Improving Heat Transfer in Parabolic Trough Solar Collectors by Magnetic Nanofluids

A parabolic trough solar collector(PTSC)converts solar radiation into thermal energy.However,low thermal efficiency of PTSC poses a hindrance to the deployment of solar thermal power plants.Thermal performance of PTSC is enhanced in this study by incorporating magnetic nanoparticles into the working fluid.The circular receiver pipe,with dimensions of 66 mm diameter,2 mm thickness,and 24 m length,is exposed to uniform temperature and velocity conditions.The working fluid,Therminol-66,is supplemented with Fe3O4 magnetic nanoparticles at concentrations ranging from 1%to 4%.The findings demonstrate that the inclusion of nanoparticles increases the convective heat transfer coefficient(HTC)of the PTSC,with higher nanoparticle volume fractions leading to greater heat transfer but increased pressure drop.The thermal enhancement factor(TEF)of the PTSC is positively affected by the volume fraction of nanoparticles,both with and without a magnetic field.Notably,the scenario with a 4%nanoparticle volume fraction and a magnetic field strength of 250 G exhibits the highest TEF,indicating superior thermal performance.These findings offer potential avenues for improving the efficiency of PTSCs in solar thermal plants by introducing magnetic nanoparticles into the working fluid.

The regulation of ferrocene-based catalysts on heat transfer in highpressure combustion of ammonium perchlorate/hydroxyl-terminated polybutadiene/aluminum composite propellants

The regulation of the burning rate pressure exponent for the ammonium perchlorate/hydroxylterminated polybutadiene/aluminum(AP/HTPB/Al)composite propellants under high pressures is a crucial step for its application in high-pressure solid rocket motors.In this work,the combustion characteristics of AP/HTPB/Al composite propellants containing ferrocene-based catalysts were investigated,including the burning rate,thermal behavior,the local heat transfer,and temperature profile in the range of 7-28 MPa.The results showed that the exponent breaks were still observed in the propellants after the addition of positive catalysts(Ce-Fc-MOF),the burning rate inhibitor((Ferrocenylmethyl)trimethylammonium bromide,Fc Br)and the mixture of Fc Br/catocene(GFP).However,the characteristic pressure has increased,and the exponent decreased from 1.14 to 0.66,0.55,and 0.48 when the addition of Ce-FcMOF,Fc Br and Fc Br/GFP in the propellants.In addition,the temperature in the first decomposition stage was increased by 7.50℃ and 11.40℃ for the AP/Fc Br mixture and the AP/Fc Br/GFP mixture,respectively,compared to the pure AP.On the other hand,the temperature in the second decomposition stage decreased by 48.30℃ and 81.70℃ for AP/Fc Br and AP/Fc Br/GFP mixtures,respectively.It was also found that Fc Br might generate ammonia to cover the AP surface.In this case,a reaction between the methyl in Fc Br and perchloric acid caused more ammonia to appear at the AP surface,resulting in the suppression of ammonia desorption.In addition,the coarse AP particles on the quenched surface were of a concave shape relative to the binder matrix under low and high pressures when the catalysts were added.In the process,the decline at the AP/HTPB interface was only exhibited in the propellant with the addition of Ce-Fc-MOF.The ratio of the gas-phase temperature gradient of the propellants containing catalysts was reduced significantly below and above the characteristic pressure,rather than 3.6 times of the difference in the blank propellant.Overall,the obtained results demonstrated that the pressure exponent could be effectively regulated and controlled by adjusting the propellant local heat and mass transfer under high and low pressures.

Effect of bipolar-plates design on corrosion,mass and heat transfer in proton-exchange membrane fuel cells and water electrolyzers:A review

Attaining a decarbonized and sustainable energy system,which is the core solution to global energy issues,is accessible through the development of hydrogen energy.Proton-exchange membrane water electrolyzers(PEMWEs)are promising devices for hydrogen production,given their high efficiency,rapid responsiveness,and compactness.Bipolar plates account for a relatively high percentage of the total cost and weight compared with other components of PEMWEs.Thus,optimization of their design may accelerate the promotion of PEMWEs.This paper reviews the advances in materials and flow-field design for bipolar plates.First,the working conditions of proton-exchange membrane fuel cells(PEMFCs)and PEMWEs are compared,including reaction direction,operating temperature,pressure,input/output,and potential.Then,the current research status of bipolar-plate substrates and surface coatings is summarized,and some typical channel-rib flow fields and porous flow fields are presented.Furthermore,the effects of materials on mass and heat transfer and the possibility of reducing corrosion by improving the flow field structure are explored.Finally,this review discusses the potential directions of the development of bipolar-plate design,including material fabrication,flow-field geometry optimization using threedimensional printing,and surface-coating composition optimization based on computational materials science.

