Heat Transfer Correlations Research Articles

Heat transfer and friction correlations for offset strip fins relative to the offset ratio

Heat transfer and friction correlations for offset strip fins relative to the offset ratio

Experimental and numerical investigations on thermal-hydraulic characteristics of supercritical CO2 flows in printed circuit heat exchangers

In the supercritical CO2 (SCO2) Brayton cycle, the pre-cooler is employed to cool SCO2 to be near the pseudo-critical point state to minimise compression work and achieve high cycle efficiency. The dramatic variation in thermophysical properties of SCO2 makes heat transfer and flow very complex in the pre-cooler, bringing a lot of difficulty to the design of the related components and system. This study attempts to address this issue. The experiment and simulation are carried out to analyse the influences of mass flux, inlet temperature, and pressure on the thermal-hydraulic characteristics of SCO2 flows in a straight-channel printed circuit heat exchanger (PCHE) employed as a pre-cooler, and the underlying heat transfer mechanism is analysed as well. The local heat transfer coefficient (h) is higher when the phenomenon that the local temperature of SCO2 (Tf) is equal to the pseudo-critical temperature (Tpc) appears in the laminar sublayer than when this phenomenon appears in the buffer layer. The new heat transfer and flow correlations are presented, and the genetic algorithm and back-prediction (GA-BP) neural network is employed to predict the local heat transfer and flow performance. The maximum relative error between the Nusselt number (Nu) predicted by the new heat transfer correlation and Nu obtained via experiment and simulation is within ±20%. The maximum relative error between the Nu predicted by the GA-BP neural network and the Nu obtained through experiment and simulation is within ±15%. The maximum relative error between the Fanning friction factor (f) predicted by the new friction factor correlation and f obtained via experiment and simulation is within ±5%. The maximum relative error between f predicted by the GA-BP neural network and f obtained through experiment and simulation is within ±4%. The present investigations analyse the thermal-hydraulic characteristics of SCO2 in the pre-cooler prototype and could provide useful guidance for the design of pre-coolers for the SCO2 Brayton cycle.

Heat Transfer and Friction Correlations for R134a With Offset Strip Fin Surface

Single phase heat transfer analysis of R134a refrigerant (liquid phase) has been carried out using Computational Fluid Dynamics (CFD) approach for offset strip fin. Colburn j factor and Fanning friction factor are predicted for offset strip fin. The correlations are developed at Reynolds number range of 100-15000. The effect of fin geometry (fin spacing, fin height, fin thickness and lance length) on the enhanced heat transfer and pressure drops were investigated. Colburn j factor and fanning friction factor f, correlations have proposed in terms Re and geometry parameters (h/s, t/s, t/l) for liquid refrigerant R134a in the present study. Two separate correlations have proposed for the low and high Re regions i.e. Between Re of 100-1000 and Re of 1000-15000. The numerical results are validated with experimental results, results are found in good agreement with experimental results. Variation is found less than 5%.

Investigation of flow and heat transfer characteristics of supercritical argon in conical Hampson heat exchangers for a J-T cryocooler

The Hampson-type heat exchanger is critical for the rapid cooling of a conical J-T cryocooler, and its internal flow and heat transfer characteristics directly affect the performance of the conical cryocooler. The flow and heat transfer characteristics of supercritical argon are studied using a numerical model of a conical helical tube in this work. The simulated results show that supercritical argon flow in the conical helical tube is mainly influenced by the combined effect of variable thermophysical properties and the secondary flow produced by centrifugal force. The buoyancy has little impact on heat transfer. The heat transfer coefficient reaches its maximum at the pseudo-critical region. A more significant heat transfer coefficient and faster heat exchanger cooling rate can be achieved by increasing the mass flow rate and maintaining the fluid in the tube close to the pseudo-critical region. At a cone angle of 50°, the maximum total heat exchange quantity is observed. With a greater temperature drop per unit length, a stronger heat transfer effect can be achieved close to the outlet of the tube. Based on the numerical analyses, a new correlation for heat transfer is proposed.

