Nusselt number correlation for turbulent heat transfer of helium-xenon gas mixtures

A gas-cooled nuclear reactor combined with a Brayton cycle shows promise as a technology for highpower space nuclear power systems.Generally,a helium-xenon gas mixture with a molecular weight of14.5-40.0 g/mol is adopted as the working fluid to reduce the mass and volume of the turbomachinery.The Prandtl number for helium-xenon mixtures with this recommended mixing ratio may be as low as 0.2.As the convective heat transfer is closely related to the Prandtl number,different heat transfer correlations are often needed for fluids with various Prandtl numbers.Previous studies have established heat transfer correlations for fluids with medium-high Prandtl numbers(such as air and water)and extremely lowPrandtl fluids(such as liquid metals);however,these correlations cannot be directly recommended for such helium-xenon mixtures without verification.This study initially assessed the applicability of existing Nusselt number correlations,finding that the selected correlations are unsuitable for helium-xenon mixtures.To establish a more general heat transfer correlation,a theoretical derivation was conducted using the turbulent boundary layer theory.Numerical simulations of turbulent heat transfer for helium-xenon mixtures were carried out using Ansys Fluent.Based on simulated results,the parameters in the derived heat transfer correlation are determined.It is found that calculations using the new correlation were in good agreement with the experimental data,verifying its applicability to the turbulent heat transfer for helium-xenon mixtures.The effect of variable gas properties on turbulent heat transfer was also analyzed,and a modified heat transfer correlation with the temperature ratio was established.Based on the working conditions adopted in this study,the numerical error of the property-variable heat transfer correlation was almost within 10%.

Pipes with Trapezoidal Cut Twisted Tape Inserts in the Laminar Flow Regime:Nusselt Number and Friction Coefficient Analysis

The thermal behavior of pipes with a twisted tape inside(used to enhance heat transfer through the tube wall)is studied in the laminar flow regime.Oil is used as the work fluid with the corresponding Reynolds Number spanning the interval 200–2000.It is found that in such conditions the‘Nusselt Number’(Nu)gradually increases with reducing the tape twist ratio,whereas the friction factor is detrimentally affected by the presence of the tape(as witnessed by the comparison with the companion case where a plain tube is considered).In particular,it is shown that the heat transfer efficiency can be improved by nearly 69%if tape inserts with a relatively low twist ratio are used.On the basis of these findings,it is concluded that loose fit tape inserts are superior to tight fit tapes in terms of heat transfer and ease of replacement.

A Review on Thermophysical Properties and Nusselt Number Behavior of Al2O3 Nanofluids in Heat Exchangers

During the last several years,the increase in cooling power requirements for heat exchangers have led to an escalation in heat transfer studies being performed on the use of nanofluids as heat transfer fluids.However,limited effort has been attempted to relate and interpret these findings or the anomalies associated with them.The paper compiles test data from several studies conducted on different types of heat exchangers.In this review,a concentrated effort is spent to clarify the ambiguities regarding the effect of nanoparticle size on the nanofluid thermal conductivity and Nusselt number.Results show that the nanofluid thermal conductivity is not influenced by the nanoparticle size,but by the clustering of the particles themselves.The less compact the structure of the nanoparticle clustering is,the greater the enhancement in the nanofluid thermal conductivity is.Data were also compiled to interpret the relation between the nanofluid flow pattern,nanoparticles volume fraction in the base fluid,and the convective heat transfer.The results from the majority of the heat exchanger studies show an increase in the heat transfer coefficient with the increase in nanoparticle volume fraction.However,studies conducted on plate heat exchanges display some inconsistencies.In the majority of the heat exchanger studies with the exception of few,the decrease in the nanoparticle size is shown to result in an enhancement of the bulk fluid Nusselt number.Compiled test data also reveal that the effectiveness of the alumina nanoparticles is dependent on the flow pattern.The increase in the nanoparticles concentration is shown to result in an increase in the nanofluid heat transfer enhancement as the fluid is transitioning from laminar to turbulent flow.In general,the smaller the nanoparticle size is,the greater the enhancement in the fluid Nusselt number is.