Heat transfer and temperature evolution in underground mininginduced overburden fracture and ground fissures: Optimal time window of UAV infrared monitoring

Heat transfer and temperature evolution in overburden fracture and ground fissures are one of the essential topics for the identification of ground fissures via unmanned aerial vehicle(UAV) infrared imager. In this study, discrete element software UDEC was employed to investigate the overburden fracture field under different mining conditions. Multiphysics software COMSOL were employed to investigate heat transfer and temperature evolution of overburden fracture and ground fissures under the influence of mining condition, fissure depth, fissure width, and month alternation. The UAV infrared field measurements also provided a calibration for numerical simulation. The results showed that for ground fissures connected to underground goaf(Fissure Ⅰ), the temperature difference increased with larger mining height and shallow buried depth. In addition, Fissure Ⅰ located in the boundary of the goaf have a greater temperature difference and is easier to be identified than fissures located above the mining goaf. For ground fissures having no connection to underground goaf(Fissure Ⅱ), the heat transfer is affected by the internal resistance of the overlying strata fracture when the depth of Fissure Ⅱ is greater than10 m, the temperature of Fissure Ⅱ gradually equals to the ground temperature as the fissures’ depth increases, and the fissures are difficult to be identified. The identification effect is most obvious for fissures larger than 16 cm under the same depth. In spring and summer, UAV infrared identification of mining fissures should be carried out during nighttime. This study provides the basis for the optimal time and season for the UAV infrared identification of different types of mining ground fissures.

Effect of phosphorus content on interfacial heat transfer and film deposition behavior during the high-temperature simulation of strip casting

The interfacial wettability and heat transfer behavior are crucial in the strip casting of high phosphorus-containing steel.A hightemperature simulation of strip casting was conducted using the droplet solidification technique with the aims to reveal the effects of phosphorus content on interfacial wettability,deposited film,and interfacial heat transfer behavior.Results showed that when the phosphorus content increased from 0.014wt%to 0.406wt%,the mushy zone enlarged,the complete solidification temperature delayed from1518.3 to 1459.4℃,the final contact angle decreased from 118.4°to 102.8°,indicating improved interfacial contact,and the maximum heat flux increased from 6.9 to 9.2 MW/m2.Increasing the phosphorus content from 0.081wt%to 0.406wt%also accelerated the film deposition rate from 1.57 to 1.73μm per test,resulting in a thickened naturally deposited film with increased thermal resistance that advanced the transition point of heat transfer from the fifth experiment to the third experiment.

Thermal runaway evolution of a 280 Ah lithium-ion battery with LiFePO_(4) as the cathode for different heat transfer modes constructed by mechanical abuse

Lithium iron phosphate batteries have been increasingly utilized in recent years because their higher safety performance can improve the increasing trend of recurring thermal runaway accidents.However,the safety performance and mechanism of high-capacity lithium iron phosphate batteries under internal short-circuit challenges remain to be explored.This work analyzes the thermal runaway evolution of high-capacity LiFePO_(4) batteries under different internal heat transfer modes,which are controlled by different penetration modes.Two penetration cases involving complete penetration and incomplete penetration were detected during the test,and two modes were performed incorporating nails that either remained or were removed after penetration to comprehensively reveal the thermal runaway mechanism.A theoretical model of microcircuits and internal heat conduction is also established.The results indicated three thermal runaway evolution processes for high-capacity batteries,which corresponded to the experimental results of thermal equilibrium,single thermal runaway,and two thermal runaway events.The difference in heat distribution in the three phenomena is determined based on the microstructure and material structure near the pinhole.By controlling the heat dissipation conditions,the time interval between two thermal runaway events can be delayed from 558 to 1417 s,accompanied by a decrease in the concentration of in-situ gas production during the second thermal runaway event.

