Temperature Boundary Research Articles

Elucidating optimal nanohole structures for suppressing phonon transport in nanomeshes

Nanomeshes, often referred to as phononic crystals, have been extensively explored for their unique properties, including phonon coherence and ultralow thermal conductivity (κ). However, experimental demonstrations of phonon coherence are rare and indirect, often relying on comparison with numerical modeling. Notably, a significant aspect of phonon coherence, namely the disorder-induced reduction in κ observed in superlattices, has yet to be experimentally demonstrated. In this study, through atomistic modeling and spectral analysis, we systematically investigate and compare phonon transport behaviors in graphene nanomeshes, characterized by 1D line-like hole boundaries, and silicon nanomeshes, featuring 2D surface-like hole boundaries, while considering various forms of hole boundary roughness. Our findings highlight that to demonstrate a disorder-induced reduction in κ of nanomeshes, optimal conditions include low temperature, smooth and planar hole boundaries, and the utilization of thick films composed of 3D materials.

An Edge-based Interface Tracking (EBIT) method for multiphase flows with phase change

In this paper, the Edge-Based Interface Tracking (EBIT) method is extended to simulate multiphase flows with phase change. As a novel Front-Tracking method, the EBIT method binds interfacial markers to the Eulerian grid to achieve automatic parallelization. To include phase change effects, the energy equation for each phase is solved, with the temperature boundary condition at the interface sharply imposed. When using collocated grids, the cell-centered velocity is approximately projected. This will lead to unphysical oscillations in the presence of phase change, as the velocity will be discontinuous across the interface. It is demonstrated that this issue can be addressed by using the ghost fluid method, in which the ghost velocity is set according to the jump condition, thereby removing the discontinuity. A series of benchmark tests are performed to validate the present method. It is shown that the numerical results agree very well with the theoretical solutions and the experimental results.

Thermal-hydraulic phenomena and heat removal performance of a passive containment cooling system according to exit loss coefficient

The natural circulation system has been widely studied for use in various applications because of its inherent advantage. However, it has a key weakness called flow instability that makes the system unstable. Through massive previous research, the mechanisms of flow instability were analyzed, but there was an ambiguous aspect related to the effect of experimental parameters on the phenomenon. Particularly, there has been no report on the heat transfer performance of the system when flow instability phenomena were present. In this study, thermal-hydraulic phenomena of a two-phase natural circulation system that functions as a passive containment cooling system (PCCS) was investigated according to experimental parameters, namely, the temperature boundary (120–158 °C) and exit loss coefficient (0–34.5) under atmospheric pressure conditions. The experimental results showed five different flow types in the loop. The flow modes that occurred by the interaction between flashing and boiling were classified by referring to the mass flow rate, void fraction, and visualization data. The system was more unstable when the temperature boundary conditions increased, but it was more stable when the exit loss coefficient increased. These results have only been confirmed in our research. The reason for the results is that the flow conditions are located on the boundary between Density Wave Oscillation I and the stable flow region, and that boundary does not have clear criteria. In addition, comparing the heat transfer performance of a system by heat rate can confirm the effect of flow instability on the thermal performance of the passive cooling system. As a result, the high exit loss coefficient stabilizes the system better than the low case and has similar heat removal performance.

Flow and Heat Transfer Characteristics in the Entry and Stabilized Flow Regions of a Circular Channel Rotating About a Parallel Axis

Abstract Cooling of heavy-duty electrical machines such as generators and motors is crucial for the smooth operations without thermal runaway. A commonly employed technique for the cooling of rotors in these machines is to place channels at different radial locations for the continuous passage of coolant. These channels are therefore rotating about a parallel axis, and the rotation-induced forces alter the flow and thermal behavior of the coolant compared to stationary channels. The present study reports a detailed numerical investigation on a long circular channel rotating about a parallel axis. The objective is to analyze the flow, heat transfer, and rotation-induced forces (Coriolis and centrifugal forces) in the entry region as well as in the region where flow is stable (the term ‘stable’ is used rather than ‘developed’ due to the presence of secondary flows in this region). The rotating channel was subjected to constant wall heat flux and constant wall temperature conditions at different Rotation numbers of 0, 0.15, 0.4, and 0.6. The Coriolis force is observed to be strong enough in the entry region to influence the flow. In the “stable flow” region, the centrifugal force becomes more dominant and forms counter-rotating secondary vortex pair, which causes circumferential variation in the Nusselt number. The flow and heat transfer characteristics for constant wall heat flux and wall temperature boundaries are the same for rotation conditions with similar values of rotational Grashof number. A correlation is presented for the circumferential variation of the Nusselt number in the stable flow region.

