Convection Correlations Research Articles

Reevaluation of Plate-Fin Heatsink Natural Convection Correlations for Sideways and Three-Dimensional Inclinations

The common orientations of the plate-fin heat sink for natural convection cooling of electronics are vertical and upward-facing horizontal. However, depending on various use scenarios, the heat sink may be inclined, intentionally or otherwise. In our previous papers concerning this subject, the author proposed a set of correlations for plate-fin heat sinks covering all inclination angles backward and forward (pitch rotation) from the vertical position of the heat sink. The set was based on a series of computational simulations with a validated model. At the time, tilting the heat sink sideways (roll rotation) was not considered. In the present study, though, the sideways inclination of the plate-fin heat sinks is simulated using our previous model only by adjusting the direction of the gravitational acceleration vector, thus requiring no additional validation. It is determined that the previously proposed correlation is valid up to 80° sideways inclinations of the heat sink. Interesting flow structures are observed when the heat sink is tilted 90° sideways. Furthermore, it is demonstrated that the correlation surprisingly remains valid if the heat sink is simultaneously rotated in both axes (pitch and roll).

Applying a heat transfer mathematical model for the cryopreservation of rainbow trout (Oncorhynchus mykiss) sperm: How straw location over liquid nitrogen level affects freezing rate and fertilization yield

Cryopreservation of rainbow trout semen under field conditions was analyzed. Straw location over liquid nitrogen level is a crucial variable that affects freezing rate and fertilization yield due to changes in nitrogen vapor external temperature. The objectives were: to analyze cryopreservation protocols by experimentally measuring the cooling rates and fertilization yield of 0.5 ml plastic straws located in nitrogen vapor at different heights corresponding to different external temperatures; to numerically simulate the freezing process, by solving the heat transfer partial differential equations with the corresponding thermo-physical properties of the biological system and the plastic straw; to evaluate and analyze the surface heat transfer coefficient (h) during the freezing process of the straws; to introduce a new variable, the characteristic freezing time (tc), that enables comparison between protocols; this variable was defined as the elapsed period between the initial freezing temperature and a final reference temperature of −40 °C (temperature in which more than 80 % of the water is in a frozen state). The mathematical model predicted the temperature distribution inside the straw, showing a low effect of straw plastic materials (polyethylene-terephthalate glycol, polyvinyl-chloride, and polypropylene) on freezing rates. The average h value obtained from numerical simulations was 25.5 W/m2 K, close to that obtained from the analytical Nusselt correlation for natural convection. An improvement on fertilization trials was observed when the average external nitrogen temperature was −129.6 °C (temperature range: −94 to −171 °C) with an average tc of 56.8 s (ranging between 47 and 72 s). These results corresponded to a height above the level of liquid nitrogen of 2 cm. Comparison with literature reported data showed satisfactory results. Applying mathematical models in the cryobiology field achieved results that are relevant for cryopreservation activities.

Wind-tunnel experiments on cross-ventilative cooling in a generic isolated building with one heated wall: Impact of opening size

This paper presents wind-tunnel experiments of cross-ventilative cooling in a generic isolated building with an interior heated side wall. Two different sizes of openings are considered: large and small openings. Particle image velocimetry (PIV) is used to determine velocities in the vertical centerplane. Air temperatures in the vertical centerplane are measured using negative temperature coefficient (NTC) sensors. Surface temperatures on the heated wall are measured using an infrared camera. Surface heat fluxes are obtained using heat flux sensors. In both cases the indoor airflow is dominated by the jet through the openings, with higher velocities in the building with large openings. The air temperatures measured with small openings are up to 7.5 % larger than those with large openings. The surface heat fluxes are up to 20 % higher in the building with large openings. The interior convective heat transfer coefficients vary considerably across the heated wall for both opening sizes and can be very different (up to 5 times higher) from those obtained by existing internal convective heat transfer coefficient correlations. The measurement results give insight into the complexity of ventilative cooling and can be used to validate computational fluid dynamics (CFD) simulations of cross-ventilative cooling.

