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To deal with inverse nonlinear heat transfer problems in a two-dimensional heat conduction problem, this paper presents a hybrid approach combining fuzzy logic and the extended Kalman filter (EKF). The proposed algorithm has been applied to the real-time reconstruction of the temperature field, time-varying convective heat transfer coefficient, and time-varying boundary heat flux using temperature data from a set of sensors. The effects of the covariance of the initial estimation error, the time step of data acquisition by the sensors, and the number of installed sensors on the precision and stability of the estimation results has been investigated by numerical experiments. To compare and validate the results, all these parameters were investigated using the EKF method. The results show that the adaptive fuzzy extended Kalman filter (FEKF) method for estimating temperature, convection coefficient, and heat flux at the boundaries is precise and stable. The comparison shows that the performance of the FEKF method in parameter estimation is better than the EKF method, and the highest increase in precision and stability of the results is related to the convective heat transfer coefficient. [ABSTRACT FROM AUTHOR]

In this paper, by means of the finite element method, the MHD free convection flow of non-Newtonian nanoliquid inside a halved annulus enclosure considering a constant heat flux is being applied to the straight walls has been analyzed. The enclosure is loaded with water and nanoparticles of alumina (Al 2 O 3) the combination of these tows produces a liquid that shows shear-thinning behavior. The governing parameters of this study are the Rayleigh number (103 ≤ Ra ≤ 106), inclination angle (0 ≤ α ≤ 90), power-law index (0.6 ≤ n ≤ 1) and Hartmann number (0 ≤ Ha ≤ 100). The outcomes indicate that the inclination angle of the cavity and the Hartmann number can be considered as effective control parameters at different Rayleigh numbers. While the magnetic field is applied the velocity field retarded and hence convection heat transfer and the Nusselt number diminished, and the increment of power-law index prompts the heat transfer to drop. It is shown that the power-law index and Hartmann reduces the local Nusselt number. Also, the average Bejan numbers corresponding of active parameters are discussed in this study. [ABSTRACT FROM AUTHOR]

In this paper, enhancement for convection heat transfer of turbulent flow in a solar central receiver tube with porous medium and non-uniform circumferential heat flux was numerically investigated. A new method was introduced to build different porous medium configurations in a unified grid system. Four kinds of enhanced receiver tubes (ERTs) with different porous insert configurations were modeled to optimize the performance of ERT. Furthermore, parameters including filling ratio of porous medium, thermal conductivity ratio (thermal conductivity of porous medium versus that of working fluid), porosity and Reynolds number were analyzed. The results showed that ERT partially filled with porous medium has better heat transfer performance than that fully filled with porous medium. The configuration of porous insert for optimal thermal or thermo-hydraulic performance is interactively affected by all the parameters discussed in this paper. The thermal conductivity ratio is the most crucial parameter to the thermal or thermo-hydraulic performance of ERT. The value of thermal conductivity ratio should be greater than 100 to obtain a good thermo-hydraulic performance. The ERTs with horizontal cylindrical segment shaped porous inserts and hollow cylinder shaped porous inserts are proposed because they can obtain optimal thermal or thermo-hydraulic performance. [ABSTRACT FROM AUTHOR]

This is the second of a two-part series of papers which presents the experimental results of a parametric series of liquid nitrogen chilldown tests of a stainless steel tube. Whereas the first paper in this series focused on the effect of mass flux, inlet subcooling, equilibrium quality, pressure, and axial distance from the inlet on two-phase convection heat flux for vertical upward flow only, this paper focuses on the effect of flow direction with respect to gravity. Nine different flow directions were examined, including horizontal, 30° inclined and declined, 45° inclined and declined, 60° inclined and declined, and vertical upward and downward. The experimental data covers liquid Reynolds numbers ranging from 800 to 230,000 and local pressures ranging from 150 to 725 kPa. Analysis is presented on the effect of flow direction on the measured film, transition, and nucleate boiling heat transfer coefficients as well as the critical heat flux. Finally, new heat transfer correlations to predict the data are presented for film boiling, nucleate boiling, and transition boiling. These correlations can be used for numerical simulations of cryogenic chilldown to help predict the chilldown time and propellant consumption for different system variables. [ABSTRACT FROM AUTHOR]

• The retention angle models are modified considering the flow vicious effect. • Convection mechanism is adopted at high heat flux. • The new model has satisfactory predictions for liquid film profile and heat transfer coefficient. • Flow and heat transfer characteristics at high heat flux and low temperature are analyzed. In this paper, a new analytical model is developed for the condensation of refrigerants outside low-finned tubes. It is based on the flow and heat transfer characteristics at low saturation temperatures and high heat flux, such as those in the LNG intermediate fluid vaporizer (IFV). Due to the increase of viscous effect at lower saturation temperature and higher heat flux, the previous condensate retention angle models are modified by adding the viscous term. At high heat flux and condensate rate, the condensate profile at the fin root is simplified to be arc-shaped and obtained directly by force analysis. Furthermore, considering the heat transfer enhancement caused by the circumferential flow at high heat flux, the convective mechanism is included for the heat transfer through the thick liquid film between the fins. The distributions of liquid film and fin surface temperature are also predicted. The present analytical model is in good agreement with different experimental and numerical results, while most deviations are within 10% for predicting the heat transfer coefficients at high heat flux. Because of the increased flow viscosity and surface tension, the optimal fin spacing and fin height increase as the heat flux increases and the saturation temperature decreases. [ABSTRACT FROM AUTHOR]

