Convective Heat Transfer Correlations Research Articles

Nu–Gr correlation for laminar natural convection heat transfer from a sphere submitted to a constant heat flux surface

The work numerically investigated laminar natural convection heat transfer from the single sphere with a constant heat flux surface in air over the wide range of Grashof number (10≤Gr≤107\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10 \\le Gr \\le 10^{7}$$\\end{document}). The more efficient and precise numerical method based on Bejan et al. was employed here, the accuracy of which has been confirmed through validation against a single sphere case. The heat transfer characteristics were systemically analyzed in terms of isothermal contours and streamlines around the sphere, dimensionless temperature and velocity profiles. Additionally, local Nusselt number as well as local pressure and friction drag coefficients were studied with different Grashof number. In comparison to the sphere with uniform heat flux surface, the heat transfer from the isothermal sphere was found to be enhanced attributable to a more robust buoyancy force and a steeper temperature gradient. Moreover, the average Nusselt number for the sphere with a constant heat flux between 60.4 and 98.6% of the isothermal sphere’s value, this range being contingent upon the specific Grashof number. What’s more, the proposed correlation addresses a notable void in the predictive understanding of heat transfer from the sphere with uniform heat flux, which is scenario prevalent in various engineering applications, particularly for the cooling of electrical and nuclear systems, and offer values for academic research.

1.05 MW molten salt furnace experimental investigation of full-conditional thermal energy storage for the transfer and storage of waste heat from blast furnace gas

This paper proposes the use of heat storage devices and technologies to convert the unstable heat of gas generated by the iron and steel industry into stable heat, thus realizing the controllable and stable utilization of the gas waste heat. To this end, a 1.05 MW molten salt furnace energy storage experimental system was developed, utilizing a spiral coil type molten salt furnace to heat solar salt and achieve energy transfer and storage. The study comprehensively analyzes the preheating, heating, cooling, and special working conditions of the molten salt furnace. The experimental results demonstrate that the coils can be preheated within 150 min and heats the solar salt to over 570 °C at the rated load. However, the vertical and axial directions of the coil exhibit varying degrees of thermal stress under different operating conditions. In addition, the Reynolds number and Nusselt number of the heat transfer process were calculated and the convective heat transfer correlation equation was fitted using the similarity principle to find the heat transfer efficiency of the molten salt furnace of 77.12 %. These findings are expected to address the waste blast furnace gas issue and contribute to developing a sustainable energy system in the steel industry.

CFD Analysis of Natural Convection on the Outer Surface of the Containment of APWR Model

To improve the safety of nuclear power plants, a modern NPP such as Advance Pressurize Water Reactor (APWR) is equipped with a safety feature called PCCS (Passive Containment Cooling System), where naturally circulating air cools the outer surface of the containment which is used to remove decay heat released inside the containment vessel. The decay heat from the reactor core will be transferred out through the conduction mechanism and the natural convection mechanism on the outer surface of the containment vessel. Then, the hot air that forms in the gap between the containment and its baffles will rose through the chimney located at the top of the concrete building and cold air will enter through the inlet to create a natural circulation cycle. To obtain the effectiveness of the use of baffles, as a comparison, it is necessary to analyze the natural convection heat transfer on the outer surface of a containment vessel that is not equipped with a baffle. In this research, CFD analysis of natural convection on the outer surface of the containment of APWR reactor model has been done. Based on the model developed, the analysis was done to get temperature and convection heat transfer coefficient in the air flow on the containment surface. Heat flux in the containment surface varied from 500 W/m2 to 2.000 W/m2 with an increase of 500 W/m2 intervals. Based on the analysis results, the correlation equations are also proposed in this paper, namely the correlation of natural convection heat transfer for laminar regime on a vertical cylindrical with the heat flux constant in the form Nuq = a(Raq)b.

