Surface Heat Flux Distribution Research Articles

Real-time reconstruction of the time-dependent heat flux and temperature distribution in participating media by using the Kalman filtering technique

The Kalman filtering (KF) algorithm is introduced to solve the inverse coupled radiation-conduction heat transfer problem in the participating medium for the first time. The time-dependent surface heat flux and internal temperature distribution of the participating medium is reconstructed simultaneously from the (non-intrusive transient temperature) measurements made on the other surface. The governing energy equation and radiative transfer equation are calculated by using the finite volume method (FVM). Different forms of transient heat flux are employed to test the performance of the KF method. The influence of initial state, initial state error covariance, measurement noise, process noise, measurement noise covariance, process noise covariance, sampling step, refractive index, medium thickness, and absorption coefficient on the accuracy and stability are discussed thoroughly. All the retrieval results show that the surface heat flux and internal temperature distribution can be reconstructed simultaneously in real time. Compared with the hybrid algorithm of KF and recursive least-square estimator (RLSE), the KF algorithm can obtain better reconstruction results and a noticeable decrease of the sensitivity to measurement noise, initial temperature distribution, and absorption coefficient is observed from the retrieval results.

Flame Growth Around a Spherical Solid Fuel in Low Speed Forced Flow in Microgravity

To further our understanding of flammability and quenching limit of thick solid fuels, a microgravity experiment Growth and Extinction Limits is to be conducted aboard the International Space Station with the emphasis to quantify the effect of the flame heat loss to the thermally thick solid interior by directly measuring the sub-surface temperature gradient. A precursor microgravity combustion experiment in the Burning and Suppression of Solids (BASS) project was used to assess the experimental operation and validate the accompanied numerical model. The present paper reports the development of the flame model over a solid sphere in low-speed pure convective flow (less than 100 cm/s). Computed time sequence result of one of the BASS conditions is presented. The combination of gas phase reaction rate, solid internal temperature and surface heat flux distribution reveals the effect of solid in-depth heat-up on flame growth. The experimental observations agree with the trend predicted by the model. For thick solids, flame quenching limit in low speed flow is not only a function of flow speed but also the degree of solid interior heat-up. Flammability limit can have profound implication to the current spacecraft fire protection protocol that requires turning-off of circulation flow in case of detected fire. The present and the follow-up studies will provide more quantitative estimate of the low velocity-quenching limit with heated samples. For the Polymethylmethacrylate spheres investigated, the limit is lower than 2 cm/s in air.

Numerical investigation and experimental validation of an infrared measurement approach for surface heat flux distribution using a multi-color-reference

Accurate measurement of heat flux (HF) is significant in both industrial engineering and scientific research. It is acknowledged that the radiative HF can be easily determined by radiometers. In order to measure the conductive or convective HF distribution flowing across a surface, this paper presents a novel non-contact measuring method based on the infrared (IR) technique and inverse heat transfer method (IHTM). In addition, a specially designed multi-color-reference (MCR) which is composed of four sectors with four different known emissivity will be attached to the focused surface in the practical measurement. Therefore, different radiation signals among the four different sectors of MCR as well as the focused surface will be detected by an IR camera, through which a whole radiation temperature map can be obtained. Based on the differences in the radiation temperatures of the surface and MCR, the IHTM can be adopted to yield useful boundary conditions such as emissivity of the surface, convective heat transfer coefficient, and the critical HF distribution. The measuring method presented in this study combines the advantages of contact and non-contact measurement, which can accurately obtain the HF distribution under the difficult-contacted conditions such as the HF monitoring of a boiling furnace, HF estimating of the aerodynamic heating surface, etc. Numerical simulation and experimental verification were organized to justify the newly-developed measuring method. Relative error in the simulation is estimated to be less than 2%, and that in the experiment is calculated to be around 4.23%. The result displays a relatively high precision of the measuring method, demonstrating that such a method can be applied in practical application.

