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Thermal energy storage (TES) devices use phase change materials (PCMs) to store and release thermal energy. Control-oriented models are needed to predict the behavior of TES devices and experimental validation is necessary to demonstrate the predictive capabilities of these models. This paper presents an experimental validation of a switched moving boundary (MB) approach for modeling TES devices, where the dynamics of the device are captured with fewer states than traditional models. A graph-based modeling approach is used to model heat flow, while the moving boundary captures the time-varying liquid and solid regions of the TES. The model uses a finite state machine (FSM) to switch between four modes of operation based on the state-of-charge (SOC) of the TES. Results show that the switched MB approach has similar accuracy and lower computational cost compared to traditional modeling approaches when predicting the SOC of an experimental TES device. [ABSTRACT FROM AUTHOR]

This investigation is devoted to analyze the buoyancy-driven flow behavior and associated thermal dissipation rate in a nanofluid-filled annular region with five different single source-sink and three different dual source-sink arrangements along the vertical surfaces. The remaining region on the vertical boundaries and horizontal surfaces are kept adiabatic. Numerical simulations have been performed by employing the finite difference method. To analyze the impacts of different nanofluids, nanoparticle volume fraction, Rayleigh number, size, and arrangement of sources and sinks, the results are graphically represented through streamline and isotherm contours, thermal profiles, average Nusselt number, and cup-mixing temperature. The results showed that identifying an optimum location and length of source-sink with a proper selection of other control parameters can lead to enhanced thermal transport and thermal mixing in the enclosure. In particular, middle-middle thermally active location and placing source-sink separately on the vertical walls lead to the production of maximum heat transport compared to other single and dual source-sink arrangements, respectively. Also, among the two nanofluids considered in the current investigation, larger enhancement in thermal transport has been achieved for Cu-water nanofluid. The calculated enhancement ratio of the heat dissipation rate enhances with an increment in nanoparticle concentration. [ABSTRACT FROM AUTHOR]

The Borexino detector at Gran Sasso National Laboratories (INFN) has obtained extraordinary achievements for solar neutrino and geoneutrino physics during its lifetime. More recently, Borexino has provided the first experimental evidence of the subdominant CNO solar neutrino flux, thanks to an outstanding low background level obtained by means of intense purification campaigns and a continuous improvement of the detector thermal stabilization over the years. In particular, this impressive thermal steadiness has led to a progressive mitigation of the internal convective currents which are responsible for the continuous background contamination of the detector sensitive inner volume. To this purpose, numerical analyses are essential to better comprehend the detector fluid dynamics, the background behavior, and are also important to propose effective countermeasures to further reduce natural convection inside the detector. In this framework, the present work investigates the flow characteristics of the liquid scintillator by means of computational fluid dynamics analyses. In particular, a full 3D model of the Borexino inner vessel is considered in the simulations, addressing the complex nature of the natural convective currents under consideration both in transient and stationary conditions. The calculated flow pattern has been adopted to predict the transport behavior of 210Po, that is fundamental for the independent constraint of 210Bi, the main background constituent affecting CNO measurement. The convection-diffusion analysis demonstrates the applicability of the adopted methodology showing a good agreement between calculation and experimental data. [ABSTRACT FROM AUTHOR]

An analysis of natural convection in horizontal slots has been carried out. It is demonstrated that a proper combination of heating and groove patterns can create a net horizontal fluid movement, which we refer to as the horizontal chimney effect. Groove shapes that can be easily manufactured as well as heating patterns that can be easily created using heating wires were considered. It has been shown that both patterns must be properly tuned. The direction of the net horizontal flow can be changed by changing the relative positions of the patterns. Changes of groove geometry can change the flow rate by up to 100%. Simultaneous use of grooves and heating at both plates can nearly double the system effectiveness. The strength of the flow increases with reduction of the Prandtl number. [ABSTRACT FROM AUTHOR]

A numerical investigation is performed to analyze air's steady natural convection phenomena in an enclosure with partial active sidewalls. A partition is attached to the hot wall for different active locations to study the effect of the partition position on the heat transfer. First, a finite volume method solves the coupled equations of continuity, momentum, and energy. The SIMPLE algorithm is used to solve the pressure velocities coupling iteratively. Second, based on the obtained dimensionless velocity and temperature values, the distributions of the local entropy generation due to heat transfer and fluid friction and the total entropy generation are determined for different parameters. The results are presented graphically in streamlines, isotherms, and average Nusselt numbers. Three different configurations of active region arrangement are considered in this study, while the partition length has been changed. In order to identify the optimum location of the partition for better heat transfer, the effect of entropy generation has been studied. The heat transfer rate decreases with the increased partition length, especially for l = L/2. Thus, the maximum average Nusselt number occurs for the middle-middle arrangement, while the minimum one occurs for the bottom-bottom arrangement. The numerical investigations in this analysis are made over a wide range of parameters, Rayleigh number 10³ to 105, dimensionless partitions length (l = L/8, L/4, L/2), and irreversibility coefficients 10-4< ϕ < 10-2; however, the Prandtl numbers was fixed to 0.71. [ABSTRACT FROM AUTHOR]

