Estimation Of Surface Heat Flux Research Articles

Methodology of surface heat flux estimation for 2D multi-layer mediums

Surface heat flux is an important parameter in various industrial applications. It is often estimated based on measured temperature by solving inverse heat conduction problems (IHCPs). In the present work, a filter solution to solve 1D single-layer IHCPs is applied to calculate the surface heat flux for 2D multi-layer mediums. An optimal comparison criterion is implemented for 2D IHCPs to optimize the key regularization parameters. Afterward, the 2D filter solution is used for heat flux estimation with thin-film thermocouple (TFTC) and fine thermocouple (FTC) measurements during cryogen spray cooling. The accuracy of the estimated heat fluxes is tested with the measured temperature response to cryogen spray cooling. A small error (maximum value of 1.0740°C) is observed between the temperature simulated based on estimated heat fluxes and the measured temperature. The maximum heat flux obtained by the 2D filter solution is 13.6% higher than that obtained by 1D method for TFTC measurement. This finding indicates that lateral heat transfer cannot be disregarded, especially when the heat conductivity coefficient of the material is large.

A simple temperature domain two‐source model for estimating agricultural field surface energy fluxes from Landsat images

AbstractA simple and robust satellite‐based method for estimating agricultural field to regional surface energy fluxes at a high spatial resolution is important for many applications. We developed a simple temperature domain two‐source energy balance (TD‐TSEB) model within a hybrid two‐source model scheme by coupling “layer” and “patch” models to estimate surface heat fluxes from Landsat thematic mapper/Enhanced Thematic Mapper Plus (TM/ETM+) imagery. For estimating latent heat flux (LE) of full soil, we proposed a temperature domain residual of the energy balance equation based on a simplified framework of total aerodynamic resistances, which provides a key link between thermal satellite temperature and subsurface moisture status. Additionally, we used a modified Priestley‐Taylor model for estimating LE of full vegetation. The proposed method was applied to TM/ETM+ imagery and was validated using the ground‐measured data at five crop eddy‐covariance tower sites in China. The results show that TD‐TSEB yielded root‐mean‐square‐error values between 24.9 (8.9) and 78.2 (21.4) W/m2 and squared correlation coefficient (R2) values between 0.60 (0.51) and 0.97 (0.90), for the estimated instantaneous (daily) surface net radiation, soil, latent, and sensible heat fluxes at all five sites. The TD‐TSEB model shows good accuracy for partitioning LE into soil (LEsoil) and canopy (LEcanopy) components with an average bias of 11.1% for the estimated LEsoil/LE ratio at the Daman site. Importantly, the TD‐TSEB model produced comparable accuracy but requires fewer forcing data (i.e., no wind speed and roughness length are needed) when compared with two other widely used surface energy balance models. Sensitivity analyses demonstrated that this accurate operational model provides an alternative method for mapping field surface heat fluxes with satisfactory performance.

Estimation of surface heat flux in continuous casting mould with limited measurement of temperature

Continuous casting mould is exposed to high heat flux due to its contact with the hot molten metal. The state of heat transfer in a mould and steel solidification depends on the magnitude of the mould boundary heat flux. In the present study, a mathematical model is developed to determine the heat flux across the hot surface of continuous casting mould from limited temperature measurement. The model is based on two-dimensional inverse heat transfer technique that was solved using the conjugate gradient method. Direct problem which involves two-dimensional conduction in the mould is first solved and validated. The inverse problem was tested by using the simulated temperature data obtained from the solution of a direct problem, where good agreement between the actual and estimated boundary heat flux is found. The Gaussian noises are added to the simulated temperatures to mimic the temperature measurement errors for testing anti-noise ability of the inverse problem model. Further, boundary heat flux is also estimated for a continuous casting mould using actually measured plant data. The model is applied to three test cases with temperature data obtained under different operating conditions and the results are analyzed. It has been observed that the proposed methodology results in accurate boundary heat flux estimation. Higher boundary heat flux are obtained for cases with higher casting speed as compared to cases with lower casting speed.