• Development of turbulent heat flux models suitable for low-to-medium Pr fluids using deep neural network. • Establishment of turbulent heat flux models suitable for complex conditions with flow separations. • Adopting proper orthogonal decomposition method to carry out the triple decomposition for unsteady flow. Turbulent heat flux (THF) models are used for the closure of the THF term when solving the steady/unsteady Reynolds-averaged scalar transport equation to simulate the turbulent heat transfer in industry. It is known that the simple gradient diffusion hypothesis (SGDH) has deficiencies under complex conditions with flow separations. To develop a more general THF model, this paper firstly establishes a high-fidelity database of forced convective heat transfer passing a circular cylinder under different Prandtl number (Pr) conditions at the Reynolds number (Re) of 500 via the direct numerical simulations. Proper orthogonal decomposition method is then employed for the triple decomposition on unsteady turbulent flow with the first two orders of eigenmodes reconstructing the large-scale field and the remaining reconstructing the turbulent field. Then, architectures using different neural network structures based on tensor basis neural network (TBNN), including MLP-TBNN-THF which adopts the multilayer perceptron (MLP) and ResNet-TBNN-THF that uses the residual network (ResNet), are constructed to predict normalized THF from large-scale flow features and Pr. Posterior tests are carried out on different Pr s and three different Re s: 500, 5000 and 16900 using the well-trained TBNN-THF models to evaluate their performance and generalization capability. Most models proposed in this paper predict the heat transfer more accurately than the SGDH model, even when extended to conditions out of the range trained. The failure of the isotropic assumption of SGDH model is observed in most regions. In that case, it is vitally necessary to use a model like proposed in this paper to simulate the THF term more accurately. In conclusion, the THF model, which is appropriate for complex working conditions and fluids with small-to-medium range of Pr , obtained by deep learning method in this paper, is helpful to improve the prediction accuracy of temperature field or concentration field by steady or unsteady Reynolds-averaged Naiver-Stokes approach in engineering. Besides, the current framework can be generalized to scalar-flux modeling under other conditions with the supplement of more databases in the future. [ABSTRACT FROM AUTHOR]

This paper presents the modeling of the liquid film distribution and heat transfer during convective boiling in horizontal, annular flows to be applied in such applications where non-uniform heat flux occurs. In general, prediction methods in the literature totally ignore the influence of the non-uniformity in the annular film (thin at top while thick at bottom) on the heat transfer process whereas local measurements around the perimeter of horizontal tubes show a significant variation, up to a factor of four times or more in thickness and up to 25-30% or more in heat transfer from top to bottom. Therefore, starting with the original suite for symmetrical annular flow models for convective boiling, condensation, entrainment, void fraction and two-phase pressure drops (Cioncolini and Thome (2009, 2011, 2012, 2012) [8-11]) and their recent paper (Cioncolini and Thome (2013) [13]) for predicting the threshold between symmetric and asymmetric annular flow, the new features added here are the predictions of the asymmetric annular film thickness and perimeter-wise heat transfer coefficients around the internal perimeter of horizontal tubes. To do this, a new set of 24 algebraic equations is proposed to provide the void fraction, liquid entrainment, pressure drop, liquid film distribution and heat transfer around the perimeter with a simple calculation procedure. Predictions of the new model have been compared against experimental databases with a satisfactory agreement. [ABSTRACT FROM AUTHOR]

• Infra-red (IR) measurements are synchronized with high-speed camera visualizations. • A time scale related to flow dynamics characterizes the transient heat convection. • Space-time diagrams of wall temperature allows a better understanding of the ONB. • A very strong time and space variation of the wall heat flux is observed. • The overheated wall temperature at ONB is well predicted by modified Hsu's model. This paper presents an investigation of the transient Onset of Nucleate Boiling (ONB) on a vertical heated surface cooled by an upward flow. The duct geometry used (semi-annulus with a heated inner wall) make this study very similar to a fuel rod in a Pressurised Water Reactor (PWR). This test section is then heated with different power steps to show the ONB and observe its propagation along the wall. The fluid used is the refrigerant HFE7000 flowing with flow rates corresponding to Reynolds numbers from 0 to 60,000 and subcoolings Jakob numbers from 8 to 33. Synchronised infra-red (IR) thermal measurements and high-speed camera visualizations provided new data which helped to develop models to characterise the Onset of Nucleate Boiling and the transition to the Fully Developed Nucleate Boiling regime (FDNB). This very finely characterized local behaviour provides an original insight for the onset of nucleate boiling in such sub-cooled convective configuration. It is shown that boiling is initiated by nucleation at a few specific sites and then propagates in the wake of a large vapor pocket flowing along the wall. Analysis of wall to fluid heat transfer evidences a short heat transfer degradation phase below the first vapor pocket, followed by a very effective cooling in its wake. The wall to fluid heat transfer during this transition toward fully developed nucleate boiling appears uncorrelated to the power dissipated within the heating element or to flow conditions. [ABSTRACT FROM AUTHOR]

In order to improve the heat transfer performance of microchannels, considering from balance flow resistance and increasing heat transfer area, a non-closed droplet pin fin array microchannel has been designed. The purpose of this paper is to study the inner influence of non-closed droplet structure on convection heat transfer by means of simulation. Through the simulation tool ANSYS Fluent, the working conditions of heat flux density from 5 W/cm2 to 85 W/cm2 are simulated respectively, with the inlet flow as 1.5 kg/h and the inlet fluid temperature as 40 °C unchanged. Along with the increase of heat flux density (5 W/cm2 ⩽ q ⩽ 85 W/cm2), the pressure drop, the bottom temperature as well as the heat transfer coefficient continue to rise, but the rising rates are various. Such variation could be explained by the different heat exchange processes: single phase heat transfer, bubble nucleation, growth and migration and then dry phenomenon, which can be observed from the vapor phase distribution results. The distribution of vapor phase under multiple heat flux explains the variation of pressure and temperature in different stages. It could be concluded that the non-closed droplet pin fin has a strong fractal effect on the fluid. After multiple shunting and confluence, the flow velocity of the fluid on both sides is significantly greater than that between the fins, whose average velocity is 0.135 m/s faster than that between the pins. Besides, the heat transfer effect of the corresponding walls on both sides is also better than that between the pin fins. Because the pin fin has the characteristics of droplet structure, the boundary layer on both sides of the pin fin will be separated and the heat transfer performance will be enhanced. The temperature of the pin fin head is lower, and the temperature of the pin fin tail is higher, with an average difference as about 9.32 °C. The comparison research between non-closed droplet and traditional droplet pin fin has been conducted, as well. It could be concluded that when 5 W/cm2< q < 60 W/cm2, the heat transfer coefficient of the opening droplet microchannel is higher, with pressure drop lower. The main reason is that the improvement of the non-closed structure reduces the kinetic energy loss caused by the collision, and promotes the emergence and growth of the vaporization core. • With the increase of heat flux, the pressure drop increases slowly, rapidly and slowly. • With the increase of heat flux, the initial point of phase transition gradually moves forward from the rear section. • The non-closed structure has a strong fractal effect on the fluid. • The boundary layer on both sides of pin fin will be damaged and the heat transfer performance will be enhanced. [ABSTRACT FROM AUTHOR]