This paper presents the results of a numerical simulation for the natural convection inside an enclosure that has an inner open square at its center. The inner square is open at the top and connected to the ceiling of the enclosure. The open inner square distorts the convection patterns, slows down the flow, and provides a compartment to confine the fluid at the core of the enclosure. Ultimately, this lowers the local Nusselt number, Nu, along the hot wall, and reduces the heat flux through the enclosure. The analysis shows the effects of changing the dimensions of the inner square on the heat flux through the enclosure for a range of Rayleigh numbers-from 103 to 106. Short-sided inner squares work as flow deflectors while long-sided inner squares provide compartments to accommodate new flow circulation at the core of the enclosure. The inner square is most effective when the length of its sides equals the width of the stagnant core inside the empty enclosure at the same Rayleigh number, and the heat flux at this condition is the lowest. Inner squares made of thermally conducting materials can reduce the heat flux through the enclosure by 70%, while adiabatic inner squares can reduce the heat flux by 90%. Inner squares reduce the external heat load on buildings when fitted inside the holes of hollow bricks used in building facades. The external heat flux can be lowered by 30%-55% depending on the material of the inner square and outer side temperature. [ABSTRACT FROM AUTHOR]

The heat transfer effect of a sectioned wall made of five volumes filled with a phase change material (PCM) coupled to an air cavity is presented. The analysis system was equipped with a heat source next to the sectioned wall and an opposite isothermal wall. The experimental study was carried out by measuring the temperature of the five PCM volumes, likewise in four profiles along the air cavity. For the numerical formulation of the phase change of the PCM wall, the enthalpy method was used. With the validated model, the temperature fields, velocity contours, liquid fraction contours, and heat transfer coefficients are presented and discussed. The comparison between the numerical model and the experimental data presented a general average percentage difference in the range of 3.8-7% for the temperature of the air profiles, while for the PCM was 0.9-3.2%. The numerical results showed that the amount of liquid PCM in the enclosure can be reduced by dividing the wall into segments. Additionally, the heat transfer mechanism of conduction was noted between PCM volumes due to the union of these. [ABSTRACT FROM AUTHOR]

An experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers (⁠1.18≤Ra≤242⁠). Both the experiments and the SPH calculations were performed for positive (-0.1≤ΔT≤10 K) and negative (-10≤ΔT≤-0.1 K) temperature differences between the source and the surrounding fluid. In all cases, a pair of steady, counter-rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for ΔT>0 and a vertically descending flow just below the source for ΔT<0⁠. The maximum flow velocities always occur within the ascending/descending plumes. The SPH predictions are found to match the experimental observations acceptably well with root-mean-square errors (RMSE) in the velocity profiles of the order of ∼10-5 m s-1. The fact that the SPH method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach. [ABSTRACT FROM AUTHOR]

Three-dimensional continuity, momentum, and energy equations have been solved around a perforated vertical hollow cylinder to predict the buoyancy-induced flow field and the temperature distribution around it. Finite volume method (FVM) has been implemented for the discretization of the underlying governing equations. Second-order upwind scheme has been adopted to discretize the convective terms in the momentum and energy equation. Results have been obtained by varying the input parameters like hole diameter to cylinder length ratio (d/L), pitch to length ratio (P/L), angular pitch (?), cylinder length to diameter ratio (L/D), and Rayleigh number (Ra) spanning from 0.005 to 0.08, 0.1 to 0.3333, 30?deg to 180?deg, 2 to 20, and 104 to 108, respectively. It has been found that the average surface Nusselt number (Nu) for the outer surface increases with the diameter of the hole for Ra of 106, however for Ra of 108, it marginally decreases up to d/L of 0.01 and then increases. Nu for the inner surface increases when d/L is more than 0.04 for all Ra. The cylinder with the staggered holes shows a slightly higher Nu compared to the inline holes. Nu for the inner and outer surface at a lower pitch is less than that of the higher pitch when d/L is less than 0.02 for all Ra. The heat transfer rate of the perforated cylinder is more than the nonperforated cylinder for all the cases when L/D is less than 10 and Ra less than 106. However, for Ra more than 106, the perforated cylinder always loses more heat compared to the nonperforated one for all L/D. Finally, the correlation for Nu has been proposed as a function of the pertinent input parameters for future reference in the academic as well as industrial practices. [ABSTRACT FROM AUTHOR]

The influence of the thermophysical variable properties on the buoyancy-driven flows of liquid sodium and gallium established in a cylindrical cavity is numerically investigated, for the entire range of Rayleigh number corresponding to practical applications. Axisymmetric turbulent simulations (initially steady) are obtained, considering appropriate boundary and reference conditions for simulating the emergency cooling of a nuclear reactor. The results obtained for different heating intensities are analyzed and compared. In the case of sodium, the expected decay in the heat transfer coefficients is less relevant than that previously obtained for airflows. In turn, strong differences in the gallium thermal behavior are encountered. In fact, a trend opposite to that of sodium is detected for wide ranges of Rayleigh number and heating parameter. Additional transient simulations are carried out to complete a comparative assessment of the performance of both liquid sodium and gallium as cooling agents. [ABSTRACT FROM AUTHOR]