Association of the North Atlantic Surface Turbulent Heat Fluxes with Midlatitude Cyclones

Abstract Atmospheric mechanisms leading to the formation of very strong turbulent air–sea heat fluxes in the North Atlantic are analyzed using the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR) for the winter periods from 1979 to 2010. Surface turbulent flux extremes were quantified by considering both absolute and relative extremeness of these fluxes. For all cases of very strong surface turbulent fluxes, regional composites of the associated atmospheric conditions were built using reanalysis output. These composites clearly demonstrate a critical role of the cyclone–anticyclone interaction zone in forming very strong surface fluxes. The implied importance of cyclones followed by anticyclones in generation of surface air–sea heat flux extremes was demonstrated by the analysis of case studies. We further used the results of numerical cyclone tracking to identify extratropical cyclones associated with air–sea flux events of different intensities and to quantify the life cycle characteristics of these cyclones. Analysis of frequency distribution of surface heat fluxes has shown that extreme fluxes over the North Atlantic are associated with less than 30% of winter cyclones and that this association occurs mostly during the initial stage of their life cycle. Analysis of life cycle characteristics of these cyclones shows, in turn, that they are considerably more intense than most North Atlantic cyclones and are characterized by rapid deepening and slower propagation. We argue that variability of the North American high is a key factor controlling atmospheric conditions favorable for the occurrence of high turbulent air–sea heat fluxes in the North Atlantic mid- and subpolar latitudes.

Transient heat transfer characterization of impinging hot / cold jets by analytical IHCP

Unknown transient surface temperature and heat flux distribution at the impingement side (front side) is estimated from known temperature distribution at non-impingement side (back side) using analytical solution to three dimensional inverse heat conduction problem (IHCP). Back side input temperature data are obtained by running forward code in Fluent. Hot as well as cold impinging jets are characterized with the help of this solution. Laminar and turbulent jets at nozzle to plate spacing (Z/d) equal to 4 are considered. Hot gas at temperature 500 K and 3000 K is impinged on a 1 mm flat plate which considered initially at temperature 300 K in case of heating application. Whereas in cooling application, flat plate is initially assumed at temperature 673 K and isothermal air jet at 293 K is impinged on it. The temperature and heat flux estimation data by present technique is in very good agreement with the simulation data.

The heat transfer characteristics and rewetting behavior of hot horizontal downward facing surface by round water jet impingement

Present paper reports the heat transfer characteristics and rewetting behavior of 0.15 mm thick hot horizontal stainless steel foil (SS-304) by circular impinging jet from bottom side through experimental investigation. The transient temperature of the hot foil is recorded by using thermal imaging camera (A655sc, FLIR system). Tests are performed for a varied range of Reynolds number (Re = 2500–10,000), nozzle to plate distance (z/d = 4–10) and initial surface temperature 500 ± 10 °C. Transient temperature obtained from thermal imaging camera is used to evaluate various parameters such as surface heat flux distribution, rewetting time, rewetting temperature and rewetting velocity. Surface heat flux is found to attain maximum value at the stagnation point and gradually decreases in the radial direction away from the stagnation point. Based on the experimental investigation correlations have been proposed to predict various parameters such as surface heat flux, rewetting temperature and non-dimensional rewetting velocity as a function of various parameters, namely, Reynolds number, non-dimensional radial distance and non-dimensional nozzle to plate distance.

Numerical study of the radiation effect on the jet array impinging heat transfer in a feeding pipe

ABSTRACTThe present study deals with the turbine casing radiation effect on the impinging cooling encountered in the blade tip active clearance control (ACC) system of aero-engine turbine. To this end, numerical simulations are carried out for a simplified model, that is, a pipe with a single row of impinging jets. The effects of the nozzle-to-plate distance to the diameter of the impinging hole (H/d = 2–8), the number of the holes (n = 17–68), the impinging wall temperature (Tp = 400–800 K), and the inlet Reynolds number (Re = 5,000–20,000) on the flow and heat transfer are investigated. Analysis is performed on the radiation heat transfer effects on the corresponding flow fields and surface heat flux distributions. The results indicate that, with the radiation included in the simulations, the mass flow rate of the cooling jet near the end of the pipe decreases significantly under the conditions of high wall temperature and small nozzle-to-plate distance. Radiation heat transfer should be accounted for in the numerical study for the casing cooling as it affects the flow and heat transfer remarkably. When the nozzle-to-plate distance is relatively large, such as H/d is larger than 8, the radiative heating leads to uniform heat flux and the radiative heating can suppress the uneven distributions of the heat flux.