Nanoparticle aggregation kinematics and nanofluid flow in convectively heated outer stationary and inner stretched coaxial cylinders: Influenced by linear, nonlinear, and quadratic thermal radiation

The consequence of nanoparticle aggregation and convective boundary condition on the nanofluid stream past the co-axial cylinder with radiation impact is investigated in the present examination. The influence of linear, nonlinear, and quadratic thermal radiation on the nanofluid flow is analyzed. The outer cylinder stays stable, while the inner cylinder deforms horizontally in the axial direction, allowing fluid to flow. By using similarity variables, the governing equations are transformed into ordinary differential equations (ODEs). Subsequently, the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method is employed to solve the reduced ODEs. The upshot of several nondimensional terms on the temperature and velocity profiles is displayed with graphical representation. The comparison of linear, quadratic, and nonlinear thermal radiation on the thermal profile is illustrated. The upsurge in curvature parameter increases velocity and thermal profile. The increase in radiation parameter intensifies the temperature profile. The thermal profile improves with a rise in the values of radiation parameter. The radiation parameter generates thermal energy in the flow zone, which is why the temperature field has improved. The thermal Biot number exhibits an increasing response with temperature and thermal boundary layer thickness. The linear thermal radiation shows better heat transfer compared to quadratic and nonlinear thermal radiation.

Study on multidimensional frost heave characteristics and thermal-hydro-mechanical predictive model

The multi-dimensional estimation of frost heave deformation is crucial for predicting soil deformation and the pressure generated during the freezing process. This study offers a comprehensive review and analysis of frost heave characteristics in the heat flow direction and the transverse direction to it. Based on the frost heave test results, an innovative method for calculating the anisotropic parameter has been introduced. This method includes only two parameters: one reflects the more pronounced characteristic of frost heave in the direction of heat flow, and the other represents the sensitivity of anisotropic parameters to constraint stress. Through comparative analysis with experimental results, this method can effectively express the evolution of the anisotropic frost heave with changes of the confining stress in different directions. Then, a combined thermal-hydraulic-mechanical coupling model is established, offering a way of applying the improved model. The coupling model can predict significant frost heave under conditions of sufficient water supply and effectively captures the frost heave characteristics under various temperature and stress boundary conditions. This research contributes significantly to predicting frost heave deformation in low-temperature natural gas pipelines and calculating the frozen soil pressure exerted on the pipelines.

Impact of the Stefan gusting on a bioconvective nanofluid with the various slips over a rotating disc and a substance-responsive species

This paper presents thorough computational and theoretical analyses of steady forced convective flow over a rotating disc submerged in a water-based nanofluid containing microorganisms. It delves into the examination of boundary layer flow characteristics of a viscous nanofluid, considering Stefan blowing effects and multiple slip conditions influenced by a magnetic field. Notably, the study accounts for novel aspects such as thermal radiation and both constructive and destructive chemical reactions. The movement of nanoparticles is elucidated based on thermophoresis and microscopic behaviors, while changes in volume fraction do not affect the thermo-physical properties of the nanofluid. To address the altered nonlinear set of differential equations, an effective numerical approach, the Keller-Box method, is implemented for critical and efficient solutions. These appropriate transformations are defined and applied. When compared to blowing suction, it shows a better enhancement in the rate of heat transfer, mass, and microorganisms. Some of the main observations are there is a decrease in wall skin friction in the directions of radial and tangential as magnetic field strength is increased. The evaluation of thermal boundary layer thickness and temperature is noted for the radiation parameter (Rd) improvement. The present analysis has applications in electromagnetic micro-pumps and nanomechanics. As to the applications in the science and engineering fields, technologies such as micro-electromechanical systems-based microfluidic devices and microfluidic-related technologies will be accepted.