In this paper, the details of a numerical study performed for the optimum fin arrangement in a solar air heater with a rectangular fin array attached to the bottom side of the absorber plate have been presented. Results have been presented for various fin sizes and spacing between the fins, while the heat transfer and fluid flow are directed by natural convection. An inclined rectangular channel similar to the dimensions of a typical solar air heater has been considered. Three different fin configurations, namely, continuous long fins for the whole length of the channel, in-line interrupted and staggered interrupted arrangements of fins, have been studied. The present analysis aims to identify the optimum configuration of the fin array for enhanced heat transfer. The spacing between the fins and the height of the fins are varied to obtain an optimum configuration. The numerical simulations are performed for heat flux (q") ranging from 250 to 750 W/m² on the absorber plate. The inclination angles of the channel (θ) have been maintained at 15 deg, 30 deg, and 45 deg from the horizontal plane. The results show that with the spacing between fins, S = 5.4 cm performs better in the case of longitudinal continuous fin arrangement. However, a fin spacing of 4.75 cm shows a higher heat transfer in the case of staggered fin configuration. In comparison with nine long uninterrupted fins, using the staggered arrangement with 15 × 10 fins saves up to 33% of fin material. [ABSTRACT FROM AUTHOR]

In this study, natural convection of non-Newtonian power-law fluids around an array of elliptic cylinders has been investigated numerically. The governing equations have been solved using an in-house computational fluid dynamics code based on the well-known finite volume method. It is assumed that the flow and temperature fields are laminar, steady, and two-dimensional. Furthermore, due to the low-temperature difference between the tube walls and the surrounding fluid, the changes in the physical properties of the fluids are neglected. The numerical results are validated against the available experimental and numerical results. The results show that by increasing the non-Newtonian fluid power-law index, the ratio of average Nusselt number of the ith cylinder to the average Nusselt number of a single cylinder under identical thermal conditions decreases. Moreover, it is found that the increase in the ratio of the distance between elliptic centers and the elliptic vertical diameter increases the ratio of the average Nusselt number of ith cylinder to the average Nusselt number for a single cylinder. Finally, a mathematical expression is given for the array averaged Nusselt number. [ABSTRACT FROM AUTHOR]

Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, "Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium," Int. J. Heat Fluid Flow, 19(6), pp. 629-635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed. [ABSTRACT FROM AUTHOR]

Mixed convection heat transfer characteristics from heat source located symmetrically inside square enclosure and cooled by Al2O3/water-based nanofluid flow was experimentally investigated. The configuration was subjected to high levels of natural convection and low rates of nanofluid flow. The nanofluid thermophysical properties were characterized using the available correlations in the literatures except the viscosity which was measured and correlated in terms of the nanoparticles loading ratios. Comparative analysis indicated that the application of nanofluid could not guarantee heat transfer enhancement in configurations dominated by natural convection. Exception heat transfer enhancement was only found when very low nanoparticles loading ratio was applied. Instead, heat transfer degradation was found especially in the cases of highest nanoparticles loading ratios. Alternatively, heat transfer enhancement was observed when the forced convection effect was substantial at the highest nanofluid flow rate. The present conclusions were justified and correlated to the findings reported in the literature. [ABSTRACT FROM AUTHOR]

Toward accelerated latent heat storage, the unconstrained melting heat transfer in spherical capsules was revisited experimentally in the presence of nano-enhanced phase-change materials (NePCMs), with an emphasis on the influence of capsule size on the rates of melting, heat transfer, and latent heat storage. It was shown that increasing the size of the spherical capsule leads to two competing effects, i.e., thicker molten layer in the close-contact melting (CCM) region and stronger natural convection. However, the NePCM with a high loading (3wt % graphite nanoplatelets (GNPs)) is not preferred for all capsule sizes as a result of the significantly deteriorated heat transfer in both CCM and natural convection, because the dramatic viscosity growth at such a high loading leads to increased thermal resistance across the molten layer and loss of natural convection that overweigh the increased thermal conductivity. The 1wt % NePCM sample was exhibited to be able to facilitate latent heat storage for two cases, i.e., in the smallest capsule having a radius of 14.92mm at a higher wall superheat of 30°C and in the intermedium 24.85mm capsule at a lower wall superheat of only 10°C. It was suggested that a relatively low loading of a specific NePCM can cause a faster rate of latent heat storage over the baseline case of the matrix phase-change material (PCM), if the capsule size (and the wall superheat) can be adjusted properly to regulate the molten layer thickness and the intensity of natural convection. [ABSTRACT FROM AUTHOR]