New correlation for transient laminar natural convection heat transfer in a differentially heated square cavity between air and a PCM layer

New correlation for transient laminar natural convection heat transfer in a differentially heated square cavity between air and a PCM layer

Study on Flow and Heat Transfer in Single Rock Fractures for Geothermal Heat Extraction

A full understanding of the fluid flow and heat transfer behaviors within a single fracture is important for geothermal heat extraction. In this study, models of single fractures with varying aperture and inner surface roughness (characterized by fractal dimension) are constructed, and a compound fracture aperture (CFA) is proposed to describe the coupled effect of fracture aperture and inner surface roughness. The effect of the fluid flow Reynolds number on heat transfer was investigated as it ranged from 4.84 to 145.63. The results show that the overall heat transfer coefficient (OHTC) in a single fracture significantly increases with the rise in fluid velocity and the compound fracture aperture. Particularly, the OHTC in a single fracture with an inner surface fractal dimension of 2.09 can be up to 1.215 times that of a parallel flat fracture when the flow velocity reaches 0.18 m/s. Moreover, for a fracture with a smaller CFA, enhancing the fracture aperture plays a decisive role in increasing the OHTC. Aperture emerges as a more sensitive optimization parameter for efficient heat extraction compared to the flow velocity. Meanwhile, based on simulation results, a convective heat transfer correlation equation is derived to provide more accurate estimates of the OHTC in rock fractures with different geometries and morphological features.

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.

The effect of the wind conditions on the thermal performance of an unglazed solar thermal collector

The paper presents a theoretical analysis performed for unglazed liquid solar thermal collectors (USTCs) to demonstrate the magnitude of the thermal performance uncertainty caused by the different wind conditions under the same wind speed. The literature currently comprises more than 90 combined convection heat transfer correlations. The difference between them is primarily caused by the difference in wind characteristics during the experiment (wind turbulence level, wind direction, etc.). A detailed validated theoretical model of a USTC and forty applicable combined convection heat transfer correlations were used to perform the analysis to demonstrate the magnitude of the thermal performance uncertainty caused by the different wind conditions. It was found that, for the low operating temperature, the uncertainties caused by the different wind conditions are ± 4 %, ± 6 %, and ± 8.5 % under wind speeds of 0 m/s, 1.5 m/s, and 3 m/s, respectively. These values are relatively small compared to the obtained average thermal performance values of 78 %, 73 %, and 65 %. In contrast, the uncertainty values are significant for relatively high operation temperatures: ± 11.5 %, ± 16.5 %, and ± 22 %, while the modelled efficiency values for these operating conditions are 15 %, 30 %, and 44 %. The analysis demonstrated that the difference in wind characteristics under the same wind speed significantly affects a USTC's thermal performance. From a practical standpoint, the USTC's thermal performance in real wind conditions may exhibit significant disparities compared to its performance tested in controlled laboratory conditions under the same wind speed. Furthermore, notably varied thermal performance can be expected for identical USTCs installed in different locations under the same wind speed due to the different wind characteristics (wind turbulence level, wind direction, etc.).

Heat and mass transfer correlations of supercritical n-decane considering the influence of pyrolysis reaction by simplifying internal heat and mass sources as pseudo-wall fluxes

The convective heat and mass transfer characteristics of the supercritical pressure (SCP) fuel in the regenerative cooling channel of hypersonic vehicles are significantly affected by pyrolysis reactions. In this study, we proposed a novel method to develop the Nusselt number (Nu) and Sherwood number (Sh) correlation of SCP fuel that considers the influence of pyrolysis reaction by simplifying internal heat and mass sources as pseudo-wall fluxes based on the differential global reaction (DGR) model of pyrolysis. The convective heat and mass transfer and pyrolysis characteristics of n-decane were investigated experimentally and numerically in a vertical downward-flow heated tube at pressures of 3-7 MPa. Theoretical analysis of the experimental conditions was conducted sequentially according to the partial differential equations (PDEs) of species continuity and energy, in which the internal source terms of heat and mass due to pyrolysis reactions were simplified and predicted using the DGR model of n-decane pyrolysis. A semi-empirical Sh correlation for predicting the radial distribution of fuel conversion was proposed associated with computational fluid dynamics (CFD) data by equivalently simplifying the internal mass source as pseudo-wall mass flux. A Nu correlation for convective heat transfer was proposed using the same methodology considering the influences of pyrolysis. The correction terms consider pyrolysis endothermicity and thermophysical property variation due to the conversion differences between the pipe wall and the bulk flow. Finally, the Nu correlation was compared to the experimental data, and the influence of heat transfer deterioration (HTD) due to pyrolysis coking was also analyzed quantitatively and empirically.