Experimental study on cooling heat transfer performance of supercritical CO2 in zigzag printed circuit heat exchanger

The zigzag printed circuit heat exchanger (PCHE) is promising as the precooler in the application of supercritical CO2 (S-CO2) Brayton cycle. In this study, the experimental investigation is conducted to explore the heat transfer performance of supercritical CO2 in the mini channels of zigzag PCHE. The experimental range of pressure, temperature and mass flux is 7.5–9.0MPa, 50–90°C and 300–600kg/(m2·s), respectively. The structural parameters of diameter, pitch, and bend angle are D=2.0mm, Lp = 7.24mm and θ = 40°, respectively. The effects of system pressure, inlet temperature, and mass flux on the heat transfer performance of supercritical CO2 are investigated by measuring multiple temperature points along the zigzag channel. The results show that the heat transfer coefficient exhibits a higher level near the pseudocritical region due to the dramatic thermophysical properties variation of supercritical CO2. Meanwhile, both the change of mass flux and pressure have a significant influence on the S-CO2 heat transfer coefficient, while the effect of inlet temperature is relatively small. Furthermore, the comparison is conducted between the existing heat transfer correlations and the experimental results. Four new cooling heat transfer correlations are proposed and compared by considering the effect of velocity change and cross-sectional thermophysical property variation on heat transfer performance. It is found that adding variates to the correlation can improve the prediction accuracy of the results while iterative calculation becomes more difficult. In order to improve the robustness and prediction accuracy, it is determined to choose the correlation without the density form, which predict 91.5% of the experimental data within ±25% error band.

Heat transfer and friction factor correlation for inclined spherical ball roughened solar air heater

Heat transfer and friction factor correlation for inclined spherical ball roughened solar air heater

Condensation heat transfer and correlation analysis in helical tube of mixed carbon-hydro refrigerant

The heat transfer coefficient of the mixed carbon-hydrogen refrigerant (hmix) in a helically tube has been confirmed as the core parameter related to natural gas liquefaction. Moreover, an experimental system of the two-phase flow in the helical pipe was designed, and a simulation model was built to analyze the changing law of hmix. The effects of operating parameters (operating pressure (2–4 MP), mass flux (200–600 kg/(m2·s), and vapor quality (0–1)) and structural parameters (spiral diameter (1–3 m), helix angle (4–14°), and inner diameter (8–12 mm)) on hmix of methane/ethane/propane in the spiral tube were examined. Subsequently, 11 heat transfer correlations were analyzed and then compared. As indicated by the comparison results, the correlations of Boyko were the most accurate among the above-mentioned correlations, laying a basis for this type of hmix. Furthermore, the mean absolute relative deviation and determination coefficient of Boyko's correlation were obtained as 20.30% and 0.48, respectively.

Heat transfer correlations and pressure drop dynamics of palm fibre wetting media for evaporative cooling at different air flow rates

The thermal and flow resistance properties of wetting pads play a key role in how effective direct evaporative cooling (DEC) systems Perform. To make an informed decision, it's crucial to study the heat transfer properties and airflow resistance manifested in pressure drop for various types of wetting media. An experimental study was conducted to determine pressure drop and heat transfer correlation constants at three airflow rates for palm fruit mesocarp fibres (PFMF) wetting media. Heat transfer and pressure drop equations were fitted with generated data to obtain correlation constants. The wetting media were effective to lower the ambient temperature at an average depression of 6.6 to 8.2 °C and increase the relative humidity of the inlet air at an average value of 25.54 to 39.32%. PFMF had a low-pressure drop per unit length, ranging from 5.29 to 7.62 Pa/m, which makes it an appealing alternative to other wetting media. New correlation constants generated for pressure drop and heat transfer data fit well with high coefficient of determination (R2) values. The average cooling efficiency ranged from 56.43 to 65.27%, while the average Merkel number was 0.16 to 0.19. The Nusselt number increased with the Reynolds number and showed a laminar flow. Amaranths stored in DEC produced respiratory heat ranging from 290.86 to 336.53 mg/kg/h for all air velocities. Considering the respiratory rate within the range of cooler temperatures, it is recommended to use the DEC only for short periods or for pre-cooling of vegetable storage.