Calculation of Mass Concrete Temperature and Creep Stress under the Influence of Local Air Heat Transfer

Temperature-induced cracking during the construction of mass concrete is a significant concern.Numerical simulations of concrete temperature have primarily assumed that the concrete is placed in an open environment.The problem of heat transfer between the air and concrete has been simplified to the concrete’s heat dissipation boundary.However,in the case of tubular concrete structures,where air inlet and outlet are relatively limited,the internal air temperature does not dissipate promptly to the external environment as it rises.To accurately simulate the temperature and creep stress in tubular concrete structures with enclosed air spaces during construction,we establish an air–concrete coupled heat transfer model according to the principles of conjugate heat transfer,and the accuracy of the model is verified through experiments.Furthermore,we conduct a case study to analyze the impact of airflow within the ship lock corridor on concrete temperature and creep stress.The results demonstrate that enhancing airflow within the corridor can significantly reduce the maximum concrete temperature.Compared with cases in which airflow within the corridor is neglected,the maximum concrete temperature and maximum tensile stress can be reduced by 12.5℃ and 0.7 MPa,respectively,under a wind speed of 4 m/s.The results of the traditional calculation method are relatively close to those obtained at a wind speed of 1 m/s.However,the temperature reduction process in the traditional method is faster,and the method yields greater tensile stress values for the corridor location.

Near-field radiative heat transfer between nanoporous GaN films

Photon tunneling effects give rise to surface waves,amplifying radiative heat transfer in the near-field regime.Recent research has highlighted that the introduction of nanopores into materials creates additional pathways for heat transfer,leading to a substantial enhancement of near-field radiative heat transfer(NFRHT).Being a direct bandgap semiconductor,GaN has high thermal conductivity and stable resistance at high temperatures,and holds significant potential for applications in optoelectronic devices.Indeed,study of NFRHT between nanoporous GaN films is currently lacking,hence the physical mechanism for adding nanopores to GaN films remains to be discussed in the field of NFRHT.In this work,we delve into the NFRHT of GaN nanoporous films in terms of gap distance,GaN film thickness and the vacuum filling ratio.The results demonstrate a 27.2%increase in heat flux for a 10 nm gap when the nanoporous filling ratio is 0.5.Moreover,the spectral heat flux exhibits redshift with increase in the vacuum filling ratio.To be more precise,the peak of spectral heat flux moves fromω=1.31×10^(14)rad·s^(-1)toω=1.23×10^(14)rad·s^(-1)when the vacuum filling ratio changes from f=0.1 to f=0.5;this can be attributed to the excitation of surface phonon polaritons.The introduction of graphene into these configurations can highly enhance the NFRHT,and the spectral heat flux exhibits a blueshift with increase in the vacuum filling ratio,which can be explained by the excitation of surface plasmon polaritons.These findings offer theoretical insights that can guide the extensive utilization of porous structures in thermal control,management and thermal modulation.

Numerical study of directional heat transfer in composite materials via controllable carbon fiber distribution

Carbon fiber reinforced polyamide 12(CF/PA12),a new material renowned for its excellent mechanical and thermal properties,has drawn significant industry attention.Using the steady-state research to heat transfer,a series of simulations to investigate the heat transfer properties of CF/PA12 were conducted in this study.Firstly,by building two-and three-dimensional models,the effects of the porosity,carbon fiber content,and arrangement on the heat transfer of CF/PA12 were examined.A validation of the simulation model was carried out and the findings were consistent with those of the experiment.Then,the simulation results using the above models showed that within the volume fraction from 0% to 28%,the thermal conductivity of CF/PA12 increased greatly from 0.0242 W/(m·K)to 10.8848 W/(m·K).The increasing porosity had little influence on heat transfer characteristic of CF/PA12.The direction of the carbon fiber arrangement affects the heat transfer impact,and optimal outcomes were achieved when the heat flow direction was parallel to the carbon fiber.This research contributes to improving the production methods and broadening the application scenarios of composite materials.

Radiative heat transfer analysis of a concave porous fin under the local thermal non-equilibrium condition:application of the clique polynomial method and physics-informed neural networks

The heat transfer through a concave permeable fin is analyzed by the local thermal non-equilibrium(LTNE)model.The governing dimensional temperature equations for the solid and fluid phases of the porous extended surface are modeled,and then are nondimensionalized by suitable dimensionless terms.Further,the obtained nondimensional equations are solved by the clique polynomial method(CPM).The effects of several dimensionless parameters on the fin's thermal profiles are shown by graphical illustrations.Additionally,the current study implements deep neural structures to solve physics-governed coupled equations,and the best-suited hyperparameters are attained by comparison with various network combinations.The results of the CPM and physicsinformed neural network(PINN)exhibit good agreement,signifying that both methods effectively solve the thermal modeling problem.