Investigating the impact of modeling assumptions and closure models on the steady-state prediction of solar-driven methane steam reforming in a porous reactor

In this work, the effect of different modeling assumptions and closure models — frequently considered in the literature of solar thermochemical reactors and closely-related areas — is investigated. The application of different modeling assumptions and closure models may strongly affect the results accuracy and compromise a meaningful comparison across literature works. The following is herein investigated: (i) the role of upstream and downstream fluid regions to the two-phase reactor region; (ii) relevance of species and gas-phase thermal diffusion mechanisms; (iii) reaction heat accounted for in gas- or solid-phase energy balance equations; (iv) local thermal equilibrium (LTE) vs. local thermal non-equilibrium (LTNE) models; (v) model dimension (one-dimensional vs. two-dimensional axisymmetric models); (vi) local volumetric convection heat transfer correlations; and (vii) effective solid thermal conductivity correlations. The relevance of this work extends well beyond the current application (methane steam reforming in a volumetric solar reactor), since similar models and assumptions have also been widely applied for predicting the performance of volumetric solar absorbers and dry reforming solar reactors. The results show that an upstream fluid region should be considered while applying inlet first-type boundary conditions and diffusion transport in the corresponding governing equations to ensure full-conservation and simultaneously to account for developing profiles upstream the reactor inlet section. For the operating conditions considered, species diffusion and gas-phase heat conduction are particularly relevant at the reactor centerline but with a negligible integral effect. A significant difference in the reactor performance is observed while accounting for the reaction heat from surface reactions in the solid- or gas-phase energy balances — for the lowest inlet gas velocity herein considered, the thermochemical efficiency (methane conversion) is approximately equal to 70.8% (76.3%) and 77.3% (84.7%) assigning the reaction heat to the gas- and solid-phase energy balances, respectively. LTE model results are strikingly different from the results obtained with the LTNE model considering the reaction heat accounted for in the gas-phase energy balance but not significantly different from the results computed with the LTNE model with the reaction heat assigned to the solid-phase energy balance. One-dimensional reactor modeling provided with an average concentrated solar heat flux value results in a similar average performance as that given by a two-dimensional model but fails to predict the high temperatures observed at reactor centerline — for the lowest inlet gas velocity, the difference between the maximum solid temperatures predicted by one- and two-dimensional models is about 340K.

Correlation of Forced Convection Heat Transfer of Isothermal Plate Under Low Pressure

With the rapid development of vacuum tube transport technology, there is increased interest in understanding the behavior of the heat transfer of rarefied gas in a vacuum tube. Currently, most empirical correlations of forced convection heat transfer are conducted at the standard atmospheric pressure, so many correlations are not applicable to conditions below the atmospheric pressure. To investigate the heat transfer property under low-pressure conditions, the forced convection between isothermal plate and air in a low-pressure environment is numerically simulated. The results show that the traditional correlation of the forced convection heat transfer between the isothermal plate and gases is different from the actual results at low pressure, and the correlation is completely invalid when the pressure is lower than 0.2 kPa. Based on the data of numerical calculation, a modified correlation of forced convection heat transfer between an isothermal plate and gases under low pressure is proposed. The correlation coefficient R is greater than 0.99, and the fitting error is less than 10% at the 95% confidence level. The change of heat transfer depends on the Reynolds number in the pressure range of 0.2–100 kPa, but the effect of Reynolds number is weakened and the effect of pressure is strengthened when the pressure is below 0.2 kPa.

