Turbulent Transfer Coefficients Research Articles

Numerical study of structural optimization for improving gas-liquid flow and microalgae carbon fixation rate in air-lift photobioreactors

In this paper, the gas-liquid flow pattern and CO2 dissolution transport process of microalgae solution in an air-lift photobioreactor (PBR) are investigated by numerical simulations. In order to promote the gas-liquid mass transfer efficiency to enhance the carbon fixation, we propose different optimization schemes for the structure. Firstly, a two-phase flow model and a mass transfer model are employed to investigate the fluid flow characteristics. The flow state is evaluated by velocity in light direction, turbulent kinetic energy (TKE), gas hold-up and CO2 mass transfer coefficient. The results show that the gas flow rate of 0.2 V/V/min is the optimum value for the inlet. Secondly, CO2 mass transfer and carbon fixation rates are analyzed for different inlet CO2 volume fractions. With the increase of CO2 volume fraction, the carbon fixation rate first increases and then decreases, the highest fixation rate reaching 2.21 × 10−4 mol m−3 s−1 at 6 %. Finally, based on numerical simulations, three optimized structures with different spacing of baffles are proposed and evaluated the performance in comparison with the original. The results show that the gas distribution and CO2 mass transfer are significantly improved, with the one-sided baffle structure is the best. In summary, this study provides a new and useful reference to evaluate the gas-liquid mixing and improve the microalgae carbon fixation rate.

Classical and local similarity in problems of turbulent convection: Extension of Prandtl semi-empirical theory for horizontal layers of water and air mediums

A variant of the local similarity theory is considered, assuming a priori specification of two basic dimensional parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. Such selection of basic parameters lets us interpret the algebraic formulas of Prandtl's semiempirical turbulence theory for the coefficients of turbulent heat transfer and kinetic energy dissipation as relationships of the local similarity theory. A priori approximations of the basic parameters are based on known relationships and consider the upper boundary of the convective layer as a solid wall. Within the framework of local similarity theory, approximations for the turbulent moments of buoyancy and vertical velocity of arbitrary order are also proposed. The correspondence of these approximations to experimental data has been established in both air and water mediums, as well as in the results of numerical modeling. Such correspondence allows us to conclude that a wide class of vertical profiles of turbulent moments in a windless convective layer depends only on two basic parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. The obtained result indicates the universal nature of the theory of local similarity and is a significant addition to the semiempirical Prandtl theory.

Opposing Mixed Convection Heat Transfer for Turbulent Single-Phase Flows

Convection, wherein forced and natural convections are prominent, is known as mixed convection. Specifically, when a forced convection flow is downward, this flow is called opposing flow. The objectives of this study are to gain a comprehensive understanding of opposing flow mixed convection heat transfer and to establish the prediction methodology by evaluating existing correlations and models. Several heat transfer correlations have been reported related to single-phase opposing flow; however, these correlations are based on experiments conducted in various channel geometries, working fluids, and thermal flow parameter ranges. Because the definition of nondimensional parameters and their validated range confirmed by experiments differ for each correlation reported in previous studies, establishing a guideline for deciding which correlation should be selected based on its range of applicability and extrapolation performance is important. This study reviewed the existing heat transfer correlations for turbulent opposing flow mixed convection and the single-phase heat transfer correlations implemented in the thermal–hydraulic system codes. Furthermore, the authors evaluated the predictive performance of each correlation by comparing them with the experimental data obtained under various experimental conditions. The Jackson and Fewster, Churchill, and Swanson and Catton correlations can accurately predict all the experimental data. The effect of the difference in the thermal boundary conditions, i.e., uniform heat flux and uniform wall temperature, on the turbulent mixed convection heat transfer coefficient is not substantial. The authors confirmed that heat transfer correlations using the hydraulic-equivalent diameter as a characteristic length can be used for predictions regardless of channel-geometry differences. Furthermore, correlations described based on nondimensional dominant parameters can be used for predictions regardless of the differences in working fluids. The authors investigated the extrapolation performance of the mixed convection heat transfer correlations for a wide range of nondimensional parameters and observed that the Jackson and Fewster, Churchill, and Aicher and Martin correlations exhibit excellent extrapolation performance with respect to natural and forced convection flows, indicating that they can be applied beyond the parameter range validated experimentally.