Toward Improved Correlations for Mixed Convection in the Downcomer of Molten Salt Reactors

Developing heat transfer correlations for buoyancy-driven flows and mixed convection is challenging, especially if the fluid’s Prandtl (Pr) number is not close to 1. For advanced nuclear reactor (Generation IV) designs, the downcomer plays a crucial role in normal operation and loss-of-power scenarios. The fluid-flow behavior in the downcomer can involve forced, mixed, or natural convection. Characterizing the heat transfer for these changing regimes is a serious challenge, especially in the heat transfer deterioration region. In this paper, the downcomer is simplified to heated parallel plates. The high–Pr number fluid FLiBe (a mixture of lithium fluoride and beryllium fluoride) is considered for all simulations. Direct numerical simulations using the graphics processing unit–based spectral element code NekRS are performed for a wide range of the Richardson number, from 0 to 400, at two different FLiBe Pr numbers (12 and 24). This results in an unprecedented 74 cases in total. Each case’s Nusselt number is calculated to evaluate existing heat transfer correlations. Moreover, we propose several new modifications for cases without satisfactory choice. As a result, several novel mixed-convection heat transfer correlations have been built for high–Pr number fluids. The correlations are expressed as a function of the buoyancy number, covering several mixed-convection regimes. The Pr number effect on the Nusselt number behavior is also analyzed in detail. We also propose a novel method to evaluate the heat transfer deterioration region. Modified Reynolds-Gnielinski forced-convection correlations are defined for the laminarization region, and a free-convection correlation is used for the natural-convection-dominated region. These correlations can describe well the trend in the heat transfer–deficient region.

Evaluation of heat transfer correlations based on input parameters in a solar parabolic trough collector using supercritical carbon dioxide

Concentrating Solar Power (CSP) technologies have emerged as leaders in generating renewable power. Parabolic trough collector (PTC) is the most widely used CSP technology for various applications of solar thermal heat at commercial level. Altering the heat transfer fluid (HTF) to supercritical CO2 (s-CO2) holds promise in improving the efficiency and operations of solar PTC. The present study discusses heat transfer correlations from literature for the horizontal flow in smooth tubes. The correlations have been evaluated for their suitability to predict the average Nusselt numbers by s-CO2 as the HTF in a solar PTC. Nusselt Numbers computed using these correlations have been compared with the validated numerical simulation. Utilizing a previously validated non-uniform solar heat flux as input for the three-dimensional finite volume method, the numerical thermal simulations were performed These correlations have been compared for the operating boundary range of the solar PTC. The impact of each thermophysical input parameter of HTF is outlined in the study. Additionally, a novel correlation is proposed based on the multiple regression of thermophysical input properties of the s-CO2 as HTF in the solar PTC. The proposed correlation based on input parameters has very high prediction accuracy. It can simplify the design analysis of the solar PTC field for the s-CO2.

Development of a New Heat Transfer Correlation for Flow of Supercritical Steam in Spiral Tubes Under Deteriorated Heat Transfer Regime

Abstract Heat transfer to supercritical steam flowing inside spiral tube under deteriorated heat transfer regime is investigated in this work using three-dimensional numerical simulations. The numerical solver is first validated with experimental results and subsequently multiple simulation cases are formulated with spiral tube by varying the flow and thermal conditions. The wall temperature and heat transfer coefficient of spiral tubes are compared with the same of straight tubes. Over the parameters range considered, the heat transfer coefficient is improved by 88% when straight tube is replaced with spiral tube, for similar flow and thermal conditions. Most significantly, the deteriorated heat transfer regime, which is otherwise witnessed in straight tubes is completely avoided by using spiral tubes, for the similar flow conditions. Tangential velocity, which arise due to centrifugal force is the primary reason of enhanced heat transfer in spiral tubes. Three standard heat transfer correlations are tested for spiral geometry under deteriorated heat transfer regime and it is found that none of those can predict the heat transfer coefficient accurately. Using the simulation results along with Buckingham π-theorem, a new correlation for heat transfer coefficient is proposed for spiral tubes carrying supercritical steam and operating under deteriorated heat transfer regime. The new correlation can predict the wall temperature and heat transfer coefficient accurately. The correlation has an error band of ±25%.

Three-dimensional numerical simulations on Poiseuille-Rayleigh-Bénard convection of air in a horizontal rectangular channel

In order to reveal the combined influences of Rayleigh (Ra) number, Reynolds (Re) number and spanwise aspect ratio (B) on the flow pattern evolution and stability, and heat transfer of Poiseuille-Rayleigh-Bénard (PRB) convection, we presented a set of three-dimensional numerical simulations on PRB convection of air in the horizontal channels using commercial software Fluent in a range of 2 ≤ B ≤ 10, 0 ≤ Re ≤ 250 and 1.7 × 103 ≤ Ra ≤ 2.5 × 104. Various flow patterns are observed, including transversal rolls, longitudinal rolls, mixed rolls and wavy flow. The results show that the number of longitudinal rolls depends on B and Ra. The critical Rayleigh numbers for appearance and destabilization of the longitudinal rolls and the transversal rolls increase with increasing Re. With increasing B, the critical Rayleigh numbers for the primary and secondary instabilities will decrease and the critical Reynolds number also decreases. The heat transfer of PRB convection is enhanced with increasing Ra and B. A heat transfer correlation of the average Nusselt number with Ra and B is established.