Atlantic meridional heat transports computed from balancing Earth's energy locally

AbstractThe Atlantic Meridional Overturning Circulation plays a major role in moving heat and carbon around in the ocean. A new estimate of ocean heat transports for 2000 through 2013 throughout the Atlantic is derived. Top‐of‐atmosphere radiation is combined with atmospheric reanalyses to estimate surface heat fluxes and combined with vertically integrated ocean heat content to estimate ocean heat transport divergence as a residual. Atlantic peak northward ocean heat transports average 1.18 ± 0.13 PW (1 sigma) at 15°N but vary considerably in latitude and time. Results agree well with observational estimates at 26.5°N from the RAPID array, but for 2004–2013 the meridional heat transport is 1.00 ± 0.11 PW versus 1.23 ± 0.11 PW for RAPID. In addition, these results have no hint of a trend, unlike the RAPID results. Strong westerlies north of a meridian drive ocean currents and an ocean heat loss into the atmosphere that is exacerbated by a decrease in ocean heat transport northward.

Surface flux and ocean heat transport convergence contributions to seasonal and interannual variations of ocean heat content

AbstractWe present an observation‐based heat budget analysis for seasonal and interannual variations of ocean heat content (H) in the mixed layer (Hmld) and full‐depth ocean (Htot). Surface heat flux and ocean heat content estimates are combined using a novel Kalman smoother‐based method. Regional contributions from ocean heat transport convergences are inferred as a residual and the dominant drivers of Hmld and Htot are quantified for seasonal and interannual time scales. We find that non‐Ekman ocean heat transport processes dominate Hmld variations in the equatorial oceans and regions of strong ocean currents and substantial eddy activity. In these locations, surface temperature anomalies generated by ocean dynamics result in turbulent flux anomalies that drive the overlying atmosphere. In addition, we find large regions of the Atlantic and Pacific oceans where heat transports combine with local air‐sea fluxes to generate mixed layer temperature anomalies. In all locations, except regions of deep convection and water mass transformation, interannual variations in Htot are dominated by the internal rearrangement of heat by ocean dynamics rather than the loss or addition of heat at the surface. Our analysis suggests that, even in extratropical latitudes, initialization of ocean dynamical processes could be an important source of skill for interannual predictability of Hmld and Htot. Furthermore, we expect variations in Htot (and thus thermosteric sea level) to be more predictable than near surface temperature anomalies due to the increased importance of ocean heat transport processes for full‐depth heat budgets.

An inverse method for the estimation of a long-duration surface heat flux on a finite solid

The nonlinear inverse heat conduction problem (IHCP) is resolved for the estimation of surface heat flux from two temperature measurements inside a finite domain. An improvement is achieved in this study by optimizing the rescaled time used to linearize the heat conduction equation with temperature-dependent thermal properties. A closed-form solution of the transient temperature is derived, considering the inhomogeneous boundary conditions. The direct solution is further incorporated into a sequential technique for inverse analysis, and the uncertainty of inverse solution with respect to input parameters is obtained. The results from a representative example show that the method is computationally efficient and the inverse solution can be stabilized by increasing the rescaled time step size. Thus, the effect of the real time step on the ill-posedness can be reduced and the increase of sampling rate in experiment is possible. The present method is useful for the prediction of long-duration heat flux in thermal engineering.

Estimation of surface heat flux in a one-dimensional hyperbolic bio-heat conduction problem with temperature-dependent properties during thermal therapy

In this study, an inverse analysis is presented to determine the time-dependent surface heat flux of a living tissue in a one-dimensional non-Fourier bio-heat conduction problem by using temperature responses measured within the medium. The properties of tissue are assumed to be function of temperature. Therefore, this problem is classified as a nonlinear inverse problem of hyperbolic bio-heat conduction. The inverse problem is solved through the minimization of an objective function by the conjugate gradient method. Three examples are presented to show that the proposed method can be implemented to estimate the unknown surface heat flux. In addition, the effects of measurement error, measurement location, initial guess, nonlinearity and thermal relation time on the precision of the estimation are investigated. The results show that the proposed method is an accurate and robust method to determine inversely the surface heat flux in hyperbolic bio-heat conduction with temperature-dependent properties.

