Numerical investigation on convective heat transfer over two heated wall-mounted cubes in tandem and staggered arrangement

In this study, laminar convective heat transfer over two heated wall-mounted cubes is investigated.Two cubes, which are under constant heat flux, are placed in different tandem and staggeredarrangements on a base plate. This problem is studied for different streamwise and spanwisedistances between two cubes in different Renolds number （Re）, by using finite-volume method.Effects of these parameters are considered on flow and heat transfer characteristics. The resultsshow that the temperature distribution is strongly dependent on flow structure and varies with anychange of flow pattern in different arrangements of cubes. In addition, it is observed that the dragcoefficient, which is influenced more by pressure forces, in staggered arrangement, is greater thantandem arrangement. Results show that by increasing the spanwise distance the amount of meanNusselt number （Nu） of Cube 2 becomes the same as Cube 1.

An Investigation into the Influence of the Airflow Path on the Convective Heat Transfer for an Eddy Current Retarder Turntable

In order to improve the convective heat transfer relating to an eddy current retarder,the finite element model has been used to assess the performances of different possible designs.In particular,assuming the steady running state of retarder as the working condition,flow and temperature fields have been obtained for the rotor.The influence of airflow path on heat dissipation has been analysed,and the influence of the temperature field distribution on the performance of retarder has been discussed accordingly.The results show that when the steady running state of the turntable is considered,the maximum temperature is lower,the level of turbulence flow is mitigated,and the temperature distribution becomes more regular.These factors contribute to improve the heat dissipation ability of the retarder.

Numerical study of convective heat transfer in static arrangements of particles with arbitrary shapes:A monolithic hybrid lattice Boltzmann-finite difference-phase field solver

A compressible lattice Boltzmann-finite difference method is extended by the phase-field approach into a monolithic scheme to study fluid flow and heat transfer through regular arrangements of solid bodies of circular,elliptical and irregular shapes.The advantage of using the phase-field method is demon-strated both in its simplicity of accounting for flow and thermal boundary conditions at solid surfaces with irregular shapes and in the capability of generating such complex-shaped objects.For an array of discs,numerical results for the overall solid-to-gas heat transfer rate are validated via experiments on flow through arrays of hot cylinders.The thus validated compressible LB-FD-PF hybrid scheme is used to study the dependence of heat transfer on flow and thermal boundary conditions(Reynolds number,temperature difference between the hot solid bodies and the inlet gas),porosity as well as on the shape of solid objects.Results are rationalized in terms of the residence time of the gas close to the solid body and downstream variations of gas velocity and temperature.Perspective for further applications of the proposed methodology are also discussed.

Topology optimization of simplified convective heat transfer problems using the finite volume method

Topology optimization of simplified convective heat transfer has been widely studied,but most existing studies are based on the finite element method(FEM);methods based on the finite volume method(FVM)have been less studied.In this paper,a topology optimization method based on FVM was proposed for a simplified convective heat transfer problem.We developed a novel adjoint sensitivity analysis method applicable to FVM,which included adjoint equations,corresponding boundary conditions,and sensitivity analysis equations.Additionally,a program for the proposed topology optimization method was developed in open field operation and manipulation(OpenFOAM)and portable,extensibletoolkit for scientific computation(PETSc).Thus,large-scale topology optimizations could be performed in parallel.Furthermore,numerical examples of the classical two-dimensional(2D)and 3D optimization problems were considered.The results verified the effectiveness and feasibility of the proposed method.The results of large-scale 3D examples show an interesting phenomenon that for the optimized designs with few features,the large-scale topology optimization is still valuable for obtaining more effective structural shapes.

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.

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.

Role of viscous heating in entransy analyses of convective heat transfer

The entransy theory is widely used and found to be effective in thermal analyses and optimizations.Some researchers considered the entransy variation due to viscous heating as part of entransy dissipation and analyzed convective heat transfer based on the differential relationship between entropy and entransy.However,it has been pointed out that the derivation of the differential relationship between entropy and entransy is incorrect.In this paper,the convective heat transfer processes with viscous heating is reconsidered and analyzed from the viewpoint of the energy conservation and the entransy balance equation.It is shown that the influence of the viscous heating is equivalent to that of an inner heat source.Therefore,the contribution of viscous heating to system entransy should not be treated as part of entransy dissipation,but entransy flow into the system.Two-stream parallel and counter flow heat exchangers with viscous heating and a thermal insulation transportation problem of heavy oil are taken as examples to verify the theoretical analyses intuitively.In the examples,the numerical results show that the entransy dissipation rates could be negative when the influence of the viscous heating on the system entransy is treated as part of the entransy dissipation.This is obviously unreasonable.Meanwhile,when the entransy contribution from the viscous heating to the system entransy is treated as entransy flow into the system,it is shown that the entransy dissipation rate is always positive,and the heat transfer processes can be well explained with the entransy theory.