Thermal-hydraulic performance of super-amphiphobic louver-fin flat-tube heat exchanger under fouled condition

Surface treatment significantly influences the performance of heat exchangers under condensation or sublimation conditions. This study experimentally investigated the thermal-hydraulic performance of the louver-fin flat-tube heat exchanger with super-amphiphobic treatment, under clean and fouled conditions, subject to the air-side Reynolds number of 40–390 and the relative humidity of 30–80 %. The results show that the coating can enhance total heat transfer by 16.5 % under fouled conditions and by 3.1 % under clean conditions, and slightly rise pressure drop under both conditions in general. Compared to the uncoated one, the super-amphiphobic heat exchanger has a better comprehensive thermal-hydraulic performance (j/f 1/3) by 25.3 % under fouled conditions, while it has an almost identical j/f 1/3 (0.3 % higher) under clean conditions. Moreover, the heat transfer and pressure drop correlations are developed. This research would provide a feasible approach to heat exchanger improvement under unfavorable circumstances.

Experimental study on convective heat transfer of S–CO2 under high heat flux

Since the S–CO2 power cycle is of great significance for energy development, in which the design of various vital components involves the heat transfer of S–CO2 at different temperatures and pressures, many researchers have conducted experimental research on the convective heat transfer characteristics of S–CO2. However, as the existing studies primarily focused on low heat flux conditions, there are some gaps in the high heat flux experimental data. In this study, by building an experimental facility, the heat transfer characteristics of S–CO2 in the range of heat flux from 500 kW/m2 to 1000 kW/m2 were studied, and the heat transfer correlation under high heat flux was fitted based on the experimental data. The results have revealed that the heat transfer of S–CO2 under high heat flux differs from that of low heat flux, and the existing empirical correlations have more significant errors under high heat flux. The newly proposed heat transfer correlation has the highest calculation accuracy, which calculates 94% of experimental data within ±30% error. It can meet the actual engineering needs.

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.

Dynamic regulation of the thermal performance of the S–CO2 minichannel using a piezoelectric oscillating fin

It is difficult to alter the thermal performance of a minichannel heat sink with a fixed structure under constant operating conditions. In particular, if the local heat transfer of the substrate cannot be regulated in real time, the dynamic heat dissipation needs of high-power electronic components cannot be met in the electrical servo systems of flight vehicles. In this paper, a new minichannel heat sink structure based on the classical rectangular channel is proposed and a piezoelectric oscillating fin (POF) is introduced to replace the fixed fin. The thermal performance of the heat sink can then be regulated using the swing of the POF, with supercritical carbon dioxide (S–CO2) as the coolant. Transient numerical simulations are applied to investigate the influence of various POF operating parameters on the heat transfer of the channel, such as the oscillation amplitude and frequency. The results demonstrate that a channel with a POF can allow for dynamic and rapid adjustment of the thermal performance through control of the oscillation frequency and amplitude of the POF, with a constant channel configuration, coolant, and operating conditions. The heat transfer can be enhanced significantly by the swing of the POF, with the local Nusselt number growing up to 8.3 times and the overall one up to 1.14 times. Both the oscillation frequency and amplitude have a positive correlation with the intensity of heat transfer. The POF also contributes to a greater pressure drop and fluctuation in pumping power. A comprehensive evaluation coefficient shows that the POF is effective at improving the overall thermal performance with a low-frequency swing, while high-frequency operation enhances the local heat transfer and decreases the local temperature near the tail end of the POF. Finally, considering the effects of the frequency and amplitude of the POF, as well as the variable thermophysical properties of the supercritical coolant, a heat transfer correlation based on the Dittus–Boelter equation is established to predict the thermal performance of the channel with a POF. This prediction has a maximum error of ±0.56%.

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.