• Derives theoretical solution of convective heat transfer from a plate with time-dependent and space-dependent temperature. • Utilizes Karman-Pohlhausen polynomials to derive solution. • Results are shown to agree with several past papers for special cases. • Applications in several practical scenarios are discussed. • Results help improve our understanding of convective heat transfer. Convective heat transfer due to laminar, incompressible flow past a flat plate has been extensively researched due to applications in a variety of engineering systems. In several cases, such as thermal management of Li-ion cells and phase change based energy storage, the flat plate temperature may vary as a function of both time and space, and the resulting plate heat flux is of interest. This paper presents an integral method based analytical model for predicting the heat flux distribution from a flat plate with a time-varying and spatially-varying temperature. Third-order Karman-Pohlhausen polynomial forms of velocity and temperature distributions are used in the integral energy equation to derive an ordinary differential equation that predicts the plate heat flux distribution in response to an arbitrary time- and space-dependent plate temperature distribution. The generalized results derived here are shown to reduce to previously reported results for special cases of only time-dependent or only spatially varying or constant plate temperature. Results are also shown to be in good agreement with finite-element simulations. The analytical model developed here is used to predict the plate heat flux in response to realistic plate temperature distributions that may be encountered in practical applications. These results improve the fundamental understanding of an important convective heat transfer process, and may help in the design and optimization of a broad variety of engineering systems involving convective heat transfer. [ABSTRACT FROM AUTHOR]

• Static mixers for enhancing convective heat transfer were additively manufactured. • Additive manufacturing enabled novel flow geometry, chevron-shaped structures. • Static mixers were monolithically integrated into liquid water channel. • Static mixers enhanced convective heat transfer coefficient about 100%. • A finite volume model suggests a guidance on the static mixer design. This paper investigates heat transfer enhancement by means of additively manufactured static mixers during liquid water cooling of a horizontal, heated flat plate. The static mixers disrupt the thermal boundary layer and induce mixing, resulting in an increased heat transfer rate of about 2X larger than flows without mixers. Simulations of the flows provided insights into the flows near the mixers, and guided selection of specific mixer geometries. The mixers were fabricated directly into the flow channels using additive manufacturing and then assembled onto the heated plate. Two types of mixing structures were analyzed: twisted tape structures that are similar to conventional static mixers; and novel chevron-shaped offset wing structures. Heat transfer performance was measured for liquid water (510 ≤ Re ≤ 1366) cooling the heated section with convective heat flux ranging between 0.1 and 0.8 W/cm2. This work demonstrates the potential of additive manufacturing to enable novel flow geometries that can enhance convection heat transfer whilst minimizing pressure drop penalties and volumes. [ABSTRACT FROM AUTHOR]

Highlights • Thermal convection was suppressed by the dielectrophoretic force. • The electroconvection has a strengthening effect on free convection heat transfer. • Strengthening effect of electroconvection increases with increasing electric field. • The strengthening effect at a low heat flux is better than that at a high heat flux. Abstract In this paper, the electrohydrodynamic (EHD) enhancement of free convection heat transfer is studied experimentally. A smooth copper heating surface is submerged in R113 liquid, the heat fluxes ranging from 4461 W/m2 to 17805 W/m2, and a high voltage ranging from 1 kV to 5 kV are applied on the heating surface. High speed photography is used to record the images of electroconvection. The results show the relationship between the intensity of the electric field, the height of the electroconvection layer and the enhancement of the heat transfer coefficient. Electric field can enhance free convection heat transfer, with the increase of the electric field the fluid disturbance on the heating surface increases obviously, and with the increase of the heat fluxes the enhancement of electric field gradually decreases. [ABSTRACT FROM AUTHOR]

Highlights • CFD study of natural convection around heated inclined plates. • Location of lift-off of plume approximately coincides with minimum heat flux point. • Relative importance of horizontal and vertical convection mechanisms is discussed. • Subtle and complex thermo-fluid-dynamics in near-horizontal configurations is revealed. • Nusselt number passes through a minimum as inclination changes from horizontal to vertical. Abstract The paper invokes the power of computational fluid dynamics (CFD) for accurate determination of the detailed thermo-fluid-dynamics of natural convective flow around heated inclined plates, with an extensive experimental validation of the computed heat transfer results. The study provides fundamental physical insight through a comprehensive understanding of the behaviour of the contours of velocity, temperature and pressure as a function of inclination angle over the entire range from the vertical (γ = 90 °) to the horizontal (γ = 0 °). In particular, the present study documents, for the first time, qualitative and quantitative behaviour of the lift-off point at which the natural convective boundary layer converts into a free plume. Similarly, the details of the spatial evolution of the velocity profile and temperature profile in the plume as a function of the inclination angle of the plate are determined for the first time. It is shown how the relative importance of indirect pressure difference and direct buoyancy, as mechanisms of natural convection, changes as the inclination angle is gradually altered from the horizontal to the vertical. Through accurate computation (and ingenious representation) of the velocity, temperature and pressure fields at small intervals of the inclination angle, the subtle and complex thermo-fluid-dynamics in near-horizontal configurations is revealed. It is shown that the non-dimensional lift-off distance changes from 0.5 (middle of the plate) to 0.9816 (nearly the trailing edge) as the angle of inclination is changed from 0 ° to 15 °. It is established that as the inclination angle is increased gradually from the horizontal position, the value of average Nusselt number Nu ‾ initially decreases slightly, passes through a minimum point and then onward increases continuously up to the vertical position of the plate. [ABSTRACT FROM AUTHOR]