An exact analytical solution for convective heat transfer in rectangular ducts

An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time.This solution is valid for both H1 and H2 boundary conditions,which are related to fully developed convective heat transfer under constant heat flux at the duct walls.The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution.The local and mean Nusselt numbers are also obtained as functions of the aspect ratio.A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions.This is one of the major innovations of the current study.The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.

Shape optimization of corrugated tube using B-spline curve for convective heat transfer enhancement based on machine learning

A significant way to achieve energy saving and emission reduction is to optimize the design of heat transfer devices.As is widely applied in industry,a corrugated tube constructed by B-spline curve is numerically investigated and the profile is optimized,using a surrogate model with considerations of performance evaluation criterion(PEC)as single objective or minimum flow resistance(f)and maximum Nusselt number(Nu)as multi-objective.The machine learning technique is used to determine the candidate samples to update the surrogate model for improving the optimization efficiency and reliability,which is validated to be effective in this paper.The optimization results show that the comprehensive performance of the corrugated tube is more sensitive to the vertical coordinates of the control points,with the appropriate increase in the number of control points for Bspline,and the better performance of corrugated tubes is achieved.The optimal profile corresponding to the best comprehensive performance is a double-crest shape.With Reynolds number(Re)increased,the wave-amplitude of the first wave gradually gets smaller,and the profile of the corrugated tube becomes smoother.With the increasing consideration of heat transfer performance over multi-objective optimization,the optimal shape gradually changes from a double-trough to a single-trough shape.Finally,the maximum PEC of 1.2415,1.1845,and 1.1504 are acquired with the Re=8000,10000,and 12000,respectively,and the maximum Nu increases from 358.540 to 478.821.Compared with the design with the maximum thermal performance,the best compromise solution from multi-objective optimization is determined at Re=8000,10000,and 12000,showing improved flow resistance of 83.917%,85.465%,and 84.473%,but with sacrificed thermal performance of 36.754%,37.088%,and 35.005%,respectively.

Role of radiative and convective heat transfer during heating of an ingot product in a tubular furnace:experiment and simulation

Convective heat transfer and radiative heat transfer are two essential heat transfer modes in the heating process of steel;it is important to understand the role of them during the heating process clearly.The effects of the convective and radiative heat transfer during the heating process of a cast ingot in a tubular furnace have been studied by the designed natural and forced convection experiments and mathematical simulations.The heating time for the center of the ingot to reach the furnace temperature is decreased with the increase in furnace temperature.According to the experimental and simulation results,a model is proposed regarding the role of radiative and convective heat transfer in the heating process.At low temperature,the convective heat transfer plays a dominant role,while at high temperature,the influence of radiative heat transfer is larger.And a critical temperature exists between them.The forced convective heat transfer can enhance the influence of the convective heat transfer.The critical temperature can be shifted to higher temperatures.

Influence of thermodynamic disfigurement on the convective heat transfer of solar greenhouse

