layout optimization for nanofluid-filled horizontal annular pipes

This paper investigates the optimization of the inner thermal layout in nanofluid-filled horizontal annular pipes under natural convection conditions. Two-dimensional models of annular pipes are established using a numerical simulation approach. Then, using this as the simulation tool, the layouts of single-, triple-, and quadruple-heat-source annular pipes are optimized. The coordinates of the inner cylinders are defined as the decision variables, and the average Nusselt number (Nu) on the cold wall surface as the objective function. For the single-cylinder model, both the Bayesian optimization algorithm (BOA) and the genetic algorithm (GA) derive the same results: an axisymmetric layout where the single heat source is positioned slightly above the axis of the annulus. However, the BOA takes much less computational time than the GA and, consequently, is chosen for cases with more complex geometry. The optimization layout of the three-cylinder model also shows an axisymmetric distribution, while the result for the four-cylinder model presents a centrally symmetric distribution. Compared to the original average Nu, the optimized ones are enhanced by 17.83%, 8.36%, and 6.18% for single-, triple-, and quadruple-heat-source annular pipes, respectively. The results of this study can be used for guiding the layout design and optimization of the nanofluid-filled exchangers with multi-inner heat sources.