Artificial neural network analysis of the Nusselt number and friction factor of hydrocarbon fuel under supercritical pressure

This paper presents the Nusselt number and friction factor model for hydrocarbon fuel under supercritical pressure in horizontal circular tubes using an artificial neural network(ANN)analysis on the basis of the back propagation algorithm.The derivation of the proposed model relies on a large number of experimental data obtained from the tests performed with the platform of supercritical flow and heat transfer.Different topology structures,training algo-rithms and transfer functions are employed in model optimization.The performance of the optimal ANN model is evaluated with the mean relative error,the determination coefficient,the number of iterations and the convergence time.It is demonstrated that the model has high prediction accuracy when the tansig transfer function,the Levenberg-Marquardt training algo-rithm and the three-layer topology of 4-9-1 are selected.In addition,the accuracy of the ANN model is observed to be the highest compared with other classic empirical correlations.Mean relative error values of 4.4%and 3.4%have been achieved for modeling of the Nusselt number and friction factor respectively over the whole experimental data set.The ANN model estab-lished in this paper is shown to have an excellent performance in learning ability and general-ization for characterizing the flow and heat transfer law of hydrocarbon fuel,which can provide an alternative approach for the future study of supercritical fluid characteristics and the associ-ated engineering applications.

管形对水平管降膜圆周膜厚和Nusselt数的影响

针对海水淡化系统的水平管降膜蒸发,建立了二维数值模型,分析了光滑圆管和6种不同截面形状的蛋形管外降膜流动及传热特性。采用VOF方法考察了不同管型对管外液膜分布和传热特性的影响。数值结果表明:蛋形管外液体沿周向流动较圆管稍快,且可获得更均匀更薄的液膜;液膜厚度随半轴比ε增大而减小,随周向先逐渐减小后迅速增加,圆管和蛋形管的液膜最小值分别出现在周向相对坐标0.69和0.70～0.84附近。蛋形管的膜内量纲1温度较圆管的小,其热边界层厚度较薄,具有更好的传热性能。拟合数据得到,ε为2.4的蛋形管具有最好的传热性能,其Nusselt数可达0.32,较圆管的高出12.68%。最后,将数值模拟结果与文献中的数据进行了对比,验证了数值模型的可行性和合理性。

Fluid flow and heat transfer characteristics of spiral coiled tube: Effects of Reynolds number and curvature ratio

Numerical analysis was performed to investigate flow and heat transfer characteristics in spiral coiled tube heat exchanger. Radius of curvature of the spiral coiled tube was gradually increased as total rotating angle reached 12n. As the varying radius of curvature became a dominant flow parameter, three-dimensional flow analysis was performed to this flow together with different Reynolds numbers while constant wall heat flux condition was set in thermal field. From the analysis, centrifugal force due to curvature effect is found to have significant role in behavior of pressure drop and heat transfer. The centrifugal force enhances pressure drop and heat transfer to have generally higher values in the spiral coiled tube than those in the straight tube. Even then, friction factor and Nusselt number are found to follow the proportionality with square root of the Dean number. Individual effect of flow parameters of Reynolds number and curvature ratio was investigated and effect of Reynolds number is found to be stronger than that of curvature effect.

Effect of Physical and Geometrical Parameters on Nuselt Number

The results of this study show that the Nusselt number decreases with the increase of the dimensionless thermal conductivity and the Prandtl, Froude numbers. The increased Reynolds, Jacob numbers and the dimensionless thickness of porous layer leads to an increase the Nusselt number.

Numerical Analysis of the Transient Process of Flow and Heat Transfer at High Rayleigh Number in a Partially Open Habitat Heated from Above

In this work, we studied the thermoconvective instabilities in a pentagonal cavity containing a Newtonian fluid. The cavity provided with a side opening is uniformly heated from above by a constant heat flux. The natural ventilation phenomenon in the classic habitat of the hot climate is thus numerically analyzed with unsteady natural convection equations formulated with vorticity and stream-function variables. The finite volume predictions of two-dimensional laminar natural convection at high Rayleigh number are presented. Results show that the incoming fresh air and the hot air discharge begin with the late start of the convection. The phenomenon intensifies with time and the birth of instabilities improves the homogenisation of temperatures which imply the elimination of very cold and very hot areas. However, the competition between the incoming fresh air and the hot air expansion leads to a perpetual displacement of the thermal front. The cross-sections at the opening of the incoming fresh and outgoing hot air are time-varying and the penetration depth of the fresh air is highlighted by the large convective cells originated from the aperture. The non monotonic variation of the Nusselt number reflects not only the multicell nature of the flow but also expresses the heat lost by the active walls due to the fresh air.