Abstract The transfer of heat by the fins is influenced by the change of the direction of the fins. This paper investigates study the effect of the direction of longitudinal fins on a three-dimensional convection heat transfer in a rectangular channel and also study the effect of the lateral and longitudinal inclination of the rectangular channel. The Grashof range from 5 × 108 to 109, Reynolds from 1000 to 2300 and Prandtl 0.71. The bottom surface of the channel is exposed to constant heat flux, while other walls are isolated. Two cases are investigated. In case one, measurements were conducted for a lateral inclination of the channel, with a range of α = 0°,30°,60°, and 90°. Case two studied the longitudinal inclination of the channel, with the lateral inclination angle fixed at α = 90° and the longitudinal inclination angle Ө = 0°, 30°, 60°, and 70°. The dimensionless of fin height was Hf/H = 0.6, and the fin spacing was S/H = 0.17. The experimental results show that the coefficient of the heat transfer for lateral inclination (α = 0°) was greater than that for a sideways orientation (α = 90°). Additionally, the average coefficient of heat transfer for both the lateral and longitudinal inclination case is increased with the longitudinal inclination angle. The empirical equations are obtained based on the experimental results. These equations correlated the Nusselt number as a dependent variable of the orientations angles, Reynolds number, and the Grashof number, these equations are consistent with experimental results. Graphical abstract Image 1 Highlights • Investigate the effect of inclination and rotation angles of rectangular duct. • Experiments conducted on laminar mixed convection heat transfer from fins array. • Optimized a constant heat flux condition by tuning inclination and rotation angle. • A novel correlations for mixed convection heat transfer for various orientations. • The higher heat transfer coefficient is observed at the highest inclination angle. [ABSTRACT FROM AUTHOR]

Highlights • A modified two-equation turbulent model with buoyancy effect correction was proposed. • Production of turbulent kinetic energy and turbulent thermal diffusion were accounted. • The modified model showed good prediction in heat transfer deterioration cases. • The value of Pr t in the buffer layer is essential for the model accuracy. Abstract The performance of the turbulent flow model for predicting the buoyancy effect on convective heat transfer of supercritical fluid is severely affected by strongly varying thermal physical properties near the pseudo-critical point. Over-prediction is attributed, at least partly, to the misuse of the constantly turbulent Prandtl number for the turbulent heat flux in the turbulence model. A method that considers the anisotropic turbulent heat flux has been proposed to improve the prediction accuracy of numerical simulation. A buoyancy effect model that accounts for the production of turbulent kinetic energy and a turbulent Prandtl number model accounting for turbulent thermal diffusion, which are both based on the anisotropic turbulent heat flux model, was adopted in the original AKN k - ε model. Experimental results and direct numerical simulations (DNS) data were used to validate the performance of the “Modified model.” The “Modified model” produced accurate predictions for all heat transfer deterioration cases examined in the present paper. The buoyancy effect model reflects the basic mechanism of heat transfer deterioration and recovery due to accurate predictions of turbulent kinetic energy. The value of Pr t in the buffer layer obtained with the turbulent Prandtl number model is essential for accurate reproductions of experimental data. [ABSTRACT FROM AUTHOR]

Abstract In this paper the relative performance of two different differential stress and flux models for computing natural convection in an enclosure is examined. One model is the low-Reynolds number differential stress and flux model and the other model is a recently developed elliptic blending based differential stress and flux model. The primary emphasis of the study is placed on investigating the accuracy of the both models for the turbulent natural convection in an enclosure. Both models are used to predict turbulent natural convections in a square cavity with hot and cold side walls and conducting top and bottom walls (Ra = 1.58 × 109). The relative performance between both models is examined through comparing their solutions with the experimental data. It is shown that both models predict the vertical mean velocity component and mean temperature well. It is also shown that the low-Reynolds number differential stress and flux model slightly under-predicts the turbulent kinetic energy and vertical turbulent heat flux. It is also noted that the implementation of the elliptic blending second moment model is easier since this model does not contain any wall-related parameters and damping functions. [ABSTRACT FROM AUTHOR]

This paper examines the influence of the distance between vertical plates on the intensity of free convective heat transfer along with the optimization of this distance. Experimental tests were carried out for one model channel of such an heat exchanger with widths s = 0. 045 , 0.085 and 0.18 m. This channel, open at the top and sides, was formed by two isothermal symmetrically heated parallel vertical plates of dimensions H = 0. 5 m and B = 0. 25 m. The influence of the heating surface temperatures t w = 30 , 40, 50, 55, 60 and 70 °C on the convective temperature fields and velocity generated inside the channels was investigated. Directly measured temperature fields, as well as velocity fields measured indirectly using the NRP, enabled the thermodynamic parameters of the heat exchanger to be determined. Based on the temperature gradient distribution ∂ T w ∂ x on the wall, its average value was determined for each of the plates and for the entire channel, after which the heat flux Q w transferred from the plates was calculated. The heat flux transferred with the air Q and the efficiency η = Q / Q w of heat transfer in the channel were determined using the balance method based on the average temperatures and air velocities at the inlet t ̄ b o t t and u ̄ i n and at the outlet t ̄ t o p and u ̄ o u t of the channel obtained from the temperature and velocity fields. A grid placed vertically in the channel, halfway across the panel width and perpendicular to the heating surfaces was used to detect the temperature field in air. The image and matrix of these temperatures were determined using a thermal imaging camera. The numerical reconstruction procedure (NRP) was used to determine the velocity field. For technical reasons and lack of time it was not possible to test more channels. Since three values of the width s were insufficient to determine s o p t , it was decided to use numerical research. For this purpose, numerical results were compared with those obtained experimentally for the channels already tested. As the compliance verification was successful, further studies of the channels were continued numerically. As a result of optimizing the heat exchange intensification, optimal widths of a single channel s o p t = 0. 035 m and n channels s 0 = 0. 0123 m, included in the heat exchanger, were obtained. • Experimental tests for one model channel of an heat exchanger were carried out. • Numerical method of reconstructing convective velocity fields in channel was used. • Verification of the NRP with experimental CTM and SNC results was conducted. • The optimal width of the isothermal, vertical channel was obtained. • The results confirmed usefulness of NRP for heat fluxes determination. [ABSTRACT FROM AUTHOR]

For the cooling of transformer in the grid, the heat transfer efficiency of mixed convection is relatively low due to the low thermal conductivity and large viscosity of transformer oil. Therefore, this paper aims to study the PCD (periodically changed direction) electrical field to enhance the mixed convective heat transfer of transformer oil. Then, a semi empirical correlation is developed to calculate the Nusselt number affected by electrical field. Specially, the influences of heat flux, electrical field intensity and switching period on the heat transfer characteristics are discussed experimentally. As a result, the result reveals that the mixed convective heat transfer is enhanced increasingly with the decrease of switching time and improvement of voltage. Thus, the PCD electric field can effectively enhance the mixed convection heat transfer. In addition, the mechanism analysis shows that the PCD electrical field leads to the continuous change of fluid mode, and the polarized molecules continuously vibrate and move within a certain range, which leads to the violent disturbance of internal fluid. Meanwhile, the secondary flow induced by the electric field results in the disruption of thermal boundary layer, which strengths the heat transfer. Finally, the predicted results of the semi-empirical correlation are in good agreement with the experimental results, and the effect of electrical field intensity and switching periods are comprehensively considered in the correlation. The present study is of great importance for the transformer cooling. [ABSTRACT FROM AUTHOR]