Convective heat transfer correlation for a single surrogate firebrand and a simplified firebrand pile on a flat plate using naphthalene sublimation in heated air flow

Previous studies have shown that most structure ignitions in wildland urban-interface fires are due to firebrand deposition and ignition. The heat transfer mechanisms involved in firebrand deposition need further study and characterization for better understanding of the firebrand ignition process. In particular, convective heat transfer correlations over a single firebrand and a pile of firebrands are lacking. Using the heat-mass transfer analogy, naphthalene sublimation experiments were conducted to determine convective heat transfer correlations for a single naphthalene cylinder (a surrogate firebrand) and an idealized three-firebrand pile resting on flat plates from mass loss measurements. These experiments were conducted in a wind tunnel using a heated (50 °C) or room temperature air flow (0.5 m/s to 2.1 m/s). There was good agreement between the Nusselt number correlation obtained using heated air and results with unheated airflows. Experiments using heated airflow reduced the experimental run times and uncertainty in mass loss measurements significantly. In general, the single firebrand had higher Nusselt numbers than the individual firebrands in the pile. In the three-firebrand pile, the firebrand at the top of the pile exhibited the highest heat transfer. The naphthalene sublimation technique can be easily extended to obtain convective heat transfer correlations for various firebrand geometries and configurations.

The Modeling of Two-way Coupled Transient Multiphase Flow and Heat Transfer during Gas Influx Management using Fiber Optic Distributed Temperature Sensing Measurements

Effective management of gas influxes during drilling for either oil-gas or geothermal wells is crucial for ensuring operational safety and minimizing non-productive times, especially for high-pressure, high-temperature (HPHT) situations. In recent years, there has been a growing demand for comprehensive modeling techniques that can accurately predict gas influx behaviors during Managed Pressure Drilling (MPD). However, many existing approaches have neglected the heat transfer processes between wellbore fluids and the surrounding formation during gas influx management, which can significantly impact the estimation accuracy.To address this issue, this paper presents an advanced transient multiphase flow and heat transfer modeling framework that integrates the solution of the energy conservation equation with the multiphase mass and momentum equations using a two-way coupled approach. A set of full-scale experimental data, including fiber-optic-based Distributed Temperature Sensing (DTS) measurements, were used to perform thorough validation and verifications of the developed modeling framework. Multiple existing heat convection correlations were benchmarked against the DTS measurements to determine the best match. The data from multi-depth downhole temperature sensors and Distributed Acoustic Sensing (DAS) were also compared to the results from numerical simulations.The estimation results of the wellbore fluids temperature profiles showed good agreement with the DTS data for both transient single-phase flow cases and gas influx management scenarios. A comparative analysis revealed that the selection of convective heat transfer correlations could significantly affect the simulation accuracy of fluid temperature distributions and gas influx behaviors. The benchmarking and optimized selection of convection correlations help to improve the performance of transient heat-transfer modeling. In addition, the two-way coupled approach shows improved accuracy compared to the decoupled methods, particularly for HPHT situations and more transient processes.

Condensation heat transfer between a vertical superhydrophobic aluminum surface and moist air under natural convection

Condensation heat transfer at superhydrophobic surfaces has raised a lot of interest due to their potential application in atmospheric water harvesting and air-conditioning. In moist air, the condensation heat transfer using a superhydrophobic surface can be negatively affected by the existence of a large amount of non-condensable gas, namely, the dry air. Besides, the air flow pattern would substantially affect the surface condensation rate due to the convective mass transfer of water vapor. In this study, the condensation regime of a superhydrophobic aluminum surface vertically positioned in quiescent moist air was visualized and the condensation rate was experimentally investigated. Condensation experiments were also performed by using hydrophobic, hydrophilic, and superhydrophilic surfaces for comparison. The condensation rate of the superhydrophobic surface was consistent with that of other surfaces, though the condensation regimes of the four surfaces were quite different. The average deviation between the experimental condensation rate and the empirical correlation of natural convection heat and mass transfer was within 12%. The result indicates that vapor transfer induced by diffusion and convection in the boundary layer rather than the heat transfer resistance associated with condensate dominates the condensation heat and mass transfer between the moist air and the superhydrophobic surface.