A general approach for predicting convective heat transfer coefficients in turbulent systems

A generalized approach for predicting turbulent convective heat transfer coefficients using large eddy simulation is presented. This model is based on semi-empirical transport theory, which links the local convective heat transfer rate to the local energy dissipation rate within the near-wall boundary layer. We apply these approaches to agitated tanks, pipe flow systems, cylinders in crossflow, and tube bundles. We validate the generality and reliability of the theoretical model against expectations from experimentally derived empirical design correlations.

Experimental and calculation investigations of hydrodynamics and heat exchange in liquid metal turbulent flows in fast reactor fuel assemblies

The formation of velocity and temperature fields in the fuel assemblies of fast reactor core occurs under the influence various factors. It is shown, that the most important factors include a complex multiply connected geometry, subject to deformation during the campaign under the influence of temperature non-uniformity and radiation effects. The results of studies of the velocity fields and shear stress, turbulence microstructure are presented. An intensification of turbulent momentum transfer in channels in azimuthal and radial directions in the area of gaps between the rods is demonstrated. The performed analysis is indicate that there are a significant difference between the experimental dependences for turbulent momentum transfer coefficients in the radial and azimuthal directions and calculated within the framework of semi-empirical models of turbulent momentum transfer as well as the anisotropy coefficients of the turbulent momentum transfer in rod bundles. The results of benchmark on the fuel assembly thermohydraulics showed that the common commercial codes describe experimental data only approximately. It is shown, that the intensification of turbulent momentum transfer in the channels of rod bundles is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the turbulent momentum transfer coefficients in the channels of rod bundles is calculated. The dependence for coefficient of inter-channel turbulent exchange of momentum is obtained and the intensification of inter-channel turbulent exchange in close-packed rod lattices is explained. A dependence for the dissimilarity coefficients of forced inter-channel convective exchange of momentum and mass, as well as energy and mass in rod bundles spaced by wire winding is obtained. The calculation methods and the numerical modeling results for temperature regime of fuel assemblies with randomly distributed initial parameters by the Monte Carlo method are presented as well as the thermomechanical analysis of the temperature field in the fuel assemblies during the campaign. An idea about the equilibrium configuration of a rod bundle in a hexagonal jacket during irradiation, the stress–strain state of an individual fuel rod and a fuel assembly jacket is obtained. The tasks of further investigations discussed.

Numerical study on heat transfer characteris tics of supercritical water in straight and helical tubes

The subcritical steam generators in high-temperature gas-cooled reactor pebble-bed modules can be replaced by supercritical steam generators to improve thermal efficiency. The axial and circumferential nonuniform flow and heat transfer characteristics of supercritical water in straight and helical tubes with varying inclinations (0–90°) are simulated to investigate the combined effects of tube structure, flow direction, thermophysical properties, property variations, buoyancy, and centrifugal forces. With heat fluxes of 233–930 kW/m2 and inlet mass fluxes of 225 or 1260 kg/(m2 s) under a working pressure of 24.5 MPa, the friction coefficients, turbulent kinetic energy, secondary flow, temperature, and heat transfer coefficients are studied in the cross section of variable structure tubes. The wall temperature and heat transfer coefficients of four regions are compared in straight and helical tubes; the maximum heat transfer coefficient appeared before the pseudo-critical point. The heat transfer coefficients are the greatest at the bottom of the straight tubes, where fluidity was high, and at the outer of the helical tubes, where the fluid velocity was high under centrifugal force. The secondary flow in the helical tubes causes a nonuniformity in the wall temperature, causing the circumferential maximum wall temperature to move.

Experimental and numerical study of heat transfer under laminarization condition in a small size supersonic nozzle

The present paper compares measured and calculated heat transfer parameters for a small-size slot supersonic nozzle. Heat transfer coefficient and temperature recovery factor were examined under conditions of partial laminarization of boundary layer caused by moderate flow acceleration and low Reynolds numbers. The transient heat transfer method was implemented for estimation of these values for the nozzle subsonic and supersonic parts. Maximum values of flow acceleration parameter K lied in the range 1.3 … 2.75∙10−6. Experimentally measured value was normalized to the developed turbulent boundary layer heat transfer coefficient and reached St/StRex = 0.5–0.7 and indicated partial laminarization phenomenon. It was shown that the temperature recovery factor hasn't been affected by the flow acceleration. The results are compared to numerical heat transfer predictions using sst, γ-sst and γ-Reθ-sst turbulence models. Numerical calculations and experimental data were found to be in reasonably good agreement for low acceleration level with K less than 0.75∙10−6. Nevertheless, γ-sst turbulence model made slightly conservative estimation whereas in contrast γ-Reθ-sst model overestimates quantities for the moderate flow acceleration conditions.