Impact of a Magnetic Dipole on Heat Transfer in Non-Conducting Magnetic Fluid Flow over a Stretching Cylinder

The thermal behavior of an electrically non-conducting magnetic liquid flowing over a stretching cylinder under the influence of a magnetic dipole is considered.The governing nonlinear differential equations are solved numerically using a finite element approach,which is properly validated through comparison with earlier results available in the literature.The results for the velocity and temperature fields are provided for different values of the Reynolds number,ferromagnetic response number,Prandtl number,and viscous dissipation parameter.The influence of some physical parameters on skin friction and heat transfer on the walls of the cylinder is also investigated.The applicability of this research to heat control in electronic devices is discussed to a certain extent.

Study of Flow and Heat Transfer in an Ejector-Driven Swirl Anti-Icing Chamber

The formation of ice on the leading edge of aircraft engines is a serious issue,as it can have catastrophic consequences.The Swirl Anti-Icing(SAI)system,driven by ejection,circulates hot fluid within a 360°annular chamber to heat the engine inlet lip surface and prevent icing.This study employs a validated Computational Fluid Dynamics(CFD)approach to study the impact of key geometric parameters of this system on flow and heat transfer characteristics within the anti-icing chamber.Additionally,the entropy generation rate and exergy efficiency are analyzed to assess the energy utilization in the system.The research findings indicate that,within the considered flow range,reducing the nozzle specific areaφfrom 0.03061 to 0.01083 can enhance the ejection coefficient by over 60.7%.This enhancement increases the air circulating rate,thereby intensifying convective heat transfer within the SAI chamber.However,the reduction inφalso leads to a significant increase in the required bleed air pressure and a higher entropy generation rate,indicating lower exergy efficiency.The nozzle angleθnotably affects the distribution of hot and cold spots on the lip surface of the SAI chamber.Increasingθfrom 0°to 20°reduces the maximum temperature difference on the anti-icing chamber surface by 60 K.

Paraffin–CaCl_(2)·6H_(2)O dosage effects on the strength and heat transfer characteristics of cemented tailings backfill

The challenge of high temperatures in deep mining remains harmful to the health of workers and their production efficiency The addition of phase change materials (PCMs) to filling slurry and the use of the cold storage function of these materials to reduce downhole temperatures is an effective approach to alleviate the aforementioned problem.Paraffin–CaCl_(2)·6H_(2)O composite PCM was prepared in the laboratory.The composition,phase change latent heat,thermal conductivity,and cemented tailing backfill (CTB) compressive strength of the new material were studied.The heat transfer characteristics and endothermic effect of the PCM were simulated using Fluent software.The results showed the following:(1) The new paraffin–CaCl_(2)·6H_(2)O composite PCM improved the thermal conductivity of native paraffin while avoiding the water solubility of CaCl_(2)·6H_(2)O.(2) The calculation formula of the thermal conductivity of CaCl_(2)·6H_(2)O combined with paraffin was deduced,and the reasons were explained in principle.(3) The“enthalpy–mass scale model”was applied to calculate the phase change latent heat of nonreactive composite PCMs.(4)The addition of the paraffin–CaCl_(2)·6H_(2)O composite PCM reduced the CTB strength but increased its heat absorption capacity.This research can give a theoretical foundation for the use of heat storage backfill in green mines.

Turbine Passage Secondary Flow Dynamics and Endwall Heat Transfer Under Different Inflow Turbulence

This study presents endwall hydrodynamics and heat transfer in a linear turbine cascade at Re 5×105 at low and high intensities of turbulence.Results are numerically predicted using the standard SST model and Reθ-γtransition model as well as using the high-resolution LES separately.The major secondary flow components,comprising the horseshoe,corner,and passage vortices are recognized and the impact on heat or mass transfer is investigated.The complicated behavior of turbine passage secondary flow generation and establishment are impacted by the perspective of boundary layer attributes and inflow turbulence.The passage vortex concerning the latest big leading-edge vane is generated by the enlargement of the circulation developed at the first instance adjacent to the pressure side becomes powerful and mixes with other vortex systems during its migration towards the suction side.The study conclusions reveal that substantial enhancements are attained on the endwall surface,for the entire spanwise blade extension on the pressure surface,and in the highly 3-D region close to the endwall on the suction surface.The forecasted suction surface thermal exchange depicts great conformity with the measurement values and precisely reproduces the enhanced thermal exchange owing to the development and lateral distribution of the secondary flows along the midspan of the blade passage downstream.The impacts of the different secondary flow structures on the endwall thermal exchange are described in depth.