Determination of a heat transfer correlation for small internal combustion engines

Small internal combustion engines (ICEs) with displacements < 100 cm3 have greater surface area-to-volume ratios that promote heat transfer through the combustion chamber walls, subsequently lowering the fuel conversion efficiency. As a result, employing common heat transfer correlations developed for larger engines to estimate wall heat transfer yields inaccurate results. Therefore, it is necessary to review literature correlations and determine their applicability for small ICEs. To this end, this paper first presents a literature review highlighting the characteristic length scales, characteristic velocities, and the properties of the working fluid for ICE convective heat transfer correlations. This information is used within a zero-dimensional ICE model to determine an appropriate heat transfer expression for a relatively small two-stroke ICE (53.2 cm3). Through parameter optimization, by matching the gross indicated power over 85 experimental data points using MATLAB’s fmincon routine, the developed expression (Nu=0.449Re3/4Pr1/3) shows good confidence with respect to the power (R2 = 0.924, RMS = 0.257) and an in-cylinder pressure data trace (R2 = 0.991, RMS = 1.52). A following parametric study varying the bore-to-stroke (BtS) ratio for small engines (0.15 cm3 to 100 cm3) finds a localized choice of the BtS and ignition timing at each displacement volume based on the minimum heat transfer due to the combination of a changing surface area and heat transfer coefficient. In the future, including the effects of volumetric efficiency and tuned exhaust pipes can enhance the scope of the proposed model.

Correlation of single-phase convective heat transfer on spray cooled plain surfaces with high Prandtl number liquids

Spray cooling with transmission oils is an innovative cooling concept for electrical machines, whereby the coolant wets the end windings directly. The thermal design process of such machines requires reliable correlations of the heat transfer coefficients obtainable. Thereby, the majority of the literature only focuses on low Prandtl number coolants at ideal nozzle distances. The transferability of the existing heat transfer models to highly viscous coolants above and below the optimal nozzle distance has yet to be investigated. Therefore, the heat transfer coefficients of spray cooling on plain surfaces with aqueous glycerol solutions (model fluid) and a transmission oil of type ATF VI was investigated. The model fluid serves the purpose of covering the entire range of material properties of commercial transmission oils with only one liquid. Prandtl numbers ranging from 80 to 340 were investigated. Various cases of spray coverage were researched by varying the nozzle distance (2mm−100mm), the spray angle (20∘−80∘) and the size of the spray cooled surface (6.35×6.35mm2;12.7×12.7mm2). Regarding the case of the optimal nozzle distance, where the spray impact area just inscribes the cooled surface, the experimental data was validated with models from the literature. Large deviations of up to 450% resulted at nozzle distances above and below the optimum. Therefore, a dimensionless correlation of the heat transfer coefficient is proposed which includes all cases of spray coverage investigated, exceeding the applicability range of the existing models. The model describes the experimental data with a mean absolute percentage error of 15%.

Experimental investigation of convective heat transfer in the aircraft cabin environment at low air pressure

The heat transfer capacity of the cabin environment under low air pressure is significantly different from that under normal pressure. The existing research on the low-pressure environment of aircraft cabins has not provided a reliable convective heat transfer correlation to guide the design of the cabin thermal environment. This investigation evaluated the heat transfer in an actual aircraft cabin under different pressures. A laboratory test was designed in a cabin mockup with controllable boundary conditions for air temperature and pressure. Based on the measurement results, the quantitative effects of low pressure on the convective heat transfer coefficient (CHTC) of the heating surface were analyzed. According to the experimental results, the CHTC of the horizontal surface in natural convection increased from 3.26 W/(m2·K) to 5.10 W/(m2·K) when the heat flux increased from 100 W/m2 to 400 W/m2, and the CHTC dropped by 23–30% when the pressure dropped from 101 kPa to 61 kPa. With the same heat flux, the average CHTC value for the vertical plate was slightly lower than that for the horizontal heating plate under normal pressure, and the trend became significant as the air pressure decreased. In general, the average CHTC for forced convection was substantially higher than that for natural convection. Consequently, correlation equations for calculating natural and forced convection on horizontal and vertical plates under low air pressure were proposed, which will aid the design of the cabin thermal environment.