长矩形腔体中混合流体的双局部行波

基于数值模拟,研究了分离比ψ=-0.4和长高比Γ=40的腔体内的双局部行波对流的动力学特性。结果发现,对流圈在端壁产生,向中心传播,到达一定位置对流圈消失;在矩形腔体中两端壁附近行波对流区域与中间部位无对流的传导区域同时共存,形成双局部行波对流;双局部行波对流中的行波由腔体两端向中部传播;腔体二分之一高度处的温度与垂直流速分布是谐波结构,波形比较光滑,浓度分布是台型结构;随着时间的发展,垂直流速最大值稳定在某个数值周期变化,下壁面努塞尔数基本稳定在某个数值,垂直流速最大值和下壁面努塞尔数及其达到稳定的时间随着相对瑞利数r的增加而增加;双局部行波对流稳定的存在于相对瑞利数r∈{1.52,1.57]的区间,双局部行波的对流区长度随着相对瑞利数r的增加呈良好的增加关系,并给出了双局部行波的对流区长度随着相对瑞利数r变化的拟合关系式。

Study of hybrid nanofluid flow in a stationary cone-disk system with temperature-dependent fluid properties

Cone-disk systems find frequent use such as conical diffusers,medical devices,various rheometric,and viscosimetry applications.In this study,we investigate the three-dimensional flow of a water-based Ag-Mg O hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties.How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds's linearized model for variable viscosity and Chiam's model for variable thermal conductivity.The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids,incorporating the experimental data.This model is developed as a coupled system of convective-diffusion equations,encompassing the conservation of momentum and the conservation of thermal energy,in conjunction with an incompressibility condition.A self-similar model is developed by the Lie-group scaling transformations,and the subsequent self-similar equations are then solved numerically.The influence of variable fluid parameters on both swirling and non-swirling flow cases is analyzed.Additionally,the Nusselt number for the disk surface is calculated.It is found that an increase in the temperature-dependent viscosity parameter enhances heat transfer characteristics in the static cone-disk system,while the thermal conductivity parameter has the opposite effect.

Effects of multiple shapes for steady flow with transformer oil+Fe_(3)O_(4)+TiO_(2) between two stretchable rotating disks

In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.

Performance Simulation of a Double Tube Heat Exchanger Based on Different Nanofluids by Aspen Plus

A heat exchanger’s performance depends heavily on the operating fluid’s transfer of heat capacity and thermal conductivity.Adding nanoparticles of high thermal conductivity materials is a significant way to enhance the heat transfer fluid’s thermal conductivity.This research used engine oil containing alumina(Al_(2)O_(3))nanoparticles and copper oxide(CuO)to test whether or not the heat exchanger’s efficiency could be improved.To establish the most effective elements for heat transfer enhancement,the heat exchangers thermal performance was tested at 0.05%and 0.1%concentrations for Al_(2)O_(3)and CuO nanoparticles.The simulation results showed that the percentage increase in Nusselt number(Nu)for nanofluid at 0.05%particle concentration compared to pure oil was 9.71%for CuO nanofluids and 6.7%for Al_(2)O_(3)nanofluids.At 0.1%concentration,the enhancement percentage in Nu was approximately 23%for CuO and 18.67%for Al_(2)O_(3)nanofluids,respectively.At a concentration of 0.1%,CuO nanofluid increased the LMTD and overall heat transfer coefficient(U)by 7.24 and 5.91%respectively.Both the overall heat transfer coefficient(U)and the heat transfer coefficient(hn)for CuO nanofluid at a concentration of 0.1%increased by 5.91%and 10.68%,respectively.The effectiveness(εn)of a heat exchanger was increased by roughly 4.09%with the use of CuO nanofluid in comparison to Al_(2)O_(3)at a concentration of 0.1%.The amount of exergy destruction in DTHX goes down as Re and volume fractions go up.Moreover,at 0.05%and 0.1%nanoparticle concentrations,the percentage increase in dimensionless exergy is 10.55%and 13.08%,respectively.Finally,adding the CuO and Al_(2)O_(3)nanoparticles improved the thermal conductivity of the main fluid(oil),resulting in a considerable increase in the thermal performance and rate of heat transfer of a heat exchanger.