Assessing salinity hazards in coastal aquifers: implications of temperature boundary conditions on aquifer–ocean interaction

Investigating the repercussions of climate change and irrigation timing on groundwater contamination necessitates thorough examination of the fluctuations in seawater and groundwater recharge temperature. This study introduces an innovative numerical approach to analyze groundwater salinity and temperature dynamics across three distinct scenarios using the SEAWAT code based on Henry's problem. The first scenario delves into the impact of seawater temperature, the second focuses on the consequences of aquifer freshwater recharge temperature, and the third amalgamates the effects of both scenarios. Remarkably, the study reveals that saltwater intrusion (SWI) experiences a decline attributable to the aquifer's heightened seawater temperature and the diminished inland freshwater temperature. Furthermore, combining these two scenarios has a more pronounced effect on aquifer pollution; the temperature-induced changes in SWI for this third scanrio reach + 8.10%, + 12.70%, + 16.20%, + 24.90%, + 28.30%, and + 31.80% compared to the case without considering the temperature effect. Notably, our results propose a potential strategy to mitigate SWI by introducing cold freshwater recharge into aquifers, such as irrigation at night time when water temperature is low. This innovative approach underscores the interconnectedness of various environmental factors. It provides a practical avenue for proactive intervention in safeguarding groundwater quality against the adverse impacts of climate change and irrigation practices.

Dynamic prediction of high-temperature points in longwall gobs under a multi-field coupling framework

Spontaneous coal combustion (SCC) in longwall gobs is a serious disaster and requires prediction tools to accurately and reliably predict the temperature in gobs, but currently, there has been a lack of simple and efficient predictors. To address this issue, the temperature distributions in a longwall gob under different mining state parameters were simulated using a multi-fields coupled model. The temperature distribution and the mining state parameters were extracted to serve as input variables for prediction. Two machine learning models, integrating parameter optimization and ensemble learning strategies, respectively, were proposed to establish the functional relationships between the dynamic change boundary temperature and the maximum temperature in the gob. The results show that these two models have good prediction accuracy on the high-temperature points in longwall gobs, indicating that the ensemble learning has improved prediction accuracy. There is a positive correlation between the number of measuring points and the prediction accuracy, and three measurement points at the key locations can deliver reliable predictive performance.

The influence of thermo-electromechanical coupling on the performance of lead-free BNT-PDMS piezoelectric composites

In recent times, there have been notable advancements in haptic technology, particularly in screens found on mobile phones, laptops, light-emitting diode (LED) screens, and control panels. However, it is essential to note that the progress in high-temperature haptic applications is still in the developmental phase. Due to their complex phase and domain structures, lead-free piezoelectric materials such as Bi0.5Na0.5TiO3 (BNT)-based haptic technology behave differently at high temperatures than in ambient conditions. Therefore, it is essential to investigate the aspects of thermal management and thermal stability, as temperature plays a vital role in the phase and domain transition of BNT material. A two-dimensional thermo-electromechanical model has been proposed in this study to analyze the thermal stability of the BNT-PDMS composite by analyzing the impact of temperature on effective electromechanical properties and mechanical and electric field parameters. However, the thermo-electromechanical modelling of the BNT-PDMS composite examines the macroscopic effects of the applied thermal field on mechanical and electric field parameters, as phase change and microdomain dynamics are not considered in this model. This study analyzes the impact of thermo-electromechanical coupling on the performance of the BNT-PDMS composite compared to conventional electromechanical coupling. The results predicted a significant improvement in piezoelectric response compared to electromechanical coupling due to the increased thermoelectric effect in the absence of phase change and microdomain switching for temperature boundary conditions below depolarization temperature ( Td∼200∘ C for pure BNT material).

Numerical simulation and optimization of Pervaporation process based on Heat-Mass-Flow coupling

Pervaporation (PV) has the advantages of low energy consumption and high separation efficiency, but the trade-off effect between flux and separation factor restricts its large-scale application. Based on the conservation equations of mass, momentum and heat, a transient model of the whole PV process coupled with heat-mass-flow was established in this paper. The effects of feed temperature, feed concentration and feed flow rate on heat and mass transfer in PV process were analyzed. TEOS crosslinked PDMS/PTFE-PVDF membrane was prepared by scraping coating method. The reliability of the model was verified by taking n-butanol/water separation system as an example. The concentration polarization and temperature boundary layer under different operating conditions are discussed. The effect of operating conditions on the separation performance was evaluated by response surface method, and the optimal operating conditions are obtained. The results show that the concentration polarization of the membrane surface becomes more obvious with the increase of feed concentration. The temperature boundary layer decreases with the increase of feed flow rate. Surprisedly, there is a significant temperature gradient in the membrane, and the maximum temperature difference between the two sides of the membrane is as high as 1.02 K. Diffusion in the membrane is the rate controlling factor of PV process. The contribution of operating conditions to the separation performance is in the order of feed temperature > feed concentration > feed flow rate. The best operating conditions are: feed temperature 350.2 K, feed concentration 3.8 wt% n-butanol/water and feed flow rate 23.6 L/h. This work provides a theoretical basis for the design of PV membrane materials and the optimization of PV operating conditions.