In this study, free convection in a cavity with differentially heated wavy walls is numerically investigated in the presence of a magnetic source. Polyharmonic spline radial basis function (RBF) is utilized to discretize the governing dimensionless equations formulated by stream function-vorticity. The effects of dimensionless Hartmann number, Rayleigh number, the number of undulations, amplitude of wave, and the location of magnetic source are visualized in streamlines and isotherms as well as calculating average Nusselt number through the heated wall. Results show that primary vortex in streamlines is altered with the impact of magnetic source. The augmentation of undulations and amplitude causes convective heat transfer to decrease if Ra = 105. The impact of location of magnetic source is noted close to the top wall. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer from horizontal solid cylinders has been studied numerically by varying the Rayleigh number in the range of (104≤Ra≤108) and (1010≤Ra≤1013) for both laminar and turbulent flows, respectively. The computations were carried out for three different geometries of three, six, and ten cylinders in a stack arranged in a triangular manner having same characteristic length scale. The present numerical investigation on natural convention is able to capture a very interesting flow pattern and temperature field over the stack of horizontal cylinders which has never been reported in the literature so far. Visualization of plume structure over the horizontal cylinders has also been obtained pictorially in the present work. From the numerical results, it has been observed that the total heat transfer is marginally higher for three-cylinder stack in the laminar range. In contrast, for turbulent flow, starting from Ra = 1010, heat transfer for six-cylinder case is higher but when Ra exceeds 5 × 1011, heat transfer for ten cylinders stack is marginally higher. The average surface Nusselt number is higher for the stack of three cylinders compared to six- and ten-cylinder cases for all range of Ra in both laminar and turbulent regimes. A correlation for the average Nusselt number has also been developed as a function of Rayleigh number which may be useful for researchers and industrial purposes. [ABSTRACT FROM AUTHOR]

Conjugate laminar natural convection heat transfer and air flow with radiation of tube solar receiver with glass window were numerically investigated. The discrete ordinate method was used to solve the radiative transfer equation. And the three-dimensional steady-state continuity, Navier-Stokes, and energy equations were solved. The temperature difference based on environment and high temperature surface of receiver is varied from 100 K to 1000 K. The influence of the surface emissivity, heating temperature, convective coefficient, and convective temperature of environment on the heat transfer from the receiver with glass window has also been investigated. The numerical results indicated that the highest temperature of glass window increases and the high temperature area becomes wide, with the temperature of heating wall and surface emissivity increasing. Adopting higher convective coefficient of glass window can reduce the peak magnitude of temperature distribution on glass window of tube receiver up to 45%. [ABSTRACT FROM AUTHOR]

The steady-periodic natural convection phenomenon inside a heated enclosure filled with disconnected, discrete solid blocks, and under horizontal, time-periodic heating is investigated numerically. This configuration is akin to several practical engineering applications, such as oven baking in food processing, heat treating of metal parts in materials processing, and storage and transportation of discrete solid goods in containerization. Because of the relative large size, and limited number of solid bodies placed inside the enclosure, the solid and fluid constituents are viewed separately and the process modeled using continuum balance equations for each with suitable compatibility conditions imposed at their interfaces. The periodic heating is driven by a sinusoidal in time hot-wall temperature, while maintaining the cold wall temperature constant, with top and bottom surfaces adiabatic. Results are presented in terms of hot and cold wall-averaged Nusselt numbers, time-varying energy capacity of the enclosure, and periodic isotherms and streamlines, for Ra varying from 10³ to 107, Pr equal to 1, and 36 uniformly distributed, conducting and disconnected solid square blocks. The results explain why and how the effect of varying Ra on the convection process is significantly affected by the presence of the solid blocks. An analytical equation, valid for time-periodic heating, is proposed for anticipating the block interference effect with great accuracy, substantiating the distinct features of Nusselt versus Rayleigh observed when the blocks are present inside the enclosure. [ABSTRACT FROM AUTHOR]

A computational study of natural convection from biheaters of finite thickness and finite conductivity placed on a finite thickness and a finite conductive bottom plate of a cavity is performed under constant heat input condition. Cavity is cooled by the sidewalls, while the top and backside of the bottom plate are insulated. Streamline, isotherms, and local heat flux distribution of the sidewalls are discussed. Base Grashof number is chosen as 2.5×106. Biheater maintains a nondimensional distance of 0.4 between them. The left heater is placed at a nondimensional distance of 0.2 from the left wall. Heater length ratio is varied from 0.4 to 1.7, while heater strength ratio is varied from 0.25 to 7.0. Optimum operating temperature condition is found from the analysis. [ABSTRACT FROM AUTHOR]

A new lattice Boltzmann (LB) model to solve the phase change problem, which is based on the enthalpy-transforming model has been developed in this paper. The problems of two-region phase change, natural convection of air, and phase change by convection are solved to verify the present LB model. In two-region phase change, the results of the present LB model agree well with that of analytical solution. The benchmark solutions are applied to evaluate the present LB model in natural convection of air and phase change material (PCM) as well. The results show that the present LB model is able to simulate the temperature distribution and capture the location of solid-liquid interface in the cavity accurately. Moreover, the present LB model is effective in computing owing to the fact that no iterations are necessary during the simulations. [ABSTRACT FROM AUTHOR]

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs. [ABSTRACT FROM AUTHOR]

The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid-porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall. [ABSTRACT FROM AUTHOR]