Asymmetrical Non-Uniform Heat Flux Distributions For Laminar Flow Heat Transfer With Mixed Convection In a Horizontal Circular Tube

ABSTRACTNon-symmetric heat flux distributions in terms of gravity in solar collector tubes influence buoyancy-driven secondary flow which has an impact on the associated heat transfer and pressure drop performance. In this study the influence of the asymmetry angle (0°, 20°, 30° and 40°) with regard to gravity for non-uniform heat flux boundaries in a horizontal circular tube was investigated numerically. A stainless steel tube with an inner diameter of 62.68 mm, a wall thickness of 5.16 mm, and a length of 10 m was considered for water inlet temperatures ranging from 290 K to 360 K and inlet Reynolds numbers ranging from 130 to 2000. Conjugate heat transfer was modelled for different sinusoidal type outer surface heat flux distributions with a base-level incident heat flux intensity of 7.1 kW/m2. It was found that average internal heat transfer coefficients increased with the circumferential span of the heat flux distribution. Average internal and axial local heat transfer coefficients and overall friction factors were at their highest for symmetrical heat flux cases (gravity at 0º) and lower for asymmetric cases. The internal heat transfer coefficients also increased with the inlet fluid temperature and decreased with an increase in the external heat loss transfer coefficient. Friction factors decreased with an increase in fluid inlet temperature or an increase in the external heat loss transfer coefficients of the tube model.

Gravity darkening in late-type stars

Context.Recent interferometric data have been used to constrain the brightness distribution at the surface of nearby stars, in particular the so-called gravity darkening that makes fast rotating stars brighter at their poles than at their equator. However, good models of gravity darkening are missing for stars that posses a convective envelope.Aim.In order to better understand how rotation affects the heat transfer in stellar convective envelopes, we focus on the heat flux distribution in latitude at the outer surface of numerical models.Methods.We carry out a systematic parameter study of three-dimensional, direct numerical simulations of anelastic convection in rotating spherical shells. As a first step, we neglect the centrifugal acceleration and retain only the Coriolis force. The fluid instability is driven by a fixed entropy drop between the inner and outer boundaries where stress-free boundary conditions are applied for the velocity field. Restricting our investigations to hydrodynamical models with a thermal Prandtl number fixed to unity, we consider both thick and thin (solar-like) shells, and vary the stratification over three orders of magnitude. We measure the heat transfer efficiency in terms of the Nusselt number, defined as the output luminosity normalised by the conductive state luminosity.Results.We report diverse Nusselt number profiles in latitude, ranging from brighter (usually at the onset of convection) to darker equator and uniform profiles. We find that the variations of the surface brightness are mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the dynamics, the heat flux is weakened in the equatorial region by the zonal wind and enhanced at the poles by convective motions inside the tangent cylinder. In the presence of a strong background density stratification however, as expected in real stars, the increase of the local Rossby number in the outer layers leads to uniformisation of the surface heat flux distribution.