Numerical modeling and parametric sensitivity analysis of heat transfer and two-phase oil and water flow characteristics in horizontal and inclined flowlines using OpenFOAM

Estimating the oil-water temperatures in flowlines is challenging especially in deepwater and ultra-deepwater offshore applications where issues of flow assurance and dramatic heat transfer are likely to occur due to the temperature difference between the fluids and the surroundings. Heat transfer analysis is very important for the prediction and prevention of deposits in oil and water flowlines, which could impede the flow and give rise to huge financial losses. Therefore, a 3D mathematical model of oil-water Newtonian flow under non-isothermal conditions is established to explore the complex mechanisms of the two-phase oil-water transportation and heat transfer in different flowline inclinations. In this work, a non-isothermal two-phase flow model is first modified and then implemented in the InterFoam solver by introducing the energy equation using OpenFOAM® code. The Low Reynolds Number (LRN) k-ε turbulence model is utilized to resolve the turbulence phenomena within the oil and water mixtures. The flow patterns and the local heat transfer coefficients (HTC) for two-phase oil-water flow at different flowlines inclinations (0°, +4°, +7°) are validated by the experimental literature results and the relative errors are also compared. Global sensitivity analysis is then conducted to determine the effect of the different parameters on the performance of the produced two-phase hydrocarbon systems for effective subsea fluid transportation. Thereafter, HTC and flow patterns for oil-water flows at downward inclinations of 4°, and 7° can be predicted by the models. The velocity distribution, pressure gradient, liquid holdup, and temperature variation at the flowline cross-sections are simulated and analyzed in detail. Consequently, the numerical model can be generally applied to compute the global properties of the fluid and other operating parameters that are beneficial in the management of two-phase oil-water transportation.

Study of steam heat transfer enhanced by CO_(2) and chemical agents: In heavy oil production

Steam flooding with the assistance of carbon dioxide (CO_(2)) and chemicals is an effective approach for enhancing super heavy oil recovery. However, the promotion and application of CO_(2) and chemical agent-assisted steam flooding technology have been restricted by the current lack of research on the synergistic effect of CO_(2) and chemical agents on enhanced steam flooding heat transfer. The novel experiments on CO_(2)–chemicals cooperate affected steam condensation and seepage were conducted by adding CO_(2) and two chemicals (sodium dodecyl sulfate (SDS) and the betaine temperature-salt resistant foaming agent ZK-05200).According to the experimental findings, a “film” formed on the heat-transfer medium surface following the co-injection of CO_(2) and the chemical to impede the steam heat transfer, reducing the heat transfer efficiency of steam, heat flux and condensation heat transfer coefficient. The steam seepage experiment revealed that the temperature at the back end of the sandpack model was dramatically raised by 3.5–12.8 °C by adding CO_(2) and chemical agents, achieving the goal of driving deep-formation heavy oil. The combined effect of CO_(2) and SDS was the most effective for improving steam heat transfer, the steam heat loss was reduced by 6.2%, the steam condensation cycle was prolonged by 1.3 times, the condensation heat transfer coefficient was decreased by 15.5%, and the heavy oil recovery was enhanced by 9.82%. Theoretical recommendations are offered in this study for improving the CO_(2)–chemical-assisted steam flooding technique.