Comparative Numerical Analysis of Heat and Mass Transfer Characteristics in Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg Fluids on a Stretched Surface

In the current research,a thorough examination unfolds concerning the attributes of magnetohydrodynamic(MHD)boundary layer flow and heat transfer inherent to nanoliquids derived from Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg compositions.Such nanoliquids are subjected to an extending surface.Consideration is duly given to slip boundary conditions,as well as the effects stemming from variable viscosity and variable thermal conductivity.The analytical approach applied involves the application of suitable similarity transformations.These conversions serve to transform the initial set of complex nonlinear partial differential equations into a more manageable assembly of ordinary differential equations.Through the utilization of the FEM,these reformulated equations are solved,considering the specified boundary conditions.The outcomes attained are graphically depicted by means of plots and tables.These visual aids facilitate a comprehensive exploration of how diverse parameters exert influence over the distributions of velocity,temperature,and concentration.Furthermore,detailed scrutiny is directed towards the fluctuations characterizing pivotal parameters,viz.,Nusselt number,skin-friction coefficient,and Sherwood number.It is identified that the Nusselt number showcases a diminishing trend coinciding with increasing values of the volume fraction parameter(φ).This trend remains consistent regardless of whether the nanoliquid under consideration is Al_(2)O_(3)-Eg or TiO_(2)-Eg based.In contrast,both the skin-friction coefficient and Sherwood number assume lower values as the volume fraction parameter(φ)escalates.This pattern remains congruent across both classifications of nanoliquids.The findings of the study impart valuable insights into the complex interplay governing the characteristics of HMT pertaining to Sisko Al_(2)O_(3)-Eg and TiO_(2)-Eg nanoliquids along an extending surface.

Experimental Study and Thermal Modelling of Cocoa Shell Convective Drying in an Indirect Solar Dryer

The concern of the present work is the convective drying of empty cocoa shells in an indirect solar dryer. Some drying experiments, using one sample, were carried out. During the experiments, the sample is introduced in the drying chamber. Then at steady time intervals, the sample is withdrawn from the drying chamber, for a rapid weighing. After each weighing, the sample is reintroduced in the dryer. At each time interval, the ambient temperature of the drying chamber and its relative humidity γ are measured by a thermo-hygrometer. From the experimental data, a theoretical determination of the moisture evaporated from the product was performed and a good agreement was found between the theoretical and experimental values, confirmed by the value of the RMSE. Those calculations used the constants in the Nusselt number found in literature. Then those constants were evaluated again, to get new values more suitable with the experimental data. The dimensionless numbers of Nusselt, Grashof and Prandtl were calculated. That allowed the calculation of the average value of the Nusselt number. The average convective heat transfer coefficient was determined.

Influence of Temperature-Dependent Thermophysical Properties of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra-Hybrid Nanofluid along a Vertical Porous Surface with Suction

The significance of the thermophysical properties of Tetra hybrid nanofluid in enhancing heat transmission in various applications like heat exchangers, automobiles, and solar storage cannot be overstated. These features can be tampered with when nanoparticles are been introduced into the base fluid to produce an improved heat carrier fluid for the system. This study investigates the impact of temperature-dependent properties on the movement of TiO2-SiO2-ZnO-Fe2O3/PAO Tetra hybrid nanofluid along a vertical porous surface with suction. The system of governing Partial Differential Equations (PDEs) was formulated and transformed into the system of coupled nonlinear third-order Ordinary Differential Equations (ODEs) by similarity techniques. The resulting ODEs were solved numerically using the shooting method and fourth order Runge-Kutta method with the aid of Maple 18.0 software. Using numerical and statistical methods, the study analyzes velocity, temperature profiles, skin friction coefficient, and Nusselt number. It was found that as the variable thermal conductivity parameter upsurges both the skin friction coefficient and Nusselt number intensify at the rate of 0.011697519 and 8.043581616 respectively. This study underscores the vital role of Tetra hybrid nanofluid’s thermophysical properties in improving heat transmission for diverse appli cations. By manipulating nanoparticles within the base fluid, the heat carrier fluid’s efficiency can be enhanced, critical for industries like automotive and enewable energy. These insights inform the design of more efficient heat exchange systems, advancing sustainability and performance in real-world scenarios.