Quantification of the heat transfer during the plasma arc re-melting of titanium alloys

This paper summarizes the development and application of an Inverse Heat Conduction Code (IHCC) to determine the surface heat flux distribution from an industrial plasma torch applied to heat a sample of Ti-6wt%Al-4wt%V (Ti64) alloy. The test (trial) was conducted within an industrial scale plasma arc furnace and the sample was instrumented with 15 thermocouples embedded below the top surface. The sample was heated for 278 s, which allowed sufficient time for a liquid pool to form within the sample. Following the trial, the sample was sectioned to obtain the liquid pool profile. The IHCC analysis method described in the paper is based on the future time-step approach and uses the commercial finite element code ABAQUS™ as the forward conduction engine. The IHCC analysis was conducted with both isotropic thermal conductivity and anisotropic thermal conductive in the liquid. The later, was used to approximate the effect of fluid flow on heat transport in the liquid. Additionally, the method used linear interpolation to vary the estimated heat flux between the discrete heat flux evaluation points associated with the thermocouple positions. The results indicated that it is critical to account for fluid flow and suggest that the heat flux distribution can be accurately described by two over-lapping Gaussian distributions: one narrow distribution associated with convective heat transfer; and a second, broader distribution, associated with radiation. An overall heat transfer efficiency of 28% was estimated from the heat flux distribution.

Transient inverse heat conduction problem of quenching a hollow cylinder by one row of water jets

In this study, a two-dimensional linear transition inverse heat conduction problem (IHCP) was solved using the Generalized Minimal Residual Method (GMRES) in quenching process by water jets. The inverse solution method was validated by set of artificial data and solution sensitivity analysis was done on data noise level, regularization parameter, cell size, etc. An experimental study has been carried out on quenching a rotary hollow cylinder by one row of subcooled water jets. The inverse solution approach enabled prediction of surface temperature and heat flux distribution of test specimen in the quenching experiments by using measured internal specimen temperature. Three different boiling curves were defined in the quenching process of a rotary cylinder. Result obtained by the inverse solution showed clear footprint of rotation in surface temperature and heat flux on each revolution of cylinder and temperature variation damping from quenching surface toward interior of specimen.

An Experimental Investigation on Heat Transfer Characteristics of Hot Surface by Using CuO–Water Nanofluids in Circular Jet Impingement Cooling

In the present study, an experimental investigation has been carried out to analyze the heat transfer characteristics of CuO–water nanofluids jet on a hot surface. A rectangular stainless steel foil (AISI-304, 0.15 mm thick) used as the test surface is electrically heated to obtain the required initial temperature (500 °C). The distribution of surface heat flux on the target surface is evaluated from the recorded thermal images during transient cooling. The effect of nanoparticle concentration and Reynolds number of the nanofluids on the heat transfer characteristics is studied. Tests are performed for varied range of Reynolds number (5000 ≤ Re ≤ 12,000), two different CuO–water nanofluids concentration (Ф = 0.15%, 0.6%) and two different nozzle to plate distance (l/d = 6, 12). The enhancement in Nusselt number for CuO–water nanofluids was found to be 14% and 90%, for nanofluids concentration of Ф = 0.15% and Ф = 0.60%, respectively, compared to pure water. The test surface characteristics after nanofluids jet impingement are studied using scanning electron microscope (SEM). Based on the investigation, a correlation among various parameters, namely, Reynolds number (Re), Prandtl number (Pr), nozzle to plate distance (l/d), and Nusselt number (Nu), is presented.

Model-based optimization of the heat flux distribution of IR-heaters for high heat flux testing

For the testing of helium cooled plasma facing components a homogeneous surface heat flux distribution has to be generated with up to 500kW/m2 in the case of the ITER Test Blanket Module. One option is to use infrared radiation heaters which consist of several quartz glass (fused silica) tubes with tungsten filaments inside to generate the required heat flux. This paper introduces the numerical model of the heater which has been investigated in the SIRHEX (“Surface Infrared Radiation Heating Experiment”) facility at KIT. The model uses a transient simulation to assess the heat flux distribution on the surface of the test mock-up. To validate the model, the numerical results are compared with the latest results from SIRHEX. Using the now qualified model, the heater set-up is optimized to generate a homogeneous distribution for a future test of a blanket first wall.