Walls thermal transmittance value (U-value) is essential to identify the performance of a wall and it is used for the energy labeling procedure. If on one hand the heat-flow meter can measure heat fluxes across its plate giving back the wall's U-value, on the other hand, if air temperatures and wall's inner surface temperatures are measured, it is necessary to set the total heat transfer coefficient value in order to calculate the heat fluxes. Many correlations were developed in scientific literature to quantify the convective heat transfer coefficient and it is possible to distinguish similarity based and experimentally ones. In this paper, the actual total heat transfer coefficients in different case studies were obtained by measuring the physical parameters that are needed to define them. Convective and radiative contributions were separately evaluated and, finally, actual convective heat transfer coefficients were compared with the same coefficients obtained by applying the correlations available in literature and with the constant value suggested by the Standard. The aim of this study is to analyze the differences between the various coefficients values and their influence on the thermal transmittance evaluation, in order to better understand the existing correlations and the UNI EN ISO 6946 applicability. This is an initial part of a research which aims to provide an overall more accurate representation of the building behavior, forthcoming developments will deal with the analysis of heat transfer on the outer side of walls. [ABSTRACT FROM AUTHOR]

We analyzed in this study the conjugate heat transfer process in the heat collecting element (HCE) for a parabolic trough concentrator. The effect of asymmetric characteristics, such as non-uniform heat flux, eccentric configuration, and incident angle, are especially considered in this paper. We constructed a two-dimensional model of surface radiative transfer coupled with convection using the finite volume method combined with the net radiation method. We presented a detailed numerical method in which we applied an additional source term method to the boundary conditions to capture the absorption and emission processes in the coating of the HCE. The results were validated against the experimental data. Thus, we were able to identify the limiting interactions between thermal radiation and convection in the annulus. We systematically analyzed the effect of the incident irradiation angle and the eccentricity of the configuration on heat loss through the annulus of the HCE under two limiting conditions: “air in annulus” and “vacuum in annulus”. The results show that asymmetric characteristics, especially the non-uniform heat flux and eccentricity configuration, have a significant influence on local heat transfer processes. These insights may be used to further optimize the configuration of the HCE for improved thermal performance. [ABSTRACT FROM AUTHOR]

• Flow boiling in micro channels with and without inlet restrictions was tested. • Heat transfer characteristics of studied geometries is generally similar. • The dominant heat transfer mechanism for subcooled flow is forced convection. • The dominant heat transfer mechanism for saturated flow is nucleate boiling. • Average heat transfer coefficient fell by up to 34.0% when restrictions were used. Flow boiling in micro channels is considered to be a promising solution for electronics cooling. However, its development is impeded by the lack of full understanding of mechanisms responsible for heat exchange and its susceptibility to instabilities. A common way of flow stabilization is employing restrictions at channel inlet, but their impact on micro channel thermal performance remains an open question. Therefore, this paper focuses on experimental determination of the dominant heat transfer mechanism during flow boiling of R245fa in 10 parallel rectangular channels with hydraulic diameter of 1 mm without inlet restrictions and with 0.5 mm wide and 2.5 mm long restrictions. Studied heat fluxes vary between 30 and 50 kW / m 2 , mass fluxes between 400 and 1000 kg / m 2 s , saturation temperatures between 49 and 82 ∘ C, inlet subcoolings between 13 and 19.4 K. For the subcooled flow the dominant heat transfer mechanism was forced convection with heat transfer coefficient rising with mass flux, vapor quality and saturation temperature. For the saturated flow nucleate boiling was the dominant mechanism with heat transfer coefficient increasing with heat flux and saturation temperature and decreasing with mass flux and vapor quality. Geometry with inlet restrictions in general exhibited similar thermal behavior, but in the subcooled zone a more pronounced positive dependence on saturation temperature and a negative dependence on mass flux especially at lower temperatures were observed. This indicates that restrictions augment nucleate boiling contribution to the forced-convection-dominated heat exchange in the subcooled zone. Restrictions yielded similar or slightly lower heat transfer coefficients. Comparing the data against 24 heat transfer models showed that the model of Thiangtham et al. was the most accurate with MAPE 23.7% and 20.2% for geometry without and with restrictions respectively. [ABSTRACT FROM AUTHOR]

Mixed convection in vertical upward heated flow has been intensively studied in the last few years since it reduces the heat transfer capability of the system in the deteriorated turbulent heat transfer (DTHT) regime. Several mixed turbulent heat transfer correlations have been proposed, but the best correlation to be used in DTHT regime for water in vertical upward heated flow is yet to be determined. Furthermore, the relation between momentum flux and heat flux in mixed convection regime is still unclear. This paper presents comparison of several mixed turbulent heat transfer correlations performance of water up-flow in a circular tube by numerical approach using v 2 – f turbulence model. The existing correlation of Symolon et al. showed the best agreement with the numerical analysis results in predicting the heat transfer capability of a water-cooled system while Petukhov and Polyakov correlation showed a good agreement to correlate the momentum and heat transport behavior in the mixed convection turbulent regime. [ABSTRACT FROM AUTHOR]