Natural convection during solidification of liquids is known to impact the freezing characteristics and also lead to defect formation. In this study, we report the findings of real-time interferometric observation of bottom-cooled solidification of pure water in a cubical cavity. The results show first quantitative evidence of full-field thermal history during solidification, clearly depicting the anomalous expansion of water below 4 °C. Furthermore, based on the strength of natural convection, characterized by the Rayleigh number, we identify and report four distinct regimes of solidification, namely--conduction dominated, early convection, front instability, and sustained convection. A critical Rayleigh number that initiates instability in the solidifying front has been proposed, which is significantly different from conventional calculations of Rayleigh number relating to the initiation of flow. The study shows full-field quantitative evidence of a well-known phenomenon and provides a further understanding of flow driven nonhomogeneities in the solidifying interfaces. [ABSTRACT FROM AUTHOR]

Natural convection of a water-based nanofluid in a partially open triangular cavity with a local heat source of constant temperature under the effect of Brownian diffusion and thermophoresis has been analyzed numerically. Governing equations formulated in dimensionless stream function and vorticity variables on the basis of two-phase nanofluid model with corresponding initial and boundary conditions have been solved by finite difference method. Detailed study of the effect of Rayleigh number, buoyancy-ratio parameter, and local heater location on fluid flow and heat transfer has been carried out. It has been revealed that an increase in the buoyancy force magnitude leads to homogenization of nanoparticles distribution inside the cavity. A growth of a distance between the heater and the cavity corner illustrates the heat transfer enhancement. [ABSTRACT FROM AUTHOR]

A liquid fluoride salt experiment has been constructed and used to acquire natural convection heat transfer data. The experiment used FLiNaK salt in a small cell that included a cylindrical electrical heater, 1.27 cm in diameter, oriented vertically in a FLiNaK bath. Thermocouples internal to the heater were used, along with FLiNaK temperature measurements and heater power measurements, to determine natural circulation heat transfer coefficients. These data were acquired for Rayleigh numbers ranging from 3 × 105 to 8 × 109 and salt temperatures from 560 °C to 640 °C. Test results show that measured heat transfer coefficients are consistent with conventional natural convection heat transfer coefficients for cylinders, but the average error can be as high as 20% using these correlations. Correlations developed by fitting the data for this experiment show much lower errors (<10%). [ABSTRACT FROM AUTHOR]

This study proposes an empirical correlation for laminar natural convection applicable to external circular finned-tube heat exchangers with wide range of configuration parameters. The transient temperature response of the heat exchangers was used to obtain the heat transfer coefficient, and the experimental data with their characteristic lengths are discussed. The data lie in the range from 1 to 1000 for Rayleigh numbers based on the fin spacing: the ratio of fin height to tube diameter ranges from 0.1 to 0.9, and the ratio of fin pitch to height ranges from 0.13 to 2.6. Sixteen sets of finned-tube electroplated with nickel-chrome were tested. The convective heat transfer coefficients on the heat exchangers were measured by elimination of the thermal radiation effect from the heat exchanger surfaces. The Nusselt number was correlated with a newly suggested composite curve formula, which converges to the quarter power of the Rayleigh number for a single cylinder case. The proposed characteristic length for the Rayleigh number is the fin pitch while that for the Nusselt number is mean flow length, defined as half the perimeter of the mean radial position inside the flow region bounded by the tube surface and two adjacent fins. The flow is regarded as laminar, which covers heat exchangers from a single horizontal cylinder to infinite parallel disks. Consequently, the result of curve fitting for the experimental data shows the reasonable physical interpretation as well as the good quantitative agreement with the correction factors. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer from an array of horizontal rectangular fins on a vertical flat plate in non-Newtonian power-law fluids has been studied. The underlying physical principles affecting heat transfer were studied using comprehensive solutions obtained from numerical investigations. Heat transfer to the power-law fluid was found to depend on the fluid rheology (power-law index) and significantly on the geometric parameters (interfin spacing, fin length) as well. The dependence was quantified using the Nusselt number (Nu) and fin effectiveness (Q/Q0). The present study shows that compared to a fin analyzed in isolation, the spatial arrangement of multiple fins relative to one another in an array does have a significant effect on the flow field around subsequent fins in power-law fluids. Therefore, the average heat transfer coefficient of the natural convection system is affected significantly. The variation of Nu with the dimensionless fin length (l/L), dimensionless interfin spacing (S/L), and fluid power-law index (n) was plotted. The dependence was found to be counter intuitive to expectations based on studies for natural convection from vertical flat plates to power-law fluids. In the present study involving fins, shear-thinning fluids (n < 1) show a decrease in heat transfer and shear-thickening fluids (n > 1) show an enhancement in heat transfer for higher l/L values. The results of the study may be useful in the design of natural convection systems that employ power-law fluids to enhance or control heat transfer. [ABSTRACT FROM AUTHOR]