Solar greenhouse is a typical greenhouse without any additional heating system,which has developed rapidly in Northern China.However,due to the construction quality,management methods,especially the long-term use and other factors,there are usually different degrees of thermodynamic disfigurements in the envelop enclosure of solar greenhouse.The purpose of this study was to investigate the influences of thermodynamic disfigurement on the temperature distribution and convective heat transfer of solar greenhouse.In this study,the east and west compartments of a typical solar greenhouse which is located in Yangling,China(108°4′E,34°16′N)were tested.The air temperature of each compartment was collected using temperature recorders,and the thermal infrared images of different compartment envelopes were obtained by a thermal infrared imager on a typical cloudy day.Convective heat transfer coefficients and heat flux densities of different compartment envelopes in the solar greenhouse were calculated.The results showed that the temperature difference can be displayed in the thermal infrared images of compartment envelopes,the surface temperature of the front roof was the lowest,followed by the back roof,the wall surface temperature was the highest.The minimum average surface temperature of the front roof in the eastern compartment was only 3.8℃,which was 6.8℃ and 9.2℃ lower than the average surface temperature of the back roof and back wall,respectively.The surface average temperature of thermodynamic disfigurements located at the bottom of the south side in the front roof of the eastern compartment,whose area accounted for 16.5%of the total front roof in the eastern compartment,was only 5.4℃.Compared with non-thermodynamic disfigurement,the average convective heat transfer coefficient and heat flux density of thermodynamic disfigurements in the front roof of the eastern compartment were increased by 20.3%and 110.3%,respectively.The average air temperature in the eastern compartment was 3.5℃ lower than the average air temperature in the western compartment of the solar greenhouse.Construction of brick wall at the bottom of the south side of the front roof in the solar greenhouse helped to increase the inner surface temperature of the front roof,with an average temperature rise of 6.2℃,and reduce the area of thermodynamic disfigurement,which only accounted for 2.6%of the total front roof in the western compartment.The average surface temperature of thermodynamic disfigurements mainly caused by the entry and exit door in the wall of the eastern compartment was only 9.8℃,which was lower 3.2℃ than the average temperature of non-thermodynamic disfigurement of the wall.Thermodynamic disfigurement helped to increase heat loss.The weighted average proportion of thermodynamic disfigurement in the western compartment was 2.1%,while that of thermodynamic disfigurement in the eastern compartment was 10.7%.The thermal insulation performance of the western compartment envelope in the solar greenhouse was better than that of the eastern compartment envelope.

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.

Convective Heat Transfer of Molten Salt in Receiver Tube with Axially and Circumferentially Non-Uniform Heat Flux

Convective heat transfer characteristics of molten salt in receiver tube under axially and circumferentially non-uniform(ACN)heat flux were experimentally investigated under Reynolds number of 16000 to 58000 and Prandtl number of 4.6 to 7.5.The results showed that flow rate,flow direction and non-uniform heat flux directly affected molten salt transfer.As coating thickness and flow velocity increased,the difference of outer wall temperature in coating side and molten salt temperature dropped.The average Nusselt number in entrance section was larger than that in middle and end sections for higher Prandtl number.The axial wall temperature difference in coating side with counter-flow heating was lower than that with parallel-flow heating,and receiver tube with counter-flow heating will cause smaller axial thermal stress.From experiment measurement and Sieder-Tate correlation,heat transfer correlation of molten salt in tube under ACN heat flux was obtained by using circumferential heat flux ratio and axial heat flux ratio,and it fit with experimental data with maximum deviation of 5%.

Convective heat transfer of nanofluids with correlations

To investigate the convective heat transfer of nanofluids, experiments were performed using silver-water nanofluids under laminar, transition and turbulent flow regimes in a horizontal 4.3 mm inner-diameter tube-in-tube counter-current heat transfer test section. The volume concentration of the nanoparticles varied from 0.3% to 0.9% in steps of 0.3%, and the effects of thermo-physical properties, inlet temperature, volume concentration, and mass flow rate on heat transfer coefficient were investigated. Experiments showed that the suspended nanoparticles remarkably increased the convective heat transfer coefficient, by as much as 28.7% and 69.3% for 0.3% and 0.9% of silver content, respectively. Based on the experimental results a correlation was developed to predict the Nusselt number of the silver-water nanofluid, with ＋10% agreement between experiments and prediction.

Comparison between conventional and deep learning-based surrogate models in predicting convective heat transfer performance of U-bend channels

Deep neural networks are efficient methods to achieve real-time visualization of physics fields.The main concerns that prevented deep learning from being implemented in the field of energy conversion were the risks of overfitting and the lack of data.Therefore,it is necessary to evaluate different kinds of surrogate modeling methods and provide guidelines for designers to choose models.In this study,three conventional models(Artificial Neural Network,Radial Bias Function,and Kriging),and two deep learning-based models(Convolutional Neural Network and Conditional Generative Adversarial Neural Network)were established to predict the flow and heat transfer performance of a U-bend with variable geometries.The models were detailly compared in terms of the single-point prediction accuracy,response accuracy,sensitivity to sample size,and other characteristics of interest.Results showed that the conventional models had slightly higher single point accuracy and the relative error of pressure loss and heat transfer were within±6.6%and±5.7%respectively,while those of the deep learning-based models were within±8.0%and±6.3%respectively.Nevertheless,the deep learning-based models had higher response accuracy and could reconstruct the distributions of surface pressure and wall heat flux with the pixel-wise absolute error within±2.0 Pa and±45 W/m^(2) respectively.The results indicated that deep learning was a promising surrogate modeling approach due to its acceptable prediction error and ability to reconstruct physical fields.This effort was expected to serve as a guide for establishing more reliable data-driven surrogate models for energy conversion and heat transfer problems.