In this paper, both experimental and numerical studies have been performed on the turbulent heat transfer of the graphene nanoplatelets nanofluids in a horizontal stainless steel tube that was subjected to a uniform heat flux at its outer surface. An experimental investigation was done to evaluate the heat transfer characteristics and the pressure drop of a graphene nanoplatelet (GNP) nanofluid and in numerical study, the finite volume method with standard k – ɛ turbulence model is employed to solve the continuity, momentum, energy and turbulence equations in three dimensional domains. The thermal conductivity and viscosity of the GNP nanofluids at concentrations of 0.025, 0.05, 0.075, and 0.1 wt% were measured prior to the heat transfer experiments. The heat transfer and the pressure drop within the flowing base fluid (distilled water) were measured and compared with the corresponding data from the correlations and numerical study. The data were satisfied within a 5% error and 2% error for the numerical work. The effects of the nanoparticle concentration and the heat flux on the enhancement of the heat transfer turbulent flow condition are presented. The Nusselt number (Nu) of the GNP nanofluid was higher than the base fluid by approximately 3–83% and increased as the flow rate and the heat flux increased. However, the increase in the pressure drop ranged from 0.4% to 14.6%. Finally, the results reveals that the GNP nanofluids could function as a good and alternative conventional working fluid in heat transfer applications. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of thermal transport in a parallel-plate channel comprised of superhydrophobic walls. The scenario analyzed is laminar, fully developed, steady flow with constant properties. The superhydrophobic walls considered here have alternating micro-ribs and cavities aligned perpendicular to the flow direction and are made of a highly conductive material. The cavities are assumed to be non-wetting and contain air whereas the bulk liquid is water. The thermal transport through the ribs is considered to have a constant heat flux while the thermal transport through the air/liquid interface over the cavity is considered to be negligible. Numerical results have been obtained for a range a Peclet numbers, cavity fractions, and relative channel widths. A limited number of results were also obtained where the rib was maintained at a constant temperature condition for comparison. In general, the thermal transport is a strong function of all the parameters explored. By comparison to previous analytical work, the influence of axial conduction is found to be significant and is most pronounced at large relative channel widths, low Peclet numbers, and large cavity fractions. Lastly, the ratio of temperature jump length to hydrodynamic slip length is presented in terms of the varied parameters and is compared to previous results where axial conduction is neglected and other work where diffusion is assumed dominant. [ABSTRACT FROM AUTHOR]

Wall curvature is a widely used technique to passively enhance convective heat transfer and it is particularly effective in the thermal processing of highly viscous fluids. These geometries produce a highly uneven convective heat flux distribution along the circumferential coordinate, impacting on the performance of the fluid thermal treatment. Although many authors have investigated the forced convective heat transfer in coiled tubes, most of them have presented the results only in terms of the Nusselt number averaged along the wall circumference. Moreover, regarding the laminar flow regime, few data about the local heat transfer coefficient are available. In this paper a procedure to estimate the local convective heat flux in coiled tubes is presented and tested: the temperature distribution maps on the external coil wall are employed as input data for the inverse heat conduction problem in the wall under a solution approach based on Tikhonov regularization method. The investigation was particularly focused on the laminar flow regime. [ABSTRACT FROM AUTHOR]

This paper presents convective heat transfer measurements on the endwall of a turbine blade cascade by means of the liquid crystal thermography. The measurement method is based on the heating, at uniform heat flux, of the endwall by means of an electronic circuit board. The heated region of the endwall surface exposed to the airflow is covered with a thermochromic liquid crystal coating. The colour map of the coating during a given test, featured by an assigned mass flow rate, is measured by using an image processing system. With a prescribed wall heat flux, the convective heat transfer coefficient is obtained, at every pixel location, from the measured temperature maps recorded at the steady-state. Heat transfer results, presented for the endwall of a high-pressure turbine cascade, have been obtained for different values of the Reynolds number. Regions of the endwall surface associated with high rates of heat transfer are well identified: the leading edge of blades, pressure and suction side corners, the blade wake and cascade throat. The spatially-resolved heat transfer measurements presented here could provide a useful baseline for a condition-specific, optimized endwall film-cooling solution that reduces overall heat transfer rates. [ABSTRACT FROM AUTHOR]

• The heat transfer of S-CO 2 in a vertical mini-channel was experimentally investigated. • Special heat transfer characteristics of S-CO 2 at low mass flux were observed. • A criterion for identifying the special heat transfer characteristics was proposed. • Effects of buoyancy and thermal acceleration performed differently at various mass fluxes. • An improved correlation was established based on experimental data. The comprehensive understanding of heat transfer characteristics to supercritical carbon dioxide in flowing channels is significant for the design and safe operation in the advanced supercritical carbon dioxide systems, especially for the heat transfer deterioration conditions that is generally occurs at relatively low mass fluxes but high heat fluxes. This paper experimentally studied the heat transfer behaviors of supercritical carbon dioxide flowing in a vertical heated mini-tube with an inner diameter of 2 mm. The experiment was conducted with pressure of 7.5–9 MPa, low (G < 200 kg·m−2·s−1)/high mass flux of (G > 200 kg·m−2·s−1) and heat flux of 45–300 kW·m−2. The effects of operational parameters, buoyancy force and flow acceleration on convective heat transfer were discussed. The results showed that at low mass fluxes, no obvious heat transfer deterioration behaviors observed even though heat load (q / G) was high. However, under the similar q / G conditions with high mass fluxes, a remarkable heat transfer deterioration occurs. Under low mass fluxes, heat transfer enhanced by the strong buoyancy force and obvious acceleration effect, but at high mass fluxes, deteriorated heat transfer mainly effected by buoyancy rather than acceleration effect. Based on the experimental data and multiple effects of buoyancy and thermal acceleration, an improved correlation considering these effects at low mass fluxes was proposed, where more than 90% data in the within ± 20% error range. [ABSTRACT FROM AUTHOR]

Theoretical analysis of heat transfer in a multilayer body is relevant for several engineering applications where heat transfer occurs through a stack of thermally dis-similar materials. In most of such literature, a constant convective heat transfer coefficient is assumed as a boundary condition at one end of the body. In contrast, there is a lack of work to model a problem with spatial variation in the convective heat transfer coefficient. This paper presents an analytical solution for thermal conduction in a multilayer rectangular body with spatially varying convective heat transfer coefficient at one end. In addition, this solution also accounts for internal heat generation and inter-layer thermal contact resistance and spatially varying heat flux on the other end of the body. The solution is derived in a series form, and it is shown that the coefficients of the series can be determined by solving a well-defined set of linear algebraic equations. The analytical solution is verified by comparison with numerical simulations, as well as with standard solution for a simplified special case. The impact of spatially varying cooling provided by jet impingement is analyzed using the analytical solution. A resource optimization problem pertaining to the optimal use of jet cooling is solved. Results presented here may benefit thermal management analysis of a broad variety of engineering applications involving heat transfer in multi-layer bodies. [ABSTRACT FROM AUTHOR]