О влиянии диффузии на точность измерения расхода жидкости методом лагранжевых меток

By solving a one-dimensional scalar transport equation with diffusion, it is shown that the diffusion effect can lead to an overestimation of the velocity determined by the Lagrangian particle tracking method, which consists in measuring the time of passage of a flow tracer between two sensors located in the channel. To obtain model signals, the transport equation was solved numerically for different initial scalar distributions, after which the scalar values at two spatial points were recorded. It is shown that in liquid metals characterized by high electrical and thermal conductivity, the effect can be no-ticeable. The limiting Peclet number, starting from which diffusion effects do not introduce error into measurements, was determined. It is shown that for high-frequency signals the diffusion effect will not manifest itself due to the rapid attenuation of perturbations. The paper provides estimates of Peclet numbers with turbulent transfer coefficients taken into account. It is shown that in developed turbulent flows the diffusion effect can appear due to a significant contribution of small-scale turbulence.

Atmospheric and Surface Processes, and Feedback Mechanisms Determining Arctic Amplification: A Review of First Results and Prospects of the (AC)3 Project

Abstract Mechanisms behind the phenomenon of Arctic amplification are widely discussed. To contribute to this debate, the (AC)3 project was established in 2016 (www.ac3-tr.de/). It comprises modeling and data analysis efforts as well as observational elements. The project has assembled a wealth of ground-based, airborne, shipborne, and satellite data of physical, chemical, and meteorological properties of the Arctic atmosphere, cryosphere, and upper ocean that are available for the Arctic climate research community. Short-term changes and indications of long-term trends in Arctic climate parameters have been detected using existing and new data. For example, a distinct atmospheric moistening, an increase of regional storm activities, an amplified winter warming in the Svalbard and North Pole regions, and a decrease of sea ice thickness in the Fram Strait and of snow depth on sea ice have been identified. A positive trend of tropospheric bromine monoxide (BrO) column densities during polar spring was verified. Local marine/biogenic sources for cloud condensation nuclei and ice nucleating particles were found. Atmospheric–ocean and radiative transfer models were advanced by applying new parameterizations of surface albedo, cloud droplet activation, convective plumes and related processes over leads, and turbulent transfer coefficients for stable surface layers. Four modes of the surface radiative energy budget were explored and reproduced by simulations. To advance the future synthesis of the results, cross-cutting activities are being developed aiming to answer key questions in four focus areas: lapse rate feedback, surface processes, Arctic mixed-phase clouds, and airmass transport and transformation.

Numerical assessment of the impact of transverse roughness ribs on the turbulent natural convection in a BIPV air channel

The effect of varying rib geometry on the turbulent natural convective heat transfer coefficient in a BIPV air channel was assessed numerically. The CFD model was validated with experimental data from the literature to within reasonable accuracy. The study investigated parameters such as the rib shape, dimensionless rib height (e/D), dimensionless rib pitch (p/e), and channel inclination angle (θ). In each case, the heat flux is varied from 100 W/m2 – 1000 W/m2. The natural convection heat transfer coefficient on the heated wall is maximized for a vertical channel with triangular rib of e/D = 0.16 and p/e = 8.84. The enhancement in heat transfer afforded by the transverse ribs translates to a reduction of the summer heat gain of up to 35.5%. The natural convection heat transfer coefficient correlates with Ras*(S/H), e/D, p/e and θ to within 15% error.

Experimental determination of the convection heat transfer coefficient in an eccentric annular duct

The use of bayonet tube heat exchangers and heaters is widespread in many industrial applications and an improvement in the heat transfer coefficient may provide benefits over other technologies. This work presents novel experimental results about the turbulent convection heat transfer coefficient of air in the annular section of a bayonet tube for two different configurations: concentric and eccentric tubes. For both configurations, the convection heat transfer coefficient was obtained at different air flow rates, therefore, at different Reynolds numbers. In the case of the eccentric configuration, the angular position of the inner tube was varied to determine the circumferential distribution of the local convective heat transfer coefficient. An increase of the convection coefficient was observed for both configurations at higher Reynolds numbers. Concerning the angular position with regard the inner tube, the largest local convective heat transfer coefficient was obtained at the angular position where the distance between the inner and outer tubes was maximum, yielding a value 22.3% higher than in the case of a concentric annular section. All these experimental results were used to propose a new correlation for the local convective heat transfer coefficient as a function of the Prandtl and Reynolds numbers, the eccentricity, and the angular position of the inner tube, with a maximum discrepancy between correlation and experimental data below 10%.