A thermodynamic model of integrated liquid-to-liquid thermoelectric heat pump systems

Thermoelectric (TE) heat pumps (TEHPs) are advantageous for heating and cooling in various applications because of their modularity and simple design. A TEHP system includes the TE modules with p- and n-type materials bonded to substrates, plus heat exchangers, thermal interfaces to the heat exchangers, and heat transfer fluids. Although modeling an individual TE module has been extensively studied, limited studies have reported performance at the larger system-level. Furthermore, no prior study has addressed the impact of temperature-dependent TE material properties (e.g., electric resistivity, thermal conductivity, and Seebeck coefficient) on overall heat-pump-system-level performance. This work presents a mathematical model for TEHP system performance based on Goldsmid's approach for TE material performance, “effective” TE material properties, Gnielinski's correlation for convective heat transfer, and thermal balance theory for a heat exchange network. This combined approach provides an accurate model of the liquid-to-liquid TEHP system. Three different approaches—one empirical, one based on the manufacturer's specifications, and one drawn from the literature—were then used to determine values for TE material properties. The first two methods treated properties as constants, while the last approach treated properties as surface-temperature-based functions. Finally, experimental TEHP data was used to validate the models, all with relative absolute deviations of approximately 10% when predicting heating capacity and 10%–25% when forecasting cooling capacity up to a 30 K surface temperature lift. The results demonstrated that, at the TEHP system level, the TE material properties could be treated as constants, avoiding solver iterations and reducing the performance uncertainty by up to 95%.

Experimental, numerical and theoretical study on heat transfer in paper honeycomb structure

The fabrication of most current thermal insulation materials from polymeric foams has created an unfavorable impact on the environment. With the aim of reducing the use of foam plastic, this paper focuses on honeycomb paperboard, an alternative thermal insulation material which is recyclable and cost-effective, and evaluates its heat transfer performance under different conditions. The experimental results show the effective thermal conductivity of honeycomb paperboard increases as the honeycomb height or the side length increases. This paper also establishes a novel theoretical model based on a newly developed convective heat transfer correlation to predict the effective thermal conductivity under different conditions. The model's results conform well to the experimental results, and the effect of convective heat transfer is investigated quantitatively using this model. As the vertical adiabatic boundary surfaces are replaced by honeycomb walls, the convection heat transfer strictly depends on the thermal boundary condition of the honeycomb walls and highly depends on honeycomb height and side length.

Experimental investigation on natural circulation heat transfer of supercritical CO2 in a closed loop

The natural circulation system based on supercritical CO2 has attracted attention due to its simple structure and safety compared with the forced circulation system. This work presented an experimental investigation of the heat transfer characteristics of CO2 based on natural circulation. Two heat transfer modes can also be observed in supercritical CO2 natural circulation, normal heat transfer and heat transfer deterioration. The development of heat transfer deterioration criterion and heat transfer correlation is significant for the application of supercritical CO2 natural circulation, but there are few related studies. Direct adoption of the supercritical CO2 forced convective criteria and heat transfer correlations to natural circulation introduces large deviations. By analyzing the existing research results of forced convection in supercritical CO2 and introducing new dimensionless parameters SBO and K, a deterioration criterion and a heat transfer correlation suitable for natural circulation of supercritical CO2 are developed based on experimental data. The new criterion can well distinguish the two heat transfer modes, and the new correlation improves markedly. The results can benefit engineering applications in advanced power cycles.

CFD Analysis of Convective Heat Transfer in a Vertical Square Sub-Channel for Laminar Flow Regime

The development of new practices in nuclear research reactor safety aspects and optimization of recent nuclear reactors needs knowledge on forced convective heat transfer within sub-channels formed between several nuclear fuel rods or heat exchanger tubes, not only in the fully developed regime but also in the developing regime or laminar flow regime. The main objective of this research was to find a new correlation equation for calculating the convective heat transfer coefficient in the vertical square sub-channels. Recently, a simulation study was conducted to find a new heat transfer correlation equation for calculating the convective heat transfer coefficient within a vertical square sub-channel in the developing regime or laminar flow regime for Reynolds number range 400 ≤ Re ≤ 1700. Simulations were carried out using a computational fluid dynamics (CFD) code and modeling already defined in the software. The novelty of the research lies in the analysis of the entrance effect for the sub-channel by proposing a new empirical correlation that can then be inserted into the STAT computer code. The surface temperature distribution around the tangential direction of the active cylinders shows that the implementation of active and dummy cylinders in the current study can simulate sub-channels that exist in a real nuclear reactor core. The current study shows that the flow simulated in this study is in its developing condition (entrance region). A new forced convective heat transfer correlation for the developing region in the form of Nu = 2.094(Gz)0.329 for the Graetz number range 161 ≤ Gz ≤ 2429 was obtained from the current study.