A Giant Impact Origin for the First Subduction on Earth

AbstractHadean zircons provide a potential record of Earth's earliest subduction 4.3 billion years ago. It remains enigmatic how subduction could be initiated so soon after the presumably Moon‐forming giant impact (MGI). Earlier studies found an increase in Earth's core‐mantle boundary (CMB) temperature due to the accumulation of the impactor's core, and our recent work shows Earth's lower mantle remains largely solid, with some of the impactor's mantle potentially surviving as the large low‐shear velocity provinces (LLSVPs). Here, we show that a hot post‐impact CMB drives the initiation of strong mantle plumes that can induce subduction initiation ∼200 Myr after the MGI. 2D and 3D thermomechanical computations show that a high CMB temperature is the primary factor triggering early subduction, with enrichment of heat‐producing elements in LLSVPs as another potential factor. The models link the earliest subduction to the MGI with implications for understanding the diverse tectonic regimes of rocky planets.

Deciphering multi-temporal scale dynamics in the concentration, sources and processes of near surface ozone over different climatic regions of India.

This study aims to investigate the factors influencing seasonal and long-term (2003-2021) changes in the near surface ozone (850 hpa) concentrations over different climatic sub-regions of India. Detailed comparison of daily (2019-2021) near surface ozone values of ERA-5 and CAAQMS (Continuous Ambient Air Quality Monitoring Stations) ground-based measurements revealed that ERA-5 is temporally in phase with CAAQMS measurements falling indifferent climatic sub-regions of India. ERA-5 near surface ozone shows statistically significant long-term (2003-2021) positive trends [2-4 percent per decade (ppd)] over most of the climatic sub-regions, over Indo-Gangetic Planes (IGPs), Southern and Central India trends are particularly strong. Trends were also estimated for each season separately, which were largely positive (2-6 ppd) over Central and Southern India in the Autumn and Winter seasons. Extensive climatological analysis reveals that the reversal of winds in the Indian monsoonal system plays a vital role in such trend patterns across the Indian subcontinent. South-westerly winds from June through September presumably bring ozone deficit air of marine origin, thus causing a dilution effect while the North-easterly winds during late Autumn and early Winters plausibly bring ozone-rich air from the stratospheric-tropospheric efflux dominated Himalayan region. It allows near surface ozone enhancement over Central and Southern India. Seasonal Principal component analysis (PCA) revealed that precursor gases (CH4 and NO2) and climatic variables especially specific humidity (SH) are the primary drivers of near surface ozone variability in the Winter season, while in Spring, climatic variables like boundary layer height (BLH), temperature (T) and SH have a significant role. Principal component regression (PCR) reveals a long-term increase in near surface ozone levels mostly dominated by precursor concentration over IGPs and Southern sub-regions. Whereas, BLH, T and SH significantly explain near surface ozone trends over North-eastern and Coastal India.

Reconciling Mars InSight Results, Geoid, and Melt Evolution With 3D Spherical Models of Convection