7 February Chamoli (Uttarakhand, India) Rock-Ice Avalanche Disaster: Model-Simulated Prevailing Meteorological Conditions

The present study aims to analyze the high-resolution model-simulated meteorological conditions during the Chamoli rock-ice avalanche event, which occurred on 7 February 2021 in the Chamoli district of Uttarakhand, India (30.37° N, 79.73° E). The Weather Research and Forecasting (WRF) model is used to simulate the spatiotemporal distribution of meteorological variables pre- and post-event. The numerical simulations are carried out over two fine resolution nested model domains covering the Uttarakhand region over a period of 2 weeks (2 February to 13 February 2021). The model-simulated meteorological variables, e.g., air temperature, surface temperature, turbulent heat flux, radiative fluxes, heat and momentum transfer coefficients, specific humidity and upper wind patterns, were found to show significant departures from their usual patterns starting from 72 h until a few hours before the rock-ice avalanche event. The average 2 m air and surface temperatures near the avalanche site during the 48 h before the event were found to be much lower than the average temperatures post-event. In-situ observations and the ERA5-Land dataset also confirm these findings. The total turbulent heat flux mostly remained downward (negative) in the 72 h before the event and was found to have an exceptionally large negative value a few hours before the rock-ice avalanche event. The model-simulated rainfall and Global Precipitation Measurement (GPM, IMERG)-derived rainfall suggest that the part of the Himalayan region falling in the simulation domain received a significant amount of rainfall on 4 February, around 48 h prior to the event, while the rest of the days pre- and post-event were mostly dry. The results presented here might be helpful in further studies to identify the possible trigger factors of this event.

Local Similarity Theory of Convective Turbulent Layer Using “Spectral” Prandtl Mixing Length and Second Moment of Vertical Velocity

Abstract Approximations of the turbulent moments of the atmospheric convective boundary layer are constructed based on a variant of the local similarity theory. As the basic parameters of this theory, the second moment of vertical velocity and the “spectral” Prandtl mixing length are used. This specific choice of the basic parameters allows us to consider the coefficient of turbulent transfer and the dissipation of kinetic energy of the Prandtl turbulence theory as the forms of the local similarity. Therefore, the obtained approximations of the turbulent moments should be considered as natural complementation to the semiempirical turbulence theory. Moreover, within the atmospheric surface layer, the approximations of the new local similarity theory are identical to the relations of the Monin–Obukhov similarity theory (MOST). Therefore, the proposed approximations should be considered as a direct generalization of the MOST under free-convection conditions. The new approximations are compared with the relations of the known local similarity theories. The advantages and limitations of the new theory are discussed. The comparison of the approximations of the new local similarity theory with the field and laboratory experimental data indicates the high effectiveness of the proposed approach.

Aerodynamic Characteristics Over Fine-Grained Gravel Surfaces in a Wind Tunnel

Gravels can protect soil from wind erosion, however, there is little known about the effects of fine-grained gravel on aerodynamic characteristics of the near-surface airflow. Drag coefficient, wind-speed gradient, and turbulent transfer coefficient over different coverages of gravel surfaces were investigated in a compact boundary-layer wind tunnel. The drag coefficient of the fine-grained gravel surface reached the maximum value at 15% coverage and then tended to stabilize at gravel coverage 20% and greater. At a height of 4 cm, near-surface airflow on gravel surfaces can be divided clearly into upper and lower sublayers, defined as the inertial and roughness sublayers, respectively. The coefficient of variation of wind speed over gravel surfaces in the roughness sublayer was 8.6 times that in the inertial sublayer, indicating a greater effect of gravel coverage on wind-speed fluctuations in the lower layer. At a height of 4 cm, wind-speed fluctuations under the observed wind speeds were independent of changes in gravel coverage. In addition, an energy-exchange region, where sand particles can absorb more energy from the surrounding airflow, was found between the roughness and inertial sublayers, enhancing the erosional state of wind-blown sand. This finding can be applied to evaluate the aerodynamic stability of the gravel surface in the Gobi Desert and provide a theoretical basis for elucidation of the vertical distributions of wind-blown sand flux.