Thermal investigations on methane-air premixed flame jets of multi-port burners

The multi-port burners are utilised in various domestic and industrial heating appliances. The thermal performance of these appliances is usually performed with loading water test. An attempt is made in this work to thermally characterise the methane-air premixed impinging flame jets of multi-port gas burner employing air jet cooling technique. The present method has an advantage that apart from the thermal efficiency, the uniformity in surface heat flux, Nusselt number and effectiveness distributions can be found. The experiments are performed with inline and staggered configurations of multi-port plate burner. The thermal performance for varying mixture Reynolds number, equivalence ratio and burner to plate spacing is presented. The inline configuration performs better in terms of thermal efficiency. However, the staggered configuration produced more uniform surface heat flux.

A modified quasi-boundary value method for solving the radially symmetric inverse heat conduction problem

In this paper, we consider a radially symmetric inverse heat conduction problem of determining the surface heat flux distribution from a fixed location inside a cylinder. This problem is ill-posed in the Hadamard sense and a conditional stability estimate is given for it. A modified quasi-boundary value regularization method is applied to formulate a regularized solution, and a sharp error estimate between the approximate solution and the exact solution is established by choosing a suitable regularization parameter. A numerical example is presented to verify the efficiency of the regularization method.

Effects of finiteness on the thermo-fluid-dynamics of natural convection above horizontal plates

A rigorous and systematic computational and theoretical study, the first of its kind, for the laminar natural convective flow above rectangular horizontal surfaces of various aspect ratios ϕ (from 1 to ∞) is presented. Two-dimensional computational fluid dynamic (CFD) simulations (for ϕ → ∞) and three-dimensional CFD simulations (for 1 ≤ ϕ < ∞) are performed to establish and elucidate the role of finiteness of the horizontal planform on the thermo-fluid-dynamics of natural convection. Great care is taken here to ensure grid independence and domain independence of the presented solutions. The results of the CFD simulations are compared with experimental data and similarity theory to understand how the existing simplified results fit, in the appropriate limiting cases, with the complex three-dimensional solutions revealed here. The present computational study establishes the region of a high-aspect-ratio planform over which the results of the similarity theory are approximately valid, the extent of this region depending on the Grashof number. There is, however, a region near the edge of the plate and another region near the centre of the plate (where a plume forms) in which the similarity theory results do not apply. The sizes of these non-compliance zones decrease as the Grashof number is increased. The present study also shows that the similarity velocity profile is not strictly obtained at any location over the plate because of the entrainment effect of the central plume. The 3-D CFD simulations of the present paper are coordinated to clearly reveal the separate and combined effects of three important aspects of finiteness: the presence of leading edges, the presence of planform centre, and the presence of physical corners in the planform. It is realised that the finiteness due to the presence of physical corners in the planform arises only for a finite value of ϕ in the case of 3-D CFD simulations (and not in 2-D CFD simulations or similarity theory). The presence of physical corners is related here to several significant aspects of the solution—the conversion of in-plane velocity to out-of-plane velocity near the diagonals, the star-like non-uniform distribution of surface heat flux on heated planforms, the three-dimensionality of the temperature field, and the complex spatial structure of the velocity iso-surfaces. A generic theoretical correlation for the Nusselt number is deduced for the averaged surface heat flux for various rectangular surfaces (1 ≤ ϕ < ∞) over a wide range of Grashof number. Innovative use of numerical visualization images is made to generate a comprehensive, quantitative understanding of the physical processes involved.