AbstractWe investigate the geodynamic and melting history of Mars using 3D spherical shell models of mantle convection, constrained by the recent InSight mission results. The Martian mantle must have produced sufficient melt to emplace the Tharsis rise by the end of the Noachian–requiring on the order of 1–3 × 109 km3 of melt after accounting for limited (∼10%) melt extraction. Thereafter, melting declined; however, abundant evidence for limited geologically recent volcanism necessitates some present‐day melt even in the cool mantle inferred from InSight data. We test models with two mantle activation energies and a range of crustal Heat Producing Element (HPE) enrichment factors and initial core‐mantle boundary temperatures. We also test the effect of including a hemispheric (spherical harmonic degree‐1) step in lithospheric thickness to model the Martian dichotomy. We find that a higher activation energy (350 kJ mol−1) rheology produces present‐day geotherms consistent with InSight results, and crustal HPE enrichment factors of 5–10‐times produce localized melting near or up to present‐day. The 10‐times crustal HPE enrichment is consistent with both InSight and geochemical results and also produces present‐day geoid power spectra consistent with Mars. However, calculations that match the present‐day geoid power spectra require more than 60% melt extraction to produce the Tharsis swell. The addition of a degree‐1 hemispheric dichotomy, as an equatorial step in lithospheric thickness, does not significantly improve upon melt production or the geoid.

Numerical modelling of thermal hysteresis in melting and solidification of phase change materials

This research focuses on exploring the impact of thermal hysteresis effects on the performance of Phase Change Materials (PCMs) used in thermal storage or buffering applications. Computational Fluid Dynamics modeling in ANSYS Fluent is employed to investigate thermal hysteresis phenomena during solid-liquid phase change. The traditional enthalpy-porosity method is extended by introducing an alternative relationship between the liquid fraction and PCM temperature, implemented in Fluent through User Defined Functions. The study demonstrates the developed model by simulating a rectangular PCM enclosure with a heated wall featuring a time-dependent temperature boundary condition. Considering convective heat transfer, a comparison is made between the newly developed hysteresis model and the default solidification-melting model of ANSYS Fluent. The new model facilitates numerical analysis of thermal hysteresis during partial and complete melting and solidification processes, enabling the study of hysteresis effects on the part-load operation of PCM systems.

Model Based Exploration of Physical Parameters for Liquid Hydrogen System Insulation Performance

Cryogenic Systems require a highly efficient insulation so as to limit the heat ingress and boil-off, which is generally achieved through the use of vacuum combined with an insulated media. The performance of Multi layer Insulation (MLI) will be investigated with detailed thermal models developed to account for all the heat transfer contributions, solid conduction, gaseous conduction and radiation. Results are presented for an usual cold vacuum pressure (CVP) corresponding to high vacuum (<10−6 torr) and compared with available experimental measurements for state of the art technologies. The nominal thermal performances are then evaluated for a cold temperature of 20K (representative of liquid hydrogen storage temperature), for a degraded CVP with hydrogen and nitrogen as residual gasses and for increased hot boundary temperatures. Other parameters are also discussed such as, the number of layers, material, layers density, venting options, assembly process and material optical properties. Finally, a sensitivity of the thermal performance is also presented with a pressure gradient through the insulation thickness, that could be induced by cryopumping, materials outgassing, pumping times or small leakages.

Thermal conductivity and mechanical properties of polymeric aerogels for cryogenic insulation applications

Non-vacuum insulation systems are frequently applied in the thermal management of low temperature systems as well as for the use and storage of cryogens. Aerogels are known for their low density, high mesoporosity, high surface areas, low thermal conductivity and high acoustic impedance. This study focuses on polymeric aerogels that can be mass produced as large monoliths while maintaining the low thermal conductivity over a wide temperature range. The manufacturing flexibility of polymeric aerogels allows fabrication of monolithic blocks and sheets that can be applied in various configurations to insulate cryogenic and superconducting devices. To measure the thermal conductivity, an immersion calorimeter was developed and has been operated at different cold boundary temperatures. The calorimeter heats a hollow cylinder of insulating material on the inside surface and the surrounding bath maintains a cold boundary. This calorimeter was used to measure the thermal conductivity of commercially available FoamGlass and a hollow cylinder of a polymeric aerogel machined from a cast cylinder. The thermal conductivity of the FoamGlass and the polymeric aerogel are compared at room temperature (290 K), ice bath (273 K), and at liquid nitrogen (80 K) cold boundary temperatures. Room temperature measurements of the modulus of elasticity and yield strength using an optical technique are also reported for flat specimens of the aerogel made from the same stock as the cylindrical specimens tested for thermal conductivity. Mechanical properties of aerogels are also reported under compression and both at room temperature and at cryogenic temperature (Liquid nitrogen).