Surface heat flux estimation with embedded fiber Bragg gratings measurements: Numerical study

4 probes with Fiber Bragg Gratings (FBGs) will be integrated in Plasma Facing Component (PFC) of the WEST lower divertor in order to measure the bulk temperature distribution in the poloidal direction (11 locations equally spaced). A 2D nonlinear unsteady calculation combined with the Conjugate Gradient Method (CGM) and the adjoint state is used in order to estimate the space and time evolution of the surface heat flux based on temperature measurements. Synthetic measurements are generated assuming optical projection of the heat flux taking into account physical effects such as heat flux decay length (λq) and power spreading factor (S) in the private flux region and geometrical effects such as surface chamfering and round leading edges of the component. The inverse method is applied on different synthetic measurements in order to evaluate the ability of using FBG measurements to characterize the heat flux poloidal profile.

Heat Flux estimation in WEST divertor with embedded thermocouples

The present paper deals with the surface heat flux estimation with embedded thermocouples (TC) in a Plasma Facing Component (PFC) of the WEST Tokamak. A 2D nonlinear unsteady calculation combined with the Conjugate Gradient Method (CGM) and the adjoint state is achieved in order to estimate the time evolution of the heat flux amplitude and decay length λq. The method is applied on different synthetic measurements in order to evaluate the accuracy of the method. The synthetic measurements are generated with realistic values of λq and magnitudes as those expected for ITER.

Estimates of Global Surface Hydrology and Heat Fluxes from the Community Land Model (CLM4.5) with Four Atmospheric Forcing Datasets

Abstract Global land surface hydrology and heat fluxes can be estimated by running a land surface model (LSM) driven by the atmospheric forcing dataset. Previous multimodel studies focused on the impact of different LSMs on model results. Here the sensitivity of the Community Land Model, version 4.5 (CLM4.5), results to the atmospheric forcing dataset is documented. Together with the model default global forcing dataset (CRU–NCEP, hereafter CRUNCEP), three newly developed, reanalysis-based, near-surface meteorological datasets (i.e., MERRA, CFSR, and ERA-Interim) with the precipitation adjusted by the Global Precipitation Climatology Project monthly product were used to drive CLM4.5. All four simulations were run at 0.5° × 0.5° grids from 1979 to 2009 with the identical initialization. The simulated monthly surface hydrology variables, fluxes, and the forcing datasets were then evaluated against various observation-based datasets (soil moisture, runoff, snow depth and water equivalent, and flux tower measurements). To partially avoid the mismatch between model gridbox values and point measurements, three approaches were taken. The model simulations based on three newly constructed forcing datasets are overall better than the simulation from CRUNCEP, in particular for soil moisture and snow quantities. The ensemble mean from the CLM4.5 simulations using the four forcing datasets is generally superior to individual simulations, and the ensemble mean latent and sensible heat fluxes over global land (60°S–90°N) are 42.8 and 40.3 W m−2, respectively. The differences in both precipitation and other atmospheric forcing variables (e.g., air temperature and downward solar radiation) contribute to the differences in simulated results. The datasets are available from the authors for further evaluation and for various applications.