Numerical study on condensation heat transfer of trapezoid grooved surfaces

This article presents a numerical analysis and experimental study on condensation heat transfer and fluid flow for filmwise condensation on trapezoid grooved surfaces. First, a physical model was properly simplified based on some reasonable assumptions. Then, the coupled non-linear governing equations for the mass transfer, fluid flow, and two-dimensional thermal conduction were developed. The relationship between z-coordinate and heat transfer was obtained by solving the equations numerically. The influences of groove length and basic angle were discussed. The calculation results showed that the heat flux decreased with increase in groove length, and the decline range also decreased gradually. The calculation results also suggested that the heat flux through groove with α = 60° was lower than the groove with α = 75° at the top of the groove, while the opposite conclusion was obtained at the low parts. The distributions of wall temperature and heat flux on trapezoid groove were also studied systematically. The distribution of surface temperature and heat flux presents obvious lateral inhomogeneity, and the maximum wall temperature and heat flux were both obtained in region II. The thermal resistance of groove with α = 60° was lower but the liquid-discharged ability was better than that of groove with α = 75°. In order to validate the feasibility and reliability of the present analyses and to further investigate the heat transfer performance of trapezoid grooved surfaces, experiments were carried out with three condensing plates including two trapezoid grooved surfaces in different physical dimensions and one smooth surface. The experimental data obtained under various schooling were compared with the calculations, and the experimental results for different condensing plates are all in good agreement with the numerical model, with a maximum deviation less than 15%. Moreover, the trapezoid grooves can enhance the condensation heat transfer by 1.5–2.5 times higher than the smooth surface. The present analyses are feasible and can be used in the parameter design and heat transfer calculation of trapezoid grooved surfaces.

Determination of surface heat flux distributions by using surface temperature measurements and applying inverse techniques

The surface heat flux and its distribution in space and time is an important parameter in numerous engineering problems. In this content, we present a method for estimating transient, multidimensional heat flux distributions by measuring the temperature distribution on the surface of an object and by applying inverse techniques. The proposed method can be used for transient heat transfer processes and particularly for heat transfer problems where lateral heat conduction along the surface plays a significant role. The method is based on two-dimensional sensitivity matrices, which have been expanded to a three-dimensional sensitivity approach. Thereby, the profile of the heat flux does not have to be known beforehand. As the introduced method is applied on the surface of the investigated objects, the frequent problem with instabilities due to the ill-posedness of the inverse problem is significantly reduced and no further stabilization procedures are required. The method improves available methods based on one-dimensional heat conduction, due to the consideration of three-dimensional heat conduction.

Boiling Visualization of Two Adjacent Impinging Jets on Hot Steel Plate

The simultaneous measurement between the boiling visualization and the boiling heat transfer characteristics by two adjacent impinging jets on hot steel plate was made by the experimental technique that has a function of high-temperature flat-plate heat flux gauge. The 22 K-type thermocouples were installed at 1 mm below the surface of flat-plate heat flux gauge. The 2-D inverse heat conduction was formulated to solve the surface temperature and heat flux. The boiling visualization was synchronized with a 4K video camera which was meaningful to understand complex boiling heat transfer phenomena. The heat flux gauge was uniformly heated up to 900°C by induction heating. The successive boiling images show where the nucleate boiling starts to occur on hot surface and the film boiling turns to be collapsed. The measured surface temperature and heat flux distribution agrees well with the corresponding boiling visualization: While heat transfer at the stagnation point shows a maximum heat flux, the interaction between two adjacent impinging jets exhibits a relative high heat flux and a steep temperature gradient until the end of boiling heat transfer at which single-phase convection occurs near 200°C.

Numerical study of impinging jets heat transfer with different nozzle geometries and arrangements for a ground fast cooling simulation device

In this paper, a comparative study is performed to check the nozzle geometry and arrangement effects on impinging jets heat transfer performance to help the design of a ground fast cooling simulation device which is used for the thermal tests of high speed flight vehicles. Based on the simplified physical model, the impinging jets heat transfer is modeled using the shear-stress transport (SST) k-ω turbulence model. A total of 21 different nozzle configurations including 7 geometries are considered in the numerical simulation. Heat transfer performances concerning heat transfer intensity and heat flux uniformity in different cases are compared with each other. Analysis is given on the corresponding flow fields and surface heat flux distributions. To help the optimization of nozzle geometry and arrangement in designing the device, an indicator named QU ratio is proposed for the overall performance evaluation of the nozzle configurations. The effectiveness of the QU ratio is validated based on the numerical results and it can be used to help determine the best design for certain given conditions of the ground fast cooling device.