Parameterization of Sea Surface Drag Coefficient for All Wind Regimes Using 11 Aircraft Eddy-Covariance Measurement Databases

The drag coefficient is essential for calculating the aerodynamic friction between air and sea. In this study, we regress a set of relationships between the drag coefficient and the wind speed for different wind ranges using an observational dataset that consists of 5941 estimates of the mean flow and fluxes from 11 aircraft turbulent measurements over the sea surface. Results show that: (1) the drag coefficient is a power function of wind speed over smooth sea surface when it is no greater than 4.5 ms−1, and the drag coefficient decreases with the increase of wind speed; and (2) for rough sea surface, when the wind speed is greater than 4.5 ms−1 and less than or equal to 10.5 ms−1, the drag coefficient increases linearly with the increase of horizontal wind speed; when the wind speed is greater than 10.5 ms−1 and less than or equal to 33.5 ms−1, the drag coefficient changes parabolically with the increase of wind speed; when the wind speed is greater than 33.5 ms−1, the drag coefficient is constant. Additionally, regressed from drag coefficient, the saturated wind speed threshold is 23 ms−1. Parameterizations of turbulent heat transfer coefficient (Ch) and water vapor transfer coefficient (Ce) are also investigated.

ГИДРОДИНАМИКА ТУРБУЛЕНТНЫХ ПОТОКОВ В ТВС БЫСТРЫХ РЕАКТОРОВ (ПОЛЕ СКОРОСТИ И МИКРОСТРУКТУРА ТУРБУЛЕНТНОСТИ)

The article describes the factors under the influence of which the formation of thermohydraulic characteristics occurs in the fuel assemblies of the core of fast reactors with liquid metal cooling. It is shown that one of the most important factors is a complex multiply connected geometry of a stochastic nature, subject to deformation during the campaign under the influence of temperature irregularities and radiation effects. The paper presents and analyzes the results of experimental and computational studies of the velocity field and shear stress, the microstructure of turbulence, momentum transfer in the central and peripheral regions of fuel assemblies without and with displacers, as well as in the case of deformation of the lattice of rods. The intensification of turbulent momentum transfer in the channels in the azimuthal direction in the area of the gaps between the rods is demonstrated. The anisotropy coefficient of turbulent momentum transfer reaches 30-40 units. The performed analysis indicated a significant difference in the calculated in the framework of semi-empirical models of turbulent transfer and experimental dependences of the coefficients of turbulent transfer of momentum in the radial and azimuthal directions and the coefficients of anisotropy of turbulent transfer of momentum in rod bundles. The results of an open benchmark on the thermohydraulics of fuel assemblies showed that common commercial computational thermohydraulic codes only approximately describe the experimental data. It is shown that the intensification of turbulent momentum transfer in the channels of rod assemblies is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the kinetic energy of turbulent pulsations, azimuthal turbulent shear stresses, and turbulent momentum transfer coefficients in rod assemblies is calculated. An empirical dependence of the coefficient of interchannel turbulent impulse exchange in bundles of smooth rods is obtained, on the basis of a semi-empirical model, data on interchannel turbulent impulse exchange in assemblies of smooth rods are generalized, and the intensification of interchannel turbulent exchange in close lattices of rods is explained. Data on hydraulic resistance in bundles of smooth rods are analyzed. The tasks of further research are discussed.

Experimental and Pore-scale Analysis of Flow and Thermal Fields in a Packed Bed Channel

ABSTRACT The study investigates experimentally and numerically the problem of turbulent convective heat transfer and pressure drop in a packed bed with internal heat generation. The main objective is to develop correlations for the heat transfer between the bed and coolant as well as the pressure drop in the system using detailed experimental and 3-dimensional pore-scale numerical simulation. The system analysed is a horizontal circular channel filled with different stainless steel spheres with diameters of 5.5 mm, 6.5 mm and 7.5 mm. Dry air is used as working fluid. The study is performed for turbulent flow regimes with different Reynolds number (based on the spheres diameter) in the range of 900-2600. The spheres are heated using an electromagnetic induction heating method. Based on the experimental data, empirical correlations for turbulent pressure drop and convective heat transfer coefficient are developed. Results of pore-scale analysis show the complexity of the flow domain, which the velocity experiences a considerable increase compared to inlet velocity and is more evident in narrow gaps between spheres. Moreover, numerical results indicate the coupling of temperature and velocity fields, which a non-uniform velocity filed leads to non-uniform temperature distributions of air and solid spheres in the packed bed.