3D numerical simulations of mixed convective heat transfer and correlation development for a thermal manikin head

The head represents 10 % of the body's total surface area. Unprotected, it accounts for a significant portion of overall heat loss when exposed to cold conditions. This study was motivated by a need to clarify how the human head interacts with its environment in terms of heat exchange. Accurate estimations of heat transfer coefficients on the human head are essential for conducting thermal comfort and safety analyses in buildings. In this study, a thermal head resembling a real male human head is utilized to investigate heat transfer between the body and the surrounding environment. A three-dimensional computational fluid dynamics (CFD) model is proposed to simulate steady-state dry heat loss from the human head within a chamber. This model provides predictions for heat flux, temperature, and velocity distribution surrounding the head. A straightforward correlation, derived from numerical and experimental findings, is introduced to forecast the average Nusselt number for the head under combined natural and forced convection. This correlation, relying on dimensionless parameters (Grashof, Reynolds, and Prandtl numbers), offers enhanced accuracy, simplicity, and fewer terms. The predicted average Nusselt numbers from the proposed correlation for mixed convection closely match CFD and experimental results, with relative percentage differences within ±2 %, signifying excellent accuracy across a broader range of flow conditions, including temperature differences and air velocities. Additionally, the study explores the impact of head diameter on overall heat transfer.

Investigation of Surface-Catalycity Effects on Hypersonic Glide Vehicle Trajectory Optimization

The optimization of a hypersonic glide vehicle’s reachable domain is studied using different models to constrain the stagnation-point heat transfer. The vehicle is modeled as a high-lift common aero vehicle that uses bank-angle modulation for crossrange maneuvering with a leading-edge thermal protection system made of an ultra-high-temperature ceramic. A constrained nonlinear optimization problem is formulated to determine the range of feasible trajectories that satisfy aerodynamic heating and loading constraints. The optimal control profile is determined using a modified particle swarm optimization routine that employs a penalty function approach to handle path and terminal constraints. Baseline trajectories are determined using an existing convective heat-flux correlation, and the effect of surface catalycity on the optimized trajectories is investigated by applying a correction factor, derived from high-fidelity computational fluid dynamics simulations, to the heat-flux correlation. Results demonstrate a high sensitivity of the optimized trajectories to the underlying aerothermodynamics model such that accounting for surface catalycity expands the reachability by an order of magnitude.

Characterization of human extreme heat exposure using an outdoor thermal manikin

Extreme heat is a current and growing global health concern. Current heat exposure models include meteorological and human factors that dictate heat stress, comfort, and risk of illness. However, radiation models simplify the human body to a cylinder, while convection ones provide conflicting predictions. To address these issues, we introduce a new method to characterize human exposure to extreme heat with unprecedented detail. We measure heat loads on 35 body surface zones using an outdoor thermal manikin (“ANDI”) alongside an ultrasonic anemometer array and integral radiation measurements (IRM). We show that regardless of body orientation, IRM and ANDI agree even under high solar conditions. Further, body parts can be treated as cylinders, even in highly turbulent flow. This geometry-rooted insight yields a whole-body convection correlation that resolves prior conflicts and is valid for diverse indoor and outdoor wind flows. Results will inform decision-making around heat protection, adaptation, and mitigation.

Experimental correlation of natural convection in low Rayleigh atmospheres for vertical plates and comparison between CFD and lumped parameter analysis

This paper offers a comprehensive exploration of thermal analysis for space systems operating in low Rayleigh atmospheres, with a primary focus on enhancing the accuracy and reliability of convective heat transfer modeling. The study centers around an analysis of a vertical heated plate experiment, where a lumped parameter model is employed to encompass conductive, radiative, and convective heat transfer mechanisms. To advance the accuracy of convective heat transfer coefficient calculations, this paper introduces a novel approach involving the utilization of Nusselt number correlations. These correlations are developed through an analytical solution derived from the Navier-Stokes equations, tailored specifically for the internal natural convection problem. This approach treats convection as a heat exchange process between the heated plate and the surrounding air, thereby improving the precision of modeling internal convection within a lumped parameter framework. A specific correlation (González-Bárcena et al.) is obtained for the proposed problem, derived from experimental tests conducted in a thermal vacuum chamber, under varying pressure conditions to control the Rayleigh number. Additionally, the findings are validated using Computational Fluid Dynamics (CFD) tools to calculate the velocity and temperature fields within the cavity. The González-Bárcena et al. correlation significantly enhances temperature predictions, demonstrating an improvement of up to 10∘C when compared to conventional literature correlations. The methodology presented in this paper holds promise for extension to more complex experiments in low Rayleigh atmospheres, including those conducted in the Earth's stratosphere or on the Martian surface, thereby contributing to the advancement of thermal analysis in challenging space environments.