With the development of heat engines, in some fields the heat wall suffers from dynamic heat flux, thus some cooling control techniques are needed to meet this dynamic cooling requirement. The traditional stationary vortex generators have not met the cooling demand in these cooling fields with dynamic heat flux. Existing studies have shown that the capacity of convective heat transfer depends on the distribution characteristics of the velocity and temperature field of the cooling fluid. Therefore, considering to the factors of single-side heat transfer and fluid flow boundary layer, new and efficient mixing heat technology is increasingly demanded for many industrial fields. In this paper, the dynamic turbulence generator such as spherical cylinder is adopted to study the influence of flow vortexes on heat transfer and achieves a better distribution of velocity field and facilitates the enhancement of convective heat transfer. Research results indicate that compared to traditional stationary vortex generator technologies, vibration spherical cylinder can effectively improve heat transfer performance and leads to a lower flow resistance. As a conclusion, the flow and heat transfer performance increase with the vibration frequency increasing. When Re = 7255, the thermal hydraulic performance is increased by a maximum 24.55% than traditional stationary vortexes generator. When Re = 14510, the performance is better than stationary cylinder structure. And the vibration frequency can be adjusted timely according to cooling demand. [ABSTRACT FROM AUTHOR]

• A detailed technical description of the new type of plate was presented. • The method of its implementation, range of work and calibration has been shown. • Experimental tests using the balance and the gradient method has been conducted. • The balance method of determining the emissivity factor of heater was presented. • IR camera allows obtaining convection results unaffected by radiation component. This article examines the influence of radiative heat flux on the accuracy of the results of free convective heat transfer in air. In order to carry out these tests, based on the experience gained during the operation of a plate heated on one side, compensated by a reverse heat loss flux counter-heater, a unique double-sided heating sandwich plate was designed and built, consisting of three thin epoxy resin plates reinforced with glass fibre. The paths of surface resistance thermometers were etched using photolithography on the two outer plates laminated on one side with copper. The traces of two resistance heaters were etched on both sides of the third, bilaterally laminated middle plate. This paper provides a detailed technical description of the new type of plate, the method of its implementation and determination of its operational range, calibration procedures (separately for integrated thermometers and heaters). Also described are the methods for conducting experimental tests in the vertical using the balance method in air and in water, and the gradient method using a thermal imaging camera and a detection mesh in order to validate the results obtained. [ABSTRACT FROM AUTHOR]

The convective heat transfer coefficient on the rail surface is an important parameter to determine the temperature field of the wheel/rail contact region, especially at the condition that train operates normally and the condition that an eddy current brake is used. Because of the complex configuration of a real wheel/rail contact system, it is hard to build a model with similar geometry as the real one. In this paper, a simple experimental model is used to obtain the convective heat transfer coefficient on a circular track surface on which the wheels pass periodically. In the experimental processes uniform heat flux is applied on the track surface, and the six types of the wheels are used. The results show that when the heat transfer coefficient is presented regarding to the wheel center velocity or angular velocity, it is dependent on the wheel diameter. For the same wheel diameter, the heat transfer coefficient has a parabolic distribution characteristics regarding to the wheel center velocity, which means the heat transfer coefficient increases firstly and then decreases as the wheel center velocity increases. The maximum value of the heat transfer coefficient is independent of the wheel diameter. It is hard to find a correlation between Nusselt number and Reynolds number for the wheels with different diameters. The significant characteristic is that the frequency of the wheels pass takes a major role on the heat transfer coefficient. Therefore, the heat transfer coefficient can be correlated with the frequency of the wheels that run over the circular track. • The convective heat transfer coefficient on the track surface as wheels roll over periodically is studied. • The heat transfer coefficient changes along a parabolic line regarding the wheel rolling speed. • The heat transfer coefficient vs. modified frequency of wheels pass is independent of the wheel diameter. • The maximum heat transfer coefficient is independent of the wheel diameter. [ABSTRACT FROM AUTHOR]

• Addresses external convective heat transfer due to flow past a flat plate. • Solves the problem when plate heat flux is a function of time and space. • Represents a generalization of past work on external convective heat transfer. • Results are shown to reduce to past work for several special cases. • Results may be applicable for several practical engineering systems. Convective heat transfer due to laminar fluid flow past a flat plate is a standard problem in heat transfer. While constant heat flux or temperature along the plate is often assumed for solving such problems, there may be several practical scenarios where the heat flux along the plate varies as a function of both space and time. Developing an analytical solution for the resulting plate temperature distribution is important for understanding and optimizing the thermal performance of such systems. While some work exists on analyzing problems with time-dependent or space-dependent heat flux, there is a lack of work on the general problem where the heat flux is a function of both space and time. This paper presents a solution for this problem by solving the integral form of the energy equation, along with the use of fourth-order Karman-Pohlhausen polynomials for velocity and temperature distributions in the momentum and thermal boundary layers. A non-linear, first order, hyperbolic partial differential equation for the plate temperature is derived in response to the time- and space-varying plate heat flux. This equation is shown to agree well with results from past work for several special cases. Numerical solutions for the generalized equation are presented. Based on this approach, the plate temperature distribution is predicted for several heat flux profiles that may be of interest in practical applications. Results from this work improve our understanding of unsteady convective heat transfer, and contribute towards modeling and optimization of practical engineering systems where such phenomena occur. [ABSTRACT FROM AUTHOR]

This paper provides an hitherto new approach of a heat transfer correlation based on heat flux to mass flux ratio for predicting wall temperature of supercritical water flowing in a bare vertical tube. Totally 10,174 numbers of experimental data were collected, Out of which 4236 data are heat flux/mass flux ≤0.4 and 5938 data are heat flux/mass flux>0.4. These data were obtained from various experimental resources and Lookup table and it covers q/G ranges from 0.085 to 1.295, mass flux ranges from 201 to 3500 kgm−2 s−1, heat flux ranges from 129 to 1600 kWm−2, pressure ranges from 225 to 320 bar, diameter of the tube 4.4 to 38 mm and bulk fluid enthalpy ranges of 250 to 3200 kJkg−1 of vertical tube working at various supercritical working conditions based on normal, enhancement and deteriorated heat transfer regions. By using these data, a new heat transfer correlation is derived for finding the wall temperature by Levenberg-Marquardt (LM) algorithm of multi dimensionless analysis method with Nonlinear curve fitting method. A general form of forced convection heat transfer correlation was obtained by Buckingham Π theorem. The Wall temperatures predicted by various 7 existing correlations along with this new correlation are found by Visual basic program and compared with experimental data for evaluating the deviations. The rank was provided based on error band from ±0.5% to ±50% etc., and error analysis were conducted for proving the best fitting correlation. [ABSTRACT FROM AUTHOR]