Temporal and spatial characteristics of turbulent transfer and diffusion coefficient of PM2.5

The temporal and spatial characteristics of turbulent transfer and diffusion coefficient of PM2.5 (KC) were investigated by determining the deviation, turbulent flux and form of universal function of PM2.5 mass concentrations. Turbulence and sounding observations from December 8–25, 2019, of three sites, Tuonan, Baoding, and Renqiu stations in the North China Plain were selected. Mean PM2.5 mass fluxes during the intensive observational period of three stations were negative. The spatial distribution of PM2.5 mass flux of three stations showed no obvious tendency. Then, the fact that PM2.5 mass concentrations satisfied the Monin–Obukhov similarity were reconfirmed by examining the relationship between the normalized standard deviation of PM2.5 mass concentrations and stability factor ζ. Thus, the universal functions in the three stations were achieved. The time series and profiles of KC in the three stations were also shown. There was a good inverse correlation between KC and PM2.5 mass concentration which suggested that the influence of turbulent diffusion is remarkably important during observational time even the emission, deposition, secondary transformation can all affect the change of mass concentrations of PM2.5 in the ABL. Changes in KC obviously presented diurnal characteristics. The comparisons of KC and KM and KH suggested that the strength of turbulent PM2.5 mass flux exchange could be weaker or stronger than the strength of turbulent momentum and heat flux exchange at different stations. The magnitude relationship between KC and KH could not be completely determined, so there were limitations in using KH to replace directly KC in the existing numerical weather or climate models. Finally, the spatial distribution of KC at the three stations presented almost symmetrical characteristics from east to west (Tuonan to Renqiu); that is, Baoding always had the lowest KC, and Tuonan and Renqiu stations had higher KCs. The spatial distribution of KC at the three stations corresponded well with that of PM2.5 mass concentrations, and Baoding always had the largest PM2.5 mass concentrations.

Regular flow emergence at inclined surface in a stratified turbulent medium

The authors focus on the following effect: near an inclined surface in a temperature (density) stratified turbulent medium in a gravity field, a regular flow along the slope should appear. This is due to the existence of a region of weakened turbulent exchange near the solid surface, in other words, to the appearance of spatial inhomogeneities of the effective coefficient of turbulent heat transfer. In this case, horizontal components of the gradients of temperature, density and, consequently, hydrostatic pressure arise near an inclined surface. This, in turn, it leads to the emergence of an average (non-turbulent) slope current. The mentioned problem is just an example of a much wider range of phenomena – stratified flows in the gravity field, arising due to the horizontal inhomogeneity of the transfer coefficients. In conclusion, another example of such flow is given.

A convective analytical model in turbulent boundary layer on a flat plate based on the unifying heat flux formula

The two-dimensional (2D) convective heat fluxes are formulated for quasi-steady incompressible turbulent thermal boundary layer flow over a flat plate based on the unifying heat-flux formula developed previously. It is indicated that the total turbulent convection heat flux is the combination of three heat transport mechanisms: conduction due to random molecular motion, laminar advection due to time-averaged motion of fluid bulk and turbulent advection due to fluctuations of velocity and temperature. The interdependent relationship between two heat flux components in different directions is obtained for the quasi-steady turbulent boundary layer flow, which is proved to be equivalent to the turbulent differential and integral energy equations with constant physical properties, respectively. The turbulent thermal boundary layer is divided into laminar sublayer and turbulent layer, in which the linear and one-seventh-power temperature (velocity) profiles are adopted, respectively. Considering the different thicknesses of turbulent thermal and velocity boundary layers, the explicit analytical expression of convective turbulent heat transfer coefficient, as well as the simplified analytical expressions of boundary layer thickness ratio, is proposed based on the total turbulent convection heat transfer structure. The suggested analytical turbulent convective heat transfer coefficients (or Stanton numbers) for air and water are validated by comparing with those of previous theories and experimental measurements. Relevant key characteristics and physical insights of the turbulent structure on the flat plates are revealed in virtue of 2D analytical convective heat fluxes proposed.