Uncertainty Quantification in Land Surface Hydrologic Modeling: Toward an Integrated Variational Data Assimilation Framework

Variational data assimilation (VDA) is an effective technique for the estimation of land surface heat fluxes. In this method, sequences of remotely sensed land surface temperature measurements are assimilated into a dynamic surface energy balance model to estimate the key unknown parameters of the turbulent heat fluxes. Despite the advantages of the VDA technique in the retrieval of land surface heat fluxes, it suffers from a key limitation, which is its tendency to be ill posed. Moreover, unlike ensemble-based schemes, the VDA method itself does not provide estimates of the predictive uncertainty of estimated parameters and, thus, retrieved fluxes. This research addresses these shortcomings by proposing an uncertainty quantification (UQ) framework for the VDA technique. The proposed framework utilizes uncertainty analysis and analysis of error covariance approximation as a tool to quantify the uncertainty of estimated parameters and to guide the formulation of a well-posed estimation problem. It provides a calibration-free tool to assess the performance of the VDA technique in retrieving land surface heat fluxes over a range of land surfaces and climatic conditions. The UQ framework suggests that the VDA approach performs poorly over wet and highly vegetated land surface regions and when the difference between land surface and air temperature is low. Moreover, it reveals that characterizing the effect of vegetation dynamics on the bulk heat transfer coefficient reduces the correlation between unknown parameters and, hence, leads to a more robust estimation of parameters.

A Novel IHCP Calculation Scheme to Estimate Surface Heat Flux during Impinging Cooling

This study introduces a novel inverse heat conduction problem (IHCP) calculation scheme to solve the surface heat flux of a subject with impinging cooling. From measured temperature records, the unknown boundary condition can be derived with one of three proposed algorithms. The scheme can then be performed without multiple iterations, and is much faster than traditional methods for IHCP. An impinging cooling apparatus is established to demonstrate the proposed scheme. The apparatus is to experimentally explore three impinging patterns, three impinging positions, and three unknown boundary condition derivation algorithms. The experimental results show that the proposed calculation scheme actually saves calculation time, and provides more accurate results. The most suitable unknown boundary condition derivation algorithm is suggested for each combination of operating parameters.

Inverse estimation of near-field temperature and surface heat flux via single point temperature measurement

A concept was developed to inversely estimate the near-field temperature as well as the surface heat flux for the transient heat conduction problem with boundary condition of the unknown heat flux. The mathematical formula was derived for the inverse estimation of the near-field temperature and surface heat flux via a single point temperature measurement. The experiments were carried out in a vacuum chamber and the theoretically predicted temperatures were justified in specific positions. The inverse estimation principle was validated and the estimation deviation was evaluated for the present configuration.

Transient heat transfer behavior of water spray evaporative cooling on a stainless steel cylinder with structured surface for safety design application in high temperature scenario

High heat transfer performance of spray cooling on structured surface might be an additional measure to increase the safety of an installation against any threat caused by rapid increase in the temperature. The purpose of present experimental study is to explore heat transfer performance of structured surface under different spray conditions and surface temperatures. Two cylindrical stainless steel samples were used, one with pyramid pins structured surface and other with smooth surface. Surface heat flux of 3.60, 3.46, 3.93 and 4.91 MW/m2 are estimated for sample initial average temperature of 600, 700, 800 and 900 °C, respectively for an inlet pressure of 1.0 MPa. A maximum cooling rate of 507 °C/s was estimated for an inlet pressure of 0.7 MPa at 900 °C for structured surface while for smooth surface maximum cooling rate of 356 °C/s was attained at 1.0 MPa for 700 °C. Structured surface performed better to exchange heat during spray cooling at initial sample temperature of 900 °C with a relative increase in surface heat flux by factor of 1.9, 1.56, 1.66 and 1.74 relative to smooth surface, for inlet pressure of 0.4, 0.7, 1.0 and 1.3 MPa, respectively. For smooth surface, a decreasing trend in estimated heat flux is observed, when initial sample temperature was increased from 600 to 900 °C. Temperature-based function specification method was utilized to estimate surface heat flux and surface temperature. Limited published work is available about the application of structured surface spray cooling techniques for safety of stainless steel structures at very high temperature scenario such as nuclear safety vessel and liquid natural gas storage tanks.