Experimental correlation for external forced convection in non-standardized finned tubes perpendicular to the flow

Experimental correlation for external forced convection in non-standardized finned tubes perpendicular to the flow

Droplet supercooling in marine icing tests

Droplet supercooling in marine icing tests is studied theoretically using established correlations for convection and evaporation. The effect of freestream turbulence on heat and mass transfer is included through an empirical modification to the Nusselt and Sherwood numbers. Droplets are shown to cool following a modified exponential decay, with the trajectory length and shape determined by a thermal mixing length and a cooling exponent. The space needed for supercooling is shown to increase with (droplet diameter)1.8, and also depend on wind speed, injection speed and ambient temperature. Turbulence at realistic offshore levels shortens cooling distances by up to 50%. A reanalysis shows that previous marine icing tests have typically reached supercooling higher than 80% of cooling potential for small droplets up to 100–200 μm, and possibly up to 300–400 μm in long setups at low wind speeds if boosted by turbulence or a contracting tunnel; larger droplets have been significantly undercooled compared to field conditions.

New pressure drop and heat transfer correlations for turbulent forced convection in internally channeled tube heat exchanger ducts

In our previous paper, a novel heat exchanger concept, the so-called internally channeled tube (ICT) was suggested, based on a tubular geometry fitted with specially designed curved channels along the tube length. The enhanced heat transfer in the ICT results from extended surface area between two contacting fluids. To facilitate industrial application, ICT design methods must be developed. This work provides new equations for thermo-hydraulic characterization of ICT under turbulent flow conditions. In particular, new friction factor and Nusselt number correlations are derived based on the validated CFD simulations performed over a wide range of Reynolds numbers and geometrical parameters.

Numerical Investigation of Heat Production in the Two-Wheeler Electric Vehicle Battery via Torque Load Variation Test

Experimental studies were conducted to investigate the effect of varying torque loads on the temperature distribution on the surface of lithium-ion batteries (72 volts–20 Ah) in real commercial two-wheeler electric vehicles as part of our previous research. An electric vehicle engine was installed in a dyno testing laboratory and used as the main load for the battery. Ambient temperature and relative humidity were controlled using an air conditioning system. The test results are presented as surface temperature distributions on each side of the battery at various torque loads. The highest temperature on the battery’s surface was found to be approximately 40 °C at a torque load of 100%. Unfortunately, the heat generated by the battery during testing could not be measured for further research. This paper presents a numerical study of battery heat generation at 100% torque load using Ansys Fluent 2020 R1©. This tool is employed to calculate the heat flux from the battery surface to the ambient air. The CFD tool was initially validated against available experimental data and commonly used correlations for natural convection along a vertically heated wall. Good agreements between the current predictions and experimental data were observed for laminar flow regimes. Convective heat transfer between the battery surface and ambient air was simulated. The results indicate that the commonly used heat transfer correlation for vertical plates accurately predicts the heat transfer rate on the battery surface, and it was found that the heat generation rate is 1199 W/m3.

Optical and thermal investigation of hyperbolic cavity receiver with secondary reflector for solar parabolic dish collector

A hyperbolic-shaped cavity-type receiver with a second stage reflection for a 40 m2 solar parabolic dish concentrator (PDC) is presented in this paper,along with optical and thermal modeling. The receiver geometry and the secondary reflector complete the hyperbolic geometrical shape of the present receiver. This study aims to estimate heat losses owing to natural convection and radiation under influential parameters associated with solar parabolic dish system. Optical modeling has been performed with verified model using ASAP® 2013 V1R1. The optical simulations have been carried out for varying receiver height (h1), height of the secondary (h2) and diameter-to-total height ratios (d/h) of 0.5, 1, and 1.5 while keeping the diameter of the plane aperture of the receiver (d) constant. The optimum receiver geometry has been selected based on the performance in terms of optical efficiency. The maximum efficiency found is 91.72% for h1 = 0.75 m and d/h = 0.5 for the mounting distance of 4.21 m. The optimized shape is further studied to determine how the receiver absorptivity and the secondary reflector's reflectivity affect the optical performance. The absorptivity and reflectivity range from 0.86 to 0.94. Obtained optimum receiver geometry from the optical investigation is further analyzed to estimate the heat transfer rate. The thermal modeling is performed for 0°, 30°, 60°, and 90° orientations of the receiver in ANSYS Fluent 2020 R1. A comprehensive comparison among the available models has been reported and validated with well-established experimental data. This work has developed free convective Nusselt number correlation. It can be a valuable addition to the existing literature.