Analysis of periodic pulsating nanofluid flow and heat transfer through a parallel-plate channel in the presence of magnetic field

In this paper,we focus on the two-dimensional pulsating nanofluid flow through a parallel-plate channel in the presence of a magnetic field.The pulsating flow is produced by an applied pressure gradient that fluctuates with a small amplitude.A kind of proper transformation is used so that the governing equations describing the momentum and thermal energy are reduced to a set of non-dimensional equations.The analytical expressions of the pulsating velocity,temperature,and Nusselt number of nanofluids are obtained by the perturbation technique.In the present study,the effects of the Cu-H2O and Al_(2)O_(3)-H2O nanofluids on the flow and heat transfer in pulsating flow are compared and analyzed.The results show that the convective heat transfer effect of Cu-H2O nanofluids is better than that of Al_(2)O_(3)-H2O nanofluids.Also,the effects of the Hartmann number and pulsation amplitude on the velocity,temperature,and Nusselt number are examined and discussed in detail.The present work indicates that increasing the Hartmann number and pulsation amplitude can enhance the heat transfer of the pulsating flow.In addition,selecting an optimal pulsation frequency can maximize the convective heat transfer of the pulsating flow.Therefore,improved understanding of these fundamental mechanisms is conducive to the optimal design of thermal systems.

Numerical and theoretical investigations of heat transfer characteristics in helium-xenon cooled microreactor core

Helium-xenon cooled microreactors are a vital technological solution for portable nuclear reactor power sources.To exam-ine the convective heat transfer behavior of helium-xenon gas mixtures in a core environment,numerical simulations are conducted on a cylindrical coolant channel and its surrounding solid regions.Validated numerical methods are used to determine the effect and mechanisms of power and its distribution,inlet temperature and velocity,and outlet pressure on the distribution and change trend of the axial Nusselt number.Furthermore,a theoretical framework that can describe the effect of power variation on the evolution of the thermal boundary layer is employed to formulate an axial distribution cor-relation for the Nusselt number of the coolant channel,under the assumption of a cosine distribution for the axial power.Based on the simulation results,the correlation coefficients are determined,and a semi-empirical relationship is identified under the corresponding operating conditions.The correlation derived in this study is consistent with the simulations,with an average relative error of 5.3%under the operating conditions.Finally,to improve the accuracy of the predictions near the entrance,a segmented correlation is developed by combining the Kays correlation with the aforementioned correlation.The new correlation reduces the average relative error to 2.9%and maintains satisfactory accuracy throughout the entire axial range of the channel,thereby demonstrating its applicability to turbulent heat transfer calculations for helium-xenon gas mixtures within the core environment.These findings provide valuable insights into the convective heat transfer behavior of a helium-xenon gas mixture in a core environment.

Analysis of influence of heat exchangerfouling on heat transfer performancebased on thermal fluid coupling

A study on heat transfer performance by thermal fluid coupling simulation for the fouling in a shell-tube heat exchanger used in engineering was presented. The coupling simulation was performed in a fluid and solid domains under three different fouling conditions: fouling inside the tube, fouling outside the tube, and fouling inside the shell. The flow field, temperature, and pressure distributions in the heat exchanger were solved numerically to analyze the heat transfer performance parameters, such as thermal resistance. It is found that the pressure drop of the heat exchanger and the thermal resistance of the tube wall increase by nearly 30% and 20%, respectively, when the relative fouling thickness reaches 10%. The fouling inside the tube has more impact on the heat transfer performance of the heat exchanger, and the fouling inside the shell has less impact.

Effects of tube cross-sectional shapes on flow pattern, liquid film and heat transfer of n-pentane across tube bundles

The heat transfer of hydrocarbon refrigerant across tube bundles have been widely used in refrigeration.Three-dimensional simulation model using volume of fluid(VOF) was presented to study the effects of tube shapes on flow pattern, film thickness and heat transfer of n-pentane across tube bundles, including circle, ellipse-shaped, egg-shaped and cam-shaped tube bundles. Simulation results agree well with experimental data in the literature. The liquid film thickness of sheet flow and heat transfer for different tube shapes were obtained numerically. The flow pattern transition occurs lower vapor quality for ellipse-shaped tube than other tube shapes. For sheet flow, the liquid film on circle tube and ellipseshaped tube is symmetrically distributed along the circumferential direction. However, the liquid film on egg-shaped tube at circumferential angles(θ) = 15°–60° is thicker than θ = 135°–165°. The liquid film on cam tube at θ = 15°–60° is slightly thinner than θ = 135°–165°. The liquid film thickness varies from thinner to thicker for ellipse-shaped, cam-shaped, egg-shape and circle within θ = 15°–60°. The effect of tube shape is insignificant on thin liquid film thickness. Ellipse-shaped tube has largest heat transfer coefficient for sheet flow. In practical engineering, the tube shape could be designed as ellipse to promote heat transfer.