Algorithms for the estimation of transient surface heat flux during ultra-fast surface cooling

Surface heat flux is an important parameter in various industrial applications. This paper compared several algorithms for estimating surface heat flux using both simulated heat flux and measured temperature in response to ultra-fast surface cooling. Two different strategies were employed to measure the surface temperature, using the thin film thermocouple with a 2μm depth deposited directly on the cooling substrate surface (direct surface temperature measurement) and the fine thermocouple with a 100μm bead diameter placed on the surface of the cooling substrate and covered with aluminum foil (indirect surface temperature measurement). The algorithms of Duhamel’s theorem, sequential function specification method (SFSM) and transfer function method are briefly analyzed. A new method is proposed that the surface temperature is first calculated based on Duhamel’s theorem and then the surface heat flux can be estimated, in order to improve the accuracy of results in the case of the indirect surface temperature measurement method. The transfer function is obtained by solving an auxiliary problem and thus the transfer function method can be implemented to solve multilayer, semi-infinite inverse heat conduction problems. Accuracy and sensitivity to noise are examined using both the simulated triangular pulse heat flux and the measured temperature data. Duhamel’s theorem is insensitive to noise, but is unsuitable for predicting surface heat flux in the indirect measurement method of surface temperature. The SFS method can provide acceptable results of surface heat flux using both measurement methods. However, a noticeable discrepancy exists as the heat flux changes extremely quickly and it suffers considerably from noise. The transfer function and newly proposed methods are both effective in inhibiting noise, and produce very similar results, which match the simulated heat flux exactly and have a negligible standard deviation and residual temperature.

A Hybrid Procedure for the Sequential Estimation of Surface Heat Flux From Measurements of Surface Temperature

The sequential estimation of surface heat flux from discrete and noisy data of surface temperature is an ill-posed problem. From Duhamel's theorem and Fourier's law and using a stabilization technique based on the sequential application of the ordinary least squares (SOLS), we obtain a relatively simple but effective method. As the SOLS method uses a least squares fit over r-future and r-past temperatures, this method can be compared with the well-known function specification method (FSM). FSM is a more general method, but the numerical validations considered in this study reveal that the SOLS method gives better results. It is also shown that SOLS cannot be guided by the residual principle and consequently cannot be used in a practical scope. The ultimate goal of this study is to obtain a reliable estimation of heat flux history in an on-line industrial process where the tuneable parameter should be a time-variable r-value and it must be automatically updated from the experimental data. This requires that (i) the corresponding SOLS algorithm must be rewritten in recursive form, (ii) the classical definition of the residual principle is rewritten in recursive form, and (iii) the estimates are obtained from a hybrid procedure based on SOLS and FSM.

Online heat flux estimation using artificial neural network as a digital filter approach

Surface heat flux estimation using temperature measurement data from the interior points is known as inverse heat conduction problem (IHCP). Several methods have been developed as solution techniques for IHCP’s including analytical and numerical approaches. Digital filter representation for IHCP solution (Woodbury and Beck, 2013; Beck et al., 1985) is one of the methods which can be used for near real-time heat flux estimation. In this study, artificial neural network (ANN) is utilized as a digital filter, for near real-time heat flux estimation using temperature measurement data. Considering temperatures as the inputs and heat flux as the output, the weights can be interpreted as filter coefficients. The proposed approach is used for both constant and temperature dependent material properties. The method developed is tested through several test cases using exact solutions and numerical models. The results show that ANN can be used as a digital filter method for near real-time surface heat flux estimation. The advantages and disadvantages of the method are also discussed.