The paper analyses a novel model of unsteady convective heat transfer in a nanofluid layer on a flat vertical surface subject to instantaneous (abrupt) onset of film boiling. It occurs if heat flux suddenly switched on exceeds the critical heat flux necessary to bring a nanofluid to film boiling regime. The usual system of equations of fluid flow and convective heat transfer is supplemented by an equation for the concentration of nanoparticles. To complement the problem statement, two sets of the boundary and initial conditions were used. The first condition corresponds to problem of film boiling derived by Bromley, whereas the second was suggested by Ellion for a stationary liquid at the vapor-liquid interface. The solution of the problem enabled predicting variation of temperature distributions, Nusselt numbers, velocity profiles and friction coefficients in time. Computations were performed numerically based on the self-similar equations derived using the Lie group transformations. Results of unsteady simulations of convective heat transfer during instantaneous onset of film boiling of a nanofluid with different concentrations of nanoparticles demonstrated qualitative agreement with experiments. • Instantaneous transition to film boiling in nanofluids was studied at sudden heat input. • Unsteady convective heat transfer in the vapor film was modeled theoretically. • The problem was solved analytically and analyzed for two sets of boundary conditions. • The theoretical solution was successfully validated via comparisons with experiments. [ABSTRACT FROM AUTHOR]

• The effect of the migration on the heat transfer coefficient is experimentally presented. • The migration effect of nanofluids is experimentally considered with the N BT values. • The heat transfer coefficient of the nanofluids depends on the nanoparticles' migration. In this paper, the effect of nanoparticle migration on the convective heat transfer characteristics of EG/water-based Al 2 O 3 nanofluids flowing through a simple round tube with constant heat flux in a fully developed turbulent flow regime was investigated experimentally. Homogenous EG/water-based Al 2 O 3 nanofluids were mass-produced using a modified two-step method with both a dispersion with a nanodisperser and centrifugal decanting. The suspension stability, particle size, thermal conductivity, and viscosity of the nanofluids were systematically measured. To observe the effect of nanoparticle migration, the convective heat transfer coefficient of the nanofluids was experimentally measured according to N BT values, which indicates the ratio of the Brownian diffusivity to thermophoretic diffusivity. The convective heat transfer coefficients of nanofluids increased by at least 12.4% and up to 22.7% depending on the N BT values at the fixed Reynolds number. Moreover, the convective heat transfer coefficient of the nanofluids decreased by 7.7% (low N BT value) or increased by approximately 13.2% (high N BT value) under constant pumping power. These results indicate that the convective heat transfer coefficients of EG/water-based Al 2 O 3 nanofluids under each condition are strongly dependent on the N BT values. [ABSTRACT FROM AUTHOR]

• Different reflective thermo-insulating panels were tested in climatic chamber. • Results were employed to validate a CFD model in COMSOL. • Results were extended to evaluate their role in multilayer systems on real buildings. • An optimal air-gap thickness can be identified in multilayer systems. • The same effect of a traditional 6 cm of bulk insulation was found, without require additional spaces. The refurbishment of existing buildings represents a priority target to reduce global energy consumption. An interesting solution is represented by multilayer systems made by insulating panels mounted on a suitable frame to form non-ventilated air-gaps with the existing envelopes. This solution is attractive because it allows for renewal and energy requalification of building façades by interventions addressed exclusively to the external surfaces, without interfering with occupants. However, it produces an increase of the building volume that could be in contrast with local construction regulations. In this context, the application of reflective (low-ε) thermal insulation panels inside the air–gap seems appropriate to reduce the system thickness without penalizing the thermal transmittance of the renovated envelope. However, addressed investigations conducted on the combined convective and radiative heat transfer coefficients inside enclosures equipped with low-ε materials, are lacking. In this paper, an experimental campaign conducted in a climatic chamber by the heat flux meter method on three different samples of commercial reflective panels inside a non-ventilated air–gap has shown, for the same sample thickness, an increase of the air–gap thermal resistance up to seven times. In order to evaluate the performances on a real scale, the experimental results were employed to tune a model developed in the COMSOL environment to determine the attainable global heat transfer coefficient in real scale air cavities. The results showed that thermo-reflective panels can produce the same effect of at least 6 cm of traditional insulating materials by avoiding additional space. Moreover, useful design information concerning the attainable thermal resistance growth related to the air–gap thickness and the thermo-reflective panel emissivity, were introduced. Results showed that by setting the vertical wall height, an optimal air–gap thickness that allows for minimizing the global heat transfer coefficient, can be identified, however, this is mainly when the emissivity coefficient of the panel surfaces is lower than 0.5. Furthermore, by setting the optimal thickness, the increase of the transferred thermal flux by quadruplicating the wall height is moderate being slightly greater than 16%. By monetizing the saved volume growth, the multilayer system equipped with thermo-reflective panels is economically profitable, especially with the insulating panel cost increase and in zones where the average building value is high. [ABSTRACT FROM AUTHOR]

• Real-time surface heat flux estimation method is presented for the 3D finite domain. • Effect of the dynamic convection condition was considered in estimation. • Thermal modal analysis is applied to derive the estimation algorithm. • Novel RLSD is introduced to achieve the efficient computing and real-time estimation. • The estimated results are in good agreement with measured experimental results. This paper presents a novel surface heat flux estimation method for the 3D finite domain experiencing dynamic convection and surface heat flux. The thermal mode parameter is adopted to produce a mathematical relation between the surface heat flux history function and the transient temperature response vector with modal superposition method and to locate specific measurement point which can represent transient temperature change of the domain. The direct solution is obtained using the modal superposition method with thermal modes and modal time constants representing thermal characteristics of domain, and the proposed surface heat flux estimation method is derived by the inverse solution applying the novel recursive least square deconvolution (RLSD). The proposed method is validated by numerical tests and experiments that include two main advanced points: employment of the dynamic convection condition and implementation of efficient computing for real-time estimation. As a result, the root mean square error (RMSE) of numerical tests show the results within 2% for the maximum magnitude of hypothetical heat flux for all cases. Also the estimation result from experiment presents the RMSE within 2.5% for the maximum magnitude of measured heat flux history, achieved in only 49 s of computing time for long-term estimation of 100 min. [ABSTRACT FROM AUTHOR]