In this study, a new coupled surface shape design (SSD) methodology named direct design method is presented for the solution of problems containing different types of convection heat transfer in which a specific distribution of either heat flux or temperature is given instead of the shape of a boundary. In the proposed method, the governing equation, without using any mathematical transformation for the physical domains, is manipulated so that the grid generation, solving fluid flow, and heat transfer as well as shape updating can all be carried out simultaneously. Five different inverse shape design problems containing different types of convection heat transfer are solved by the proposed method. All the problems are also solved using the ball-spine algorithm (BSA), which is a recently developed de-coupled algorithm, for the sake of comparison. In all problems, the effects of using different under-relaxation parameters are investigated and the capability of both approaches is compared with each other. The results show that the proposed coupled method can solve the problems better than the BSA in the sense that the direct design method converges sooner than the BSA when the same under-relaxation parameter is used for both methods. Also, it is shown that the computational cost of solving a SSD problem using the direct design method is slightly greater than solving an analysis problem. [ABSTRACT FROM AUTHOR]

Turbine flexible operations with faster startups/shutdowns are required to accommodate emerging renewable power generations. A major challenge in transient thermal design and analysis is the time scale disparity. For natural cooling, the physical process is typically in hours, but on the other hand, the time-step sizes typically usable tend to be very small (subseconds) due to the numerical stability requirement for natural convection as often observed. An issue of interest is: What time-step sizes can and should be used in terms of stability as well as accuracy? In this work, the impact of flow temporal gradient and its modeling is examined in relation to numerical stability and modeling accuracy for transient natural convection. A source term-based dual-timing formulation is adopted, which is shown to be numerically stable for very large time-steps. Furthermore, a loosely coupled procedure is developed to combine this enhanced flow solver with a solid conduction solver for solving unsteady conjugate heat transfer (CHT) problems for transient natural convection. This allows very large computational time-steps to be used without any stability issues, and thus enables to assess the impact of using different time-step sizes entirely in terms of a temporal accuracy requirement. Computational case studies demonstrate that the present method can be run stably with a markedly shortened computational time compared to the baseline solver. The method is also shown to be more accurate than the commonly adopted quasi-steady flow model when unsteady effects are non-negligible. [ABSTRACT FROM AUTHOR]

The effects of nonuniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal nonequilibrium (LTNE) model are studied numerically using the finite difference method (FDM). The finite-thickness horizontal wall of the cavity is heated either uniformly or nonuniformly, and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height, and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted-average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer. [ABSTRACT FROM AUTHOR]

Presented here are the results of an experimental investigation of two ultrathin miniature loop heat pipes (mLHPs) with different internal wicking structures: one with a primary wicking structure in the evaporator and a secondary wicking structure in the liquid line, and the other only with the same primary wicking structure in the evaporator, but no secondary wick. The systematic experimental investigation was conducted using natural convection as the cooling mechanism in order to study the heat transfer performance of the two mLHPs and fully examine the effects of the secondary wick. The results indicated that both of the test articles could effectively dissipate 12 W at all test orientations with a minimum total thermal resistances of 6.38 °C/W and 6.39 °C/W, respectively. However, the results indicated that the presence of the secondary wicking structure in the liquid line at low power loads resulted in more stable startup characteristics and a weaker dependence on the different orientations. Moreover, it was demonstrated that the steady-state evaporator temperatures of the test article with the secondary wicking structure in the liquid line were much lower than those observed for a 1-mm thick copper plate with the same geometric dimensions for all heat loads in the horizontal orientation, showing a higher thermal performance. [ABSTRACT FROM AUTHOR]

The freezing of water around immersed unfinned and finned horizontal tubes is simulated numerically. The impact of natural convection as well as the water density inversion with temperature is considered. The equations governing both fluid flow and heat transfer around the tubes and through the solid-liquid interface are solved using finite difference schemes. To follow the moving solid-liquid boundary, dynamic grid generation is performed using the elliptic partial differential equation method with iterative interpolating smoothing to avoid divergence. For validation, the present results for unfinned tubes are compared with experimental studies reported in the literature. The present numerical simulations are aimed at improving our understanding of the parameters affecting the freezing process around both finned and unfinned tubes. The results showed that the flow patterns are similar in both tube configurations with one main vortex in the liquid region when there is no inversion in the water density. The presence of fins complicates the distribution of local Nusselt number along the solid-liquid interface in comparison with the unfinned tube. The impact of natural convection on the rate of ice formation is limited to the initial period of the freezing process. The results also show the freezing enhancement when utilizing fins. An accumulated ice mass correlation is developed for each tube configuration. This model can be used to optimize the design of both finned and unfinned tubes in energy storage systems, which are viable tools for air conditioning load shifting and leveling. [ABSTRACT FROM AUTHOR]