Experimental Study on Convective Heat Transfer in Tube-Side of Water Jacket-Tube Heat Exchanger by Electrohydrodynamics Effect

The electrohydrodynamics （EHD） enhancement of convection heat transfer of water in a jacket tube heat exchanger was studied through an experimental method in this paper. In the experiment,a DC high voltage electrode was set in the central tube-side of the heat exchanger,and the high voltage electrode in the tube-side was adjustable in the range of 0-40 kV. Five differ-ent combinations of heat transfer enhancement experiments were conducted under the different voltage and rate of flow. The results indicate that the maximal enhancement coefficient θ is 1.224 when the flow rate of tube-side inlet is 0.1 m3/h. It is proved that,for the work medium of water,the convective heat transfer can be enhanced by applying high electric field. The performance of EHD-enhanced is sensitive to the variation of flow rate,and in the same flow rate,there exist an optimized voltage in the EHD-enhanced process ra-ther than the monotonic positive-correlation relationship.

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%.

Experimental Investigation on Flow and Heat Transfer of Jet Impingement inside a Semi-Confined Smooth Channel

Experimental investigation is conducted to investigate the flow and heat transfer performances of jet impingement cooling inside a semi-confined smooth channel.Effects of jet Reynolds number(varied from 10 000to 45000),orifice-to-target spacing(zn=1d—4d)and jet-to-jet pitches(xn=3d—5d,yn=3d—5d)on the convective heat transfer coefficient and discharge coefficient are revealed.For a single-row jets normal impingement,the impingement heat transfer is enhanced with the increase of impingement Reynolds number or the decrease of spanwise jet-to-jet pitch.The highest local heat transfer is achieved when zn/dis 2.For the double-row jets normal impingement,the laterally-averaged Nusselt number distributions in the vicinity of the first row jets impinging stagnation do not fit well with the single-row case.The highest local heat transfer is obtained when zn/dis 1.A smaller jetto-jet pitch generally results in a lower discharge coefficient.The discharge coefficient in the double-row case is decreased relative to the single-row case at the same impingement Reynolds number.

Simulation of Heat Transfer Characteristics in Channel with Square Rib Under Uniform and Turbulent Inlet Conditions

The detailed flow structures and closely-related heat transfer characteristics are investigated along the wall of a cooling channel with rib tabulator by computation.Three typical Reynolds numbers defined by the rib height are set at 200,500,1300,and the Mach numbers is 0.2,respectively.Two inlet boundary conditions,including the uniform and the fully-developed turbulent conditions,are used to study the turbulence effects on the characteristics of heat transfer in the vicinity of rib and wall.Results show that the local Nusselt number increases when the Reynolds number rises from 200 to 1300.At lower Reynolds number,the turbulent inlet condition generates more tangible heat transfer enhancement.At higher Reynolds number,however,the uniform inlet condition contributes more to the convective heat transfer effects.The paper discovers that the high Nusselt number has a consistent correlation with the positive and negative sign alteration of the shear layer on the wall,which satisfactorily explains the mechanisms of heat transfer enhancement due to the flow.

Heat Transfer Process of Bubble during the Occurrence of Cavitation in Hydraulic System

Thermal characteristic of cavitation has great influence on the process of occurrence,development and collapse of bubble in hydraulic system. By choosing the stage of bubble growth as the research object,combining with the characteristic of the process of bubble occurrence and development in hydraulic system, and ignoring the impact of thermal radiation,the heat transfer situation of bubble growth was analyzed under appropriate assumptions of thermodynamic conditions in the bubble generation and development process. The mathematical expression of the temperature change of bubble was deduced using thermodynamic principle. Through combining the expression with classic Rayleigh-Plesset Equation,numerical calculation was carried out and the temperature variation over time( or bubble radius) was obtained. The influences of convective heat transfer coefficient of bubble and polytropic exponent on the thermodynamic process of bubble were analyzed. Finally,the thermal characteristic of bubble growth after cavitation occurrence was summarized.