Heat transfer evaluation of liquid lead-bismuth eutectic cross flow tube bundle: Experimental part

Helical coil once-through tube steam generator (HCOTSG) is an excellent form of heat exchanger. HCOTSG is adopted in various industries, such as Lead-bismuth Fast Reactor (LFR). The flow and heat transfer in the shell side of HCOTSG are important for its design and optimization. It is of great significance to carry out relevant experiments to obtain empirical correlations. In this paper, experimental study on the lead-bismuth eutectic (LBE) cross flow around the tube bundle is carried out to investigate the thermal-hydraulic characteristics based on geometric approximation of local region. Three test sections with different inclination angles of 0°, 4°, 8° are adopted in the experiments with Peclect number (Pe) up to 350. The experimental sections are uniformly heated with heat flux ranging from 20 to 100 kW/m2. The heat transfer characteristic of LBE cross flow around inclined tube bundle is obtained, considering the effects of inclination angle of the test section. The heat transfer correlation of LBE cross flow around inclined tube bundle is proposed for the first time. By comparing the data of the experiments, the results are all within the error range of 10%. The correlation is appropriate for the program development of LBE HCOTSG. This study can provide essential experimental data for the design and code development of LBE HCOTSG.

Numerical study on the heat transfer characteristics of a microchannel heat exchanger with liquid lead–bismuth eutectic and supercritical CO2 as working fluids

The Lead-cooled Fast Reactor (LFR) is a promising option for fourth-generation nuclear energy systems, with the supercritical carbon dioxide (sCO2) Brayton cycle being the preferred power cycle for future nuclear energy systems. Lead-bismuth eutectic (LBE) is a more suitable reactor coolant than lead due to its lower melting point. High-efficiency microchannel heat exchanger (MCHE) may be an ideal choice for the intermediate heat exchanger (IHX) in liquid lead–bismuth fast reactors. To prevent the channels of MCHE from being blocked by liquid LBE, a new structure of MCHE is proposed, in which the liquid LBE flow channel has a large equivalent diameter and corresponds to two sCO2 microchannels. In this study, the heat transfer characteristics of conventional and new structures of MCHE were investigated using numerical simulation. The results indicate that the temperature change at the inlet of the liquid LBE channel enhances the heat transfer of both liquid LBE and sCO2. Under constant temperature and pressure, the velocity of sCO2 has a significant effect on the convective heat transfer of sCO2, but has little effect on liquid LBE. Based on the reliability of equipment operation, this study recommends the use of the heat exchanger form in case 5. Compared with case 3, altering the velocity of liquid LBE results in a 7.1–8.3% increase in the convective heat transfer coefficient of liquid LBE, and a ∼38% increase in the convective heat transfer coefficient of sCO2. Similarly, changing the velocity of sCO2 leads to a 6.1–7.5% increase in the convective heat transfer coefficient of liquid LBE, and a 32.8–38.0% increase in the convective heat transfer coefficient of sCO2. For sCO2 heat transfer calculation, Yoon's heat transfer correlation is recommended, while Kirillov's heat transfer correlation is suggested for liquid LBE heat transfer calculation. The deviation between numerical calculation results and correlations is less than 18.1% and 12.7%, respectively.

Control-oriented modeling of a LiBr/H[formula omitted]O absorption heat pumping device and experimental validation

Absorption heat pumping devices (AHPDs, comprising absorption heat pumps and chillers) are devices that use thermal energy instead of electricity to generate heating and cooling, thereby facilitating the use of waste heat and renewable energy sources such as solar or geothermal energy. Despite this benefit, widespread use of AHPDs is still limited. One reason for this is partly unsatisfactory control performance under varying operating conditions, which can result in poor modulation and part load capability. A promising approach to tackle this issue is using dynamic, model-based control strategies, whose effectiveness, however, strongly depend on the model being used. This paper therefore focuses on the derivation of a viable dynamic model to be used for such model-based control strategies for AHPDs such as state feedback or model-predictive control. The derived model is experimentally validated, showing good modeling accuracy. Its modeling accuracy is also compared to alternative model versions, that contain other heat transfer correlations, as a benchmark. Although the derived model is mathematically simple, it does have the structure of a nonlinear differential–algebraic system of equations. To obtain an even simpler model structure, linearization at an operating point is discussed to derive a model in linear state space representation. The experimental validation shows that the linear model does have slightly worse steady-state accuracy, but that the dynamic accuracy seems to be almost unaffected by the linearization. The presented new modeling approach is considered suitable to be used as a basis for the design of advanced, model-based control strategies, ultimately aiming to improve the modulation and part load capability of AHPDs.