Natural convection is an important heat transfer mode for flexible operations of gas turbines and steam turbines. Its prediction presents considerable challenges. The strong interdependence between fluid and solid parts points to the need for coupled fluid-solid conjugate heat transfer (CHT) methods. The fundamental fluid-solid time scale disparity is further compounded by the long-time scales of practical turbine flexible operations. In addition, if a high-fidelity flow model (e.g., large eddy simulation (LES)) is adopted to resolve turbulence fluctuations, extra mesh dependency on solid domain mesh may arise. In this work, understanding of the extra solid mesh dependency in a directly coupled LES based CHT procedure is gained by an interface response analysis, leading to a simple and clear characterization of erroneously predicted unsteady interface temperatures and heat fluxes. A loosely coupled unsteady CHT procedure based on a multiscale methodology for solving problems with large time scale disparity is subsequently developed. A particular emphasis of this work is on efficient and accurate transient CHT solutions in conjunction with the turbulence eddy resolved modeling (LES) for natural convection. A two-scale flow decomposition associated with a corresponding time-step split is adopted. The resultant triple-timing formation of the flow equations can be solved efficiently for the fluid-solid coupled system with disparate time scales. The problem statement, analysis, and the solution methods will be presented with case studies to underline the issues of interest and to demonstrate the validity and effectiveness of the proposed methodology and implemented procedure. [ABSTRACT FROM AUTHOR]

Entropy generation due to natural convection has been computed for a wide range of Rayleigh numbers based on fin spacing, RaS in the entire laminar range 5≤RaS≤108, and diameter ratio 2≤D/d≤5 for an isothermal horizontal cylinder fitted with vertical annular fins. Entropy generation in the tube-fin system is predominantly due to heat transfer rather than fluid friction. The results demonstrate that the degree of irreversibility is higher in the case of the finned configuration when compared with the unfinned one. With the deployment of a merit function combining the first and second laws of thermodynamics, we have tried to show the thermodynamic performance of finned cylinder with natural convection. So, we have defined the ratio (I/Q)finned/(I/Q)unfinned which gets its minimum value at optimum fin spacing where heat transfer is maximum. A detailed view of the entropy generation around the finned cylinder has been shown for various S/d (fin spacing to tube diameter ratio) at a particular D/d (fin to tube diameter ratio) and Rayleigh number, which explains the nature and reason of entropy production. [ABSTRACT FROM AUTHOR]

Thermal analysis of fluid flow is always regarded as an important research issue within cavities in order to become familiar with the characteristics of fluid flow phenomenon in enclosures. This research paper investigates the fluid and heat transfer analysis of fluid flow inside a triangular cavity using natural element methodology (NEM). This Galerkin-based methodology has been introduced for a decade and almost demonstrated its efficiency in the numerical heat transfer analysis of problems in most engineering sciences. The fluid flow contains natural convection along with conduction and radiation heat transfer with medium's walls, which have absorbing, emitting, semitransparent, and nonscattering characteristics. The final results investigate the effects of radiative and natural convection heat transfer on the fluid flow pattern as expressed in Rayleigh number, stream function, strength of natural convection regime, etc., which are checked with other similar studies presented in the literature and shows how promising NEM can be as an efficient numerical approach to improve computational precision when dealing with fluid mechanic problems. [ABSTRACT FROM AUTHOR]

This paper provides an experimental and numerical investigation of natural convection in a square cavity. The square cavity is full of air (Pr = 0.71) and contains four heat sources of height hw, positioned symmetrically on the vertical walls of the cavity with a fifth heat source of height hB, located in the center of the bottom cavity wall. Two configurations are analyzed for Rayleigh numbers ranging from 1.00 x 104 to 1.00 x 105: configuration 1 has four cold sources located on the vertical cavity wall and configuration 2 has two hot and two cold sources located on the vertical cavity walls. An analysis of the holographic interferograms, numerical isotherms, streamlines, and velocity maps obtained demonstrates an increased development of natural convective heat transfer in configuration 1. [ABSTRACT FROM AUTHOR]