NACA0021和NACA4822翼型肋通道中环境空气流动传热特性的实验研究

针对超燃冲压发动机在更高Mach数飞行时,主动再生冷却技术面临换热能力不足的瓶颈问题,拟利用翼型肋加强再生冷却通道的传热性能.为了从原理上验证翼型肋通道的强化传热效果,搭建了环境空气在NACA0021对称翼型肋和NACA4822非对称翼型肋通道(横截面尺寸50 mm×50 mm)中的流动传热实验测试平台,基于稳态液晶技术得到受热表面的Nusselt数.通过实验研究发现:NACA0021对称翼型肋通道和NACA4822非对称翼型肋通道的传热强度分别被提升了0.17%~17.1%和18.4%~52.1%,50 m^(3)/h流量下的PEC(performance evaluation criteri-on)分别为1.04和1.24;大流量条件下,NACA4822非对称翼型肋通道可强化中间受热面的传热性能;翼型肋通道中的流动压降也会相应增大,其中NACA4822翼型肋通道中的压降最大,翼型肋的非对称性使得流动湍流强度不断积累造成下游压降存在明显升高.该研究将有助于进一步开展翼型肋通道内超临界流体的流动传热特性研究,拓宽超燃冲压发动机主动再生冷却技术的应用温区.

翅片参数对小型转子发动机端盖传热特性影响

为了探究小型风冷转子发动机散热翅片参数与端盖传热特性之间的关系。基于流体力学理论与传热学理论,建立了整机冷却散热的流固耦合三维仿真模型,对具有不同散热翅片参数的发动机进行了数值模拟,研究了翅片的高度、长度、厚度及翅片间隙对端盖表面的换热能力和综合性能的影响。结果表明,随着翅片高度的增加,端盖表面的换热能力先提高后降低,但综合性能评价指标不断减小。翅片长度小于10mm时,适当的增加翅片长度可提高换热能力。此外,随着翅片间隙与翅片厚度的增加,端盖表面的散热能力持续增强、综合评价指标不断提高。该研究可为小型风冷转子发动机端盖散热翅片的优化设计提供理论支持。

冷气流量比对三维涡轮导叶全气膜冷却效率的影响

为了研究不同主流湍流度下冷气质量流量比对三维涡轮导叶全气膜冷却特性的影响,使用热色液晶测量了在主流湍流度为1%和15%,流量比为5.5%、8.4%和12.5%下三维涡轮导叶的全气膜冷却效率分布。结果表明:在不同的叶片区域和主流湍流度下,流量比对气膜冷却特性的影响规律也有所不同;在低主流湍流度下,冷却效率整体上随着流量比的增大而升高,但是在叶片的叶尖和吸力面中截面区域冷却效率在大流量比下降低,且叶片吸力面中弦区域的冷气呈波纹状分布;高主流湍流度使冷气射流与主流之间的掺混更加剧烈,可以抑制吸力面的冷气脱离壁面且使其分布更加均匀,冷却效率随流量比增大而升高。

高炉喷吹煤粉颗粒与热风间动量能量交换的数值仿真

为了揭示高炉风口回旋区周边颗粒对煤粉颗粒受力和传热特性的影响机理,建立了基于CPU-GPU异构并行模式的三维浸没边界-格子Boltzmann法(IB-LBM)模型,针对串列三颗粒在流场中的曳力和传热特征开展数值模拟研究,详细讨论了雷诺数(10≤Re≤100)和颗粒间距(s=2D,4D)对曳力系数Cd和平均努塞尔数Nu的影响.结果表明:第2个和第3个颗粒置入后,随着Re的增大,3个颗粒的Cd均减小(Cd_(1)>Cd_(2)>Cd_(3)),而3个颗粒的Nu均增大(Nu1>Nu2>Nu3);根据数值模拟结果,分别构建了串列三颗粒的Cd与Nu的新关联式,新关联式得出的Cd和Nu预测值与数值模拟结果相比,最大误差分别为2.5449%和0.4480%,这表明该关联式适用于高炉喷吹煤粉颗粒在热风中受力和传热机制的数值仿真过程.

液力惯容器螺旋管对流换热数值模拟

采用数值模拟研究了液力惯容器螺旋管的对流换热特性。通过建立液力惯容器螺旋管的流动换热数值模型,仿真得到管内的流体流速及温度分布,采用努塞尔数描述螺旋管的对流换热能力,分析了不同参数对螺旋管流动换热特性的影响。结果表明:螺旋管的速度场和温度场均呈C型分布,表明产生了二次流现象;随着入口和壁面温度增加,努塞尔数先降低后增加;随着雷诺数、相对粗糙度、螺旋直径的增加及螺旋管内直径和螺距的减小,努塞尔数增加,对流传热能力加强。研究结论为螺旋管式液力惯容器的热力学设计提供了理论依据。