Heat transfer inside a horizontal circular enclosure with a heated semi-circular cylinder at different orientations

Natural convection inside a cylindrical enclosure is important in many industrial applications. Laminar natural convective heat transfer in the annular space between heated semi-circular cylinder in a horizontal concentric cylindrical enclosure, which has relevance to cooling of electronic components, is studied in this work. Constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions are considered on the inner cylinder, whereas the outer cylindrical enclosure is maintained at a fixed lower temperature. The Finite Volume Method (FVM) is used for the computations. The effect of the Rayleigh number ( Ra = 10 2 to 10 5 ) and the angular orientation of the semi-circular cylinder on the convective heat transfer is investigated. The fluid flow, temperature profile, and heat flow are visualized via streamlines, isotherms, and heatlines. Further, the overall heat transfer is explained based on the local and average Nusselt number on the inner cylinder wall. The effect of the angular orientation of the inner cylinder is noticeable for Ra ≥ 10 3 . The angular orientation ϕ = 90 ° greatly enhances the heat transfer as compared to all other orientations for all Ra ≥ 10 3 for both CWT and CWHF boundary conditions. The correlation between the average Nusselt and Rayleigh numbers for a particular orientation is proposed.

Study of the characteristics of the separated gravity heat pipe of a self-activated PCM wall system

Self-activated phase change material (PCM) wall integrated with radiative sky cooling (RSC) is a novel wall system that uses natural energy directly for low-energy buildings to support carbon peaking and neutrality goals. A separated gravity heat pipe (SGHP) is an effective heat transfer component for heat transport from the wall body to the radiative cooler without using mechanical energy. Its heat transfer characteristics affect the thermal performance of the wall system. In this study, a numerical Volume of Fluid (VOF) model of the SGHP is established. The thermal and flow characteristics under the small temperature difference boundary of building scenarios are simulated and analyzed. Results show that the average temperature of the working fluid inside the SGHP in the “steady stage” is about 26.3 °C when the boundary temperature of the evaporation and condensation sections are respectively 28 °C and 20 °C. The heat exchange can reach 356 W/m2 and the flow velocity of the working fluid is about 0.1 m/s. Influences of different evaporation/condensation boundary temperatures on the heat transfer effect are further studied. Compared to increasing the evaporation section temperature, decreasing the condensation section temperature is a better strategy for improving the heat exchange capacity of the SGHP.

Natural convective heat transfer of Al2O3-Cu/water hybrid nanofluid in a rectotrapezoidal enclosure under the influence of periodic magnetic field

This study seeks to examine quantitatively the two-dimensional unsteady free convective heat transfer enhancement of Al2O3-Cu/H2O hybrid nanofluid within a rectotrapezoidal-shaped structure. The lower wall is both uniformly and non-uniformly heated with different thermal boundary conditions, the top horizontal wall is adiabatic, and the vertical and inclined walls are assumed chilly. The enclosure is penetrated by a periodic magnetic field. A set of variable transformations is used to render the governing equations dimensionless, which makes it possible to identify the model parameters that control it. The finite element method is then used to numerically solve these equations. To verify the code's numerical precision, comparisons with formerly available works are performed and, a high level of agreement is obtained among the results. The generated outcomes are shown for the principal parameters that control the flow in the context of streamlines, heat lines, isotherms, average Nusselt number, friction factor, and thermal efficiency index. The findings demonstrated that the efficiency index, friction factor, and heat transmission are all considerably influenced by the Rayleigh number (Ra). The lowest Ra yields the maximum thermal efficiency. The results also revealed that the hybrid nanoparticle volume fraction and period of the magnetic field amplified the heat transfer rate and efficiency index due to the increased pumping force. It is observed that when the percentage of the mixing ratios for Cu nanoparticles rises from 0% to 100%, the heat transport in Al2O3-Cu/H2O hybrid nanofluid increases for a fixed volume fraction of hybrid nanoparticles. As compared to parabolic and sinusoidal boundary conditions, the uniform temperature boundary setting for Ra = 105 exhibits the highest average rate of heat transport of 10.04. The average Nusselt number increases by 25.12% at Ra = 103 with a 3% volume fraction of hybrid nanofluid as compared to pure water and the mixing ratios of Al2O3:Cu = 0:300 gives the highest increased rate of 16.30%. The results further illustrate that Al2O3-Cu/H2O hybrid nanofluid has the highest heat transfer rate compared to the pure water and Al2O3– H2O nanofluid.