Estimation of surface heat flux for ablation and charring of thermal protection material

Ablation of the thermal protection material of the reentry hypersonic flight vehicle is a complex physical and chemical process. To estimate the surface heat flux from internal temperature measurement is much more complex than the conventional inverse heat conduction problem case. In the paper, by utilizing a two-layer pyrogeneration-plane ablation model to model the ablation and charring of the material, modifying the finite control volume method to suit for the numerical simulation of the heat conduction equation with variable-geometry, the CGM along with the associated adjoint problem is developed to estimate the surface heat flux. This estimation method is verified with a numerical example at first, the results show that the estimation method is feasible and robust. The larger is the measurement noise, the greater is the deviation of the estimated result from the exact value, and the measurement noise of ablated surface position has a significant and more direct influence on the estimated result of surface heat flux. Furthermore, the estimation method is used to analyze the experimental data of ablation of blunt Carbon-phenolic material Narmco4028 in an arc-heater. It is shown that the estimated surface heat flux agrees with the heating power value of the arc-heater, and the estimation method is basically effective and potential to treat the engineering heat conduction problem with ablation.

A comparison of optical and microwave scintillometers with eddy covariance derived surface heat fluxes

Accurate measurements of energy fluxes between land and atmosphere are important for understanding and modeling climatic patterns. Several methods are available to measure heat fluxes, and scintillometers are becoming increasingly popular because of their ability to measure sensible (H) and latent (LvE) heat fluxes over large spatial scales. The main motivation of this study was to test the use of different methods and technologies to derive surface heat fluxes.Measurements of H and LvE were carried out with an eddy covariance (EC) system, two different makes of optical large aperture scintillometers (LAS) and two microwave scintillometers (MWS) with different frequencies at a pasture site in a semi-arid environment of New South Wales, Australia. We used the EC measurements as a benchmark. Fluxes derived from the EC system and LAS systems agreed (R2>0.94), whereas the MWS systems measured lower H (bias ∼60Wm−2) and larger LvE (bias ∼65Wm−2) than EC. When the scintillometers were compared against each other, the two LASs showed good agreement of H (R2=0.98), while MWS with different frequencies and polarizations led to different results. Combination of LAS and MWS measurements (i.e., two wavelength method) resulted in performance that fell in between those estimated using either LAS or MWS alone when compared with the EC system. The cause for discrepancies between surface heat fluxes derived from the EC system and those from the MWS systems and the two-wavelength method are possibly related to inaccurate assignment of the structure parameter of temperature and humidity. Additionally, measurements from MWSs can be associated with two values of the Bowen ratio, thereby leading to uncertainties in the estimation of the fluxes. While only one solution has been considered in this study, when LvE was approximately less than 200Wm−2, the alternate solution may be more accurate. Therefore, for measurements of surface heat fluxes in a semi-arid or dry environment, the optical scintillometer is recommended, whereas further work will be required to improve the estimation of surface heat fluxes from microwave systems.

Calculation of Heat Flux Across the Hot Surface of Continuous Casting Mold Through Two-Dimensional Inverse Heat Conduction Problem

A novel method for the estimation of the mold hot surface heat flux based on the measured responding temperatures from two columns of thermocouples that embedded inside the mold during continuous casting has been developed. The method includes a Two-Dimensional Inverse transient Heat Conduction Problem (2D-IHCP) model that was solved by the conjugate gradient method with Adjoint Equation. The model was validated by comparing the results with those calculated by a robust One-Dimensional Inverse transient Heat Conduction Problem (1D-IHCP). The solution of a test problem indicated that the Mean Absolute Percentage Error of the estimated heat flux calculated by the new method is about 9 to 40 pct of those calculated by the 1D-IHCP. Then, the method is applied to compute the heat flux for a mold simulator experiment. The results indicated that the heat fluxes and temperatures across mold hot surface calculated by 2D-IHCP show the same variation tendency as those calculated by 1D-IHCP. However, the heat fluxes calculated by 2D-IHCP are about 1.2 to 2 times larger than those calculated by 1D-IHCP for the locations below the liquid mold flux surface and are about 50 to 90 pct of those calculated by 1D-IHCP for the locations above the liquid mold flux surface.