The classical problem of constrained melting heat transfer of a phase change material (PCM) inside a spherical capsule was revisited experimentally in the presence of nanoscale thermal conductivity fillers. The model nano-enhanced PCM (NePCM) samples were prepared by dispersing self-synthesized graphite nanosheets (GNSs) into 1-dodecanol at various loadings up to 1% by mass. The melting experiments were carried out using an indirect method by measuring the instantaneous volume expansion upon melting. The data analysis was performed based on the homogeneous, single-component assumption for NePCM with modified thermophysical properties. It was shown that the introduction of nanofillers increases the effective thermal conductivity of NePCM, in accompaniment with an undesirable rise in viscosity. The dramatic viscosity growth, up to over 1 OO-fold at the highest loading, deteriorates significantly the intensity of natural convection, which was identified as the dominant mode of heat transfer during constrained melting. The loss in natural convection was found to overweigh the decent enhancement in heat conduction, thus resulting in decelerated melting in the presence of nanofillers. Except for the case with the lowest heating boundary temperature, a monotonous slowing trend of melting was observed with increasing the loading. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive analysis of the heat transfer during the melting process of a high-temperature (>800 °C) phase-change material (PCM) encapsulated in a vertical cylindrical container. The energy contributions from radiation, natural convection, and conduction have been included in the mathematical model in order to capture most of the physics that describe and characterize the problem and quantify the role that each mechanism plays during the phase-change process. Numerical predictions based on the finite-volume method have been obtained by solving the mass, momentum, and energy conservation principles along with the enthalpy porosity method to track the liquid!solid inteiface. Experiments were conducted to obtain the temperature response of the thermal energy storage (TES) cell during the sensible heating and phase-change regions of the PCM. Continuous temperature measurements of porcelain crucibles filled with ACS grade NaCl were recorded. The temperature readings were recorded at the center of the sample and at the wall of the crucible as the samples were heated in a furnace over a temperature range of 700-850 °C. The numerical predictions have been validated by the experimental results, and the effect of the controlling parameters of the system on the melt fraction rate has been evaluated. The results showed that the natural convection is the dominant heat transfer mechanism. In all the experimental study cases, the measured temperature response captured the PCM melting trend with acceptable repeatability. The uncertainty analysis of the experimental data yielded an approximate error of ±5.81 °C. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of three-dimensional (3D) natural convection aircooling of two identical heat sources, simulating electronic components, mounted in a rectangular enclosure was carried out. The governing equations were solved by using the finite-volume method based on the SIMPLER algorithm. The effects of Rayleigh number Ra, spacing between heat sources d, and aspect ratios Ax in x-direction (horizontal) and Az in z-direction (transversal) of the enclosure on heat transfer were investigated. In steady state, when d is increased, the heat transfer is more important than when the aspect ratios Ax and Az are reduced. In oscillatory state, the critical Rayleigh numbers Racr for different values of spacing between heat sources and their aspect ratios, at which the flow becomes time dependent, were obtained. Results show a strong relation between heat transfers, buoyant flow, and boundary layer. In addition, the heat transfer is more important at the edge of each face of heat sources than at the center region. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the onset of natural convection in a horizontal fluid layer due to nonuniform internal heat generation, which is relevant to a number of geophysical situations. We investigated a number of special cases, which we believe are paradigmatic. Those include linear, quadratic, concentrated, and exponential source strength distributions. Our results show that those situations that lead to a reduction/increase in the size of the region in which the basic temperature gradient is destabilizing lead to an increase/decrease in stability. [ABSTRACT FROM AUTHOR]

The main objective of this work is to investigate the performance of the v²-f model for the predictions of turbulent natural and mixed convection flows. For this purpose, a finite volume-based flow solver is developed for a collocated grid arrangement, and the v²-f model is implemented for turbulence modeling. For natural convection flows, a tall cavity with the aspect ratio of 28.68 is selected as a test case. Mixed convection in a square cavity, ascending flow in a vertical pipe with constant wall flux, and fully developed mixed convection in a vertical channel are considered as test cases for buoyancy-driven mixed convection flows. To evaluate the performance of the v²-f model, results obtained from the present study have been compared with the existing data of experimental studies or direct numerical simulations (DNS). Results obtained from two-equation models, viz., the RNG k-ε, realizable k-ε, and SST k-ω models are also presented for comparison. Overall, the v²-f model predicts flow and heat transfer characteristics of natural and mixed convection flows satisfactorily. [ABSTRACT FROM AUTHOR]

The instability of steady natural convection of a non-Fourier fluid of the single-phase lagging (SPL) type between two vertical surfaces maintained at different temperatures is studied. SPL fluids possess a relaxation time, which reflects the delay in the response of the heat flux and the temperature gradient. The SPL model is particularly relevant to low-temperature liquids, ultrafast processes, and nanofluids (with a retardation time added in this case). Linear stability analysis is employed to obtain the critical state parameters, such as critical Grashof numbers. For intermediate Prandtl numbers (Pr=7.5), when non-Fourier level exceeds a certain value, the neutral stability curve comprises a Fourier branch and an oscillatory branch. In this case, oscillatory convection increasingly becomes the mode of preference, compared to both conduction and stationary convection. Critical Grashof number decreases for fluids with higher non-Fourier levels. [ABSTRACT FROM AUTHOR]

Analytical relations between the heat flux, temperature rise, thermal boundary layer thickness, and characteristic velocity have been derived for the two-dimensional vertical channel, without use of the Boussinesq approximation. Results have been put into the context of well-established scaling behavior in the literature. In addition, useful implications of the analytical results have been described, including a criterion to determine the suitability of a heat-sink configuration to a particular application. [ABSTRACT FROM AUTHOR]

An experimental study of the effect of eccentricity on forced convective heat transfer was conducted for upward flows in vertical, open-ended annular channels with a diameter ratio of 0.61, a length to outer diameter ratio of 18:1, and both internal surfaces heated uniformly. Flows with Reynolds numbers Re = 5450, 10,000, and 27,500 and eccentricities varying from 0 to 0.9 were examined. These results are deemed to be mostly in the forced convection regime with some possible overlap with the mixed convection regime at the lowest Reynolds number considered. This work complements our previous work on natural and mixed convection using the same facility. The effect of eccentricity was not significant at lower eccentricities, but, in highly eccentric cases, the wall temperature in the narrow gap was much higher than in the wide gap and the average heat transfer coefficient was as low as one-fifth of the concentric value. For Re > 10,000, the average Nusselt number for the concentric case was nearly four times higher than the value predicted by the Dittus-Boelter correlation. [ABSTRACT FROM AUTHOR]