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.

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.

Experimental comparison and numerical study of flow and heat transfer characteristics of the pipe rows in heat pipe heat exchanger

Lube oil cooling is a very important heat transfer process on board, and the use of liquid-liquid heat pipe heat exchangers (HPHE) is easier to maintain and save energy, and does not have the risk of leakage. In this work, the heat transfer and flow in the heat pipe row of liquid-liquid HPHE is analyzed. The numerical model of HPHE based on the thermal resistance network of heat pipe is constructed and verified with the actual experimental data, and its maximum deviation is 8.1%. Results show that increasing the working fluid temperature in the evaporative section improved the operating performance of the heat pipe inside the HPHE, with the maximum equivalent thermal conductivity reaching 7112 W·m−1·K−1 at 70 °C. Furthermore, increasing the hot fluid flow rate improved the heat transfer rate of the HPHE more than increasing the cold fluid inlet flow rate. The convective heat transfer performance equations were fitted to the HPHE, with reliable accuracy within 5% obtained for both the forced convection correlations in the condensing and evaporating sections. The pipe row effect was observed to have some variability, with the periodic variation of the heat transfer coefficient per pipe row being more pronounced. The heat transfer coefficient of the pipe row at the outlet decreased by 15.5%, and the heat transfer coefficient of the pipe row at the baffle gap was also about 15% lower than that of the middle pipe row.

Transient heat transfer and temperatures in closed compressor rotors

During transient gas turbine operating cycles, the radial clearance between the rotating blades and the stationary casing is governed by the thermal stresses and radial growth of the compressor discs. Robust and accurate prediction of the temperature and heat transfer inside compressor cavities is critical to controlling these clearances and the design of reliable and efficient engines. This paper presents a fully predictive model to determine disc temperatures and shroud heat fluxes for a closed disc cavity (rotating cylindrical annulus), simulating an engine compressor. This is the first published reduced-order modelling of compressor cavities during engine transients in literature and the most detailed publication of transient experimental data in this context. Due to the conjugate nature of the heat transfer, a conduction model of the compressor disc and a model of the flow and heat transfer in the cavity between the co-rotating discs are included. The conduction was computed using a two-dimensional finite element solver, and the disc heat transfer was calculated assuming conductive laminar Ekman layers on the disc surfaces. Correlations for free convection on flat plates are used to model the heat transfer on the inner and outer radii of the rotating cavity. The transient core temperatures were calculated in a quasi-steady manner, with the heat transfer at every time step predicted assuming zero net heat flow. The model was validated using new transient data collected from the Compressor Cavity Rig at the University of Bath. The model shows consistent agreement with all experimental cases, providing insight into the conjugate relationship between the disc and shroud heat transfer, revealing that disc heat transfer is sustained long after there is no convective heat transfer from the shroud. This approach has direct application to practical thermo-mechanical codes, contributing to the design of next-generation, net-zero aerospace architectures.

Impact of human body shape on forced convection heat transfer

Predicting human thermal comfort and safety requires quantitative knowledge of the convective heat transfer between the body and its surrounding. So far, convective heat transfer coefficient correlations have been based only upon measurements or simulations of the average body shape of an adult. To address this knowledge gap, here we quantify the impact of adult human body shape on forced convection. To do this, we generated fifty three-dimensional human body meshes covering 1st to 99th percentile variation in height and body mass index (BMI) of the USA adult population. We developed a coupled turbulent flow and convective heat transfer simulation and benchmarked it in the 0.5 to 2.5m·s-1 air speed range against prior literature. We computed the overall heat transfer coefficients, hoverall, for the manikins for representative airflow with 2m·s-1 uniform speed and 5% turbulence intensity. We found that hoverall varied only between 19.9 and 23.2 W·m-2K-1. Within this small range, the height of the manikins had negligible impact while an increase in the BMI led to a nearly linear decrease of the hoverall. Evaluation of the local coefficients revealed that those also nearly linearly decreased with BMI, which correlated to an inversely proportional local area (i.e., cross-sectional dimension) increase. Since even the most considerable difference that exists between 1st and 99th percentile BMI manikins is less than 15% of hoverall of the average manikin, it can be concluded that the impact of the human body shape on the convective heat transfer is minor.

Numerical investigation on forced, natural, and mixed convective heat transfer of n-decane in laminar flow at supercritical pressures

The present study numerically investigates the forced, natural, and mixed convective heat transfer characteristics of supercritical n-decane in a tube in laminar flow, focusing on the law of mutual coupling of forced and natural convection in mixed convection. Effects of heat flux (100 W/m2–8000 W/m2) and flow direction on heat transfer are investigated. For forced convection, deterioration occurs when the wall temperature reaches the pseudo-critical temperature and the local Nusselt number decreases by up to 17.4% compared to the theoretical value at the heat flux of 2400 W/m2. For natural convection, heat transfer is continuously enhanced with the increase of heat flux. For mixed convection in upward flow, heat transfer is enhanced by the buoyancy of increasing the fluid velocity gradient near the wall. As for the downward flow, buoyancy illustrates the opposite effects. Based on numerical simulation results, the Nusselt number correlations are proposed for forced and natural convection respectively and the correlation for mixed convection is modeled employing a function of the forced and natural convection.

On the use of natural and forced convection correlations in predictive CFD simulations of liquid pool fires

This paper presents a detailed analysis of predictive numerical simulations of liquid pool fires, i.e., a 1 m – diameter methanol pool, a 0.7 m × 0.8 m ethanol pool, and a 0.18 m – diameter heptane pool. The burning rate is predicted using the ‘film’ model, including empirical correlations for heat and mass transfer. Although the forced convection approach (used in Fire Dynamics Simulator, FDS 6.7.5) yields relatively good results in fuel evaporation rate, it is somewhat questionable from a fundamental standpoint for quiescent burning conditions. Therefore, the natural convection approach is implemented in FDS 6.7.5. The predicted burning rates are similar to the forced convection approach, but the fuel surface temperature is closer to the boiling point by the natural convection approach. Based on the extensive analysis for the methanol pool fire, a modified natural convection correlation is proposed. The latter is tested for the ethanol test with satisfactory results for the peak Heat Release Rate (HRR), burning time, and surface temperature (closer to the boiling point). The modified natural convection approach is further tested for the heptane pool fire. Improved predictions are obtained for the peak burning rate, the transient stage, and the surface temperature.

Advancing OHL Rating Calculations: Modeling Mixed-Convective Cooling and Conductor Geometry

The existing standard current-temperature calculations for overhead line (OHL) conductors have been adequate for conventional conductors and their operating temperatures. However, these calculations make assumptions and include simplifications about conductor geometry and aero-thermal-dynamics, introducing an error in the High-Temperature Low-Sag conductors operating temperatures. To quantify the error introduced by the shape of strands, the paper employs a Multi-Physics Finite Element Modeling approach that calculates the conjugate heat transfer for trapezoidal stranded OHL conductors. Furthermore, it proposes corrective equations to improve the accuracy of existing methods. The equations incorporate a new Nusselt number correlation for mixed convection and capture the surface area ignored by current calculations. The outer conductor geometry assumptions and the combined natural and forced convective cooling omission in the IEEE and CIGRE methods introduce an error at low (below 0.12 m/s) cross-flow wind speeds suggesting an underestimation of conductor temperature by up to 4%. In medium wind speeds, typically at 0.5 m/s–0.61 m/s, the standard methods overestimate the conductor temperature limiting its current-carrying capability. A 5% uprating for existing OHLs is potentially feasible, particularly for the trapezoidal stranded conductors, when removing the assumptions made in existing methods.