Time-dependent Heat Transfer Coefficient Research Articles

Influence of the Shrinkage of the Inner Layer of Steel Tubes on Permissible Thermal Load

This paper presents the results of numerical simulations of heat transfer in a tube with a protective chromium layer on the inner surface made of steel, with different shrinkage temperatures. Shrinkage in the steel is an unfavorable phenomenon because it causes cracks in the chrome coating. The cracks contribute to the peeling of the protective material on the inner surface of the tube. Wear and damage to the chrome layer significantly shortens the tube’s service life. The influence of the type of steel with medium carbon content on heat transfer for a sequence of ten, thirty, and sixty heat impulses was examined. Simulations were carried out for two selected steels with clearly different shrinkage temperatures, i.e., 30HN2MFA and X37CrMoV5-1 (1.2343). In 30HN2MFA steel, the shrinkage effect occurred at a temperature of approx. 750 °C, while in X37CrMoV5-1 steel it occurred at a temperature of approx. 870 °C. In the computational model, 30 cross-sections of the three-meter-long tube were analyzed. A time-dependent heat transfer coefficient was calculated in each zone. Heat transfer simulations were carried out using COMSOL version 6.1 software. This paper shows that for X37CrMoV5-1 steel, the shrinkage temperature on the inner surface of the tube was reached after approx. 60 heat impulses, while for 30HN2MFA steel, it was reached after approx. 30. The greatest differences in the number of impulses occurred for a pipe with a 200 µm thick chrome layer.

High-precision solidification simulation by estimating heat transfer coefficients through data assimilation

Solidification analysis is important for accurately predicting casting processes. A high-precision casting simulation requires accurate data of the physical properties of materials and heat transfer parameters. In particular, the heat transfer coefficient is a major parameter influencing the casting simulation results. Because the heat transfer coefficient is not uniquely determined by the material, it is typically estimated by trial and error, which requires considerable time for accurate estimations. Therefore, we developed a method to quickly estimate the heat transfer coefficient in a casting process by combining data assimilation and solidification simulations. With this method, the time-dependent heat transfer coefficient can be estimated in an appropriate and easy manner. To reproduce the 3D temperature distribution in a casting with high accuracy, we developed a method to estimate multiple heat transfer coefficients simultaneously by combining data assimilation and 3D solidification simulation. Al–5 mass% Si alloy was cast into a sand mold with a casting size of 30 mm × 30 mm × 100 mm, and the temperature was measured at five points in the casting to obtain a cooling curve. Two cooling curves corresponding to locations of 5 mm from the casting wall were used to estimate the two heat transfer coefficients on the side and bottom surfaces, which were simultaneously estimated by data assimilation. The results confirmed that all the five cooling curves could be reproduced with a high accuracy and that high-precision casting simulation was possible.

Uncovering the non-radiative thermal characteristics of a passive radiative cooler under real operating conditions

Passive radiative cooling (PasRadCool), which emits thermal energy from objects to deep cold space through atmospheric transparency, offers complementary and alternative green energy solutions for passive cooling of buildings, clothing, and renewable energy harvesting. Depending on the spectral emissive/absorptive properties of the unit under test (UUT), radiative heat exchanges occur between the UUT, atmosphere, and sun, while at the same time non-radiative heat exchange occurs. The performance of the PasRadCool is determined by the combined thermal and thermodynamic effects of both exchange mechanisms. Although the non-radiative heat exchange, which consists of conductive and convective processes to the outer surfaces of the UUT and the surrounding air fluid, is very sensitive to environmental changes, the actual performance is not fully determined since this feature is considered statically in many studies. Herein, we propose a method that reveals the non-radiative thermal characteristics of the PasRadCool under real operating conditions. With a photonic radiative cooler structure, which we manufacture as a proof of concept, we perform nighttime field test measurements in varying non-radiative thermal conditions. The proposed method extracts the time-dependent non-radiative heat transfer coefficient of the UUT as accurately as possible. We also confirm that our experimental result shows good agreement with both numerical and analytical methods. The proposed approach, which highlights the realistic thermal management of PasRadCool, is not specific to the circumstances of our study and can be applied to all PasRadCool situations with different geometry, material, and environmental conditions.

Trefftz-Type Functions Applied for Subcooled Flow Boiling Heat Transfer Calculations in a Minichannel of Different Spatial Orientation

ABSTRACT The paper describes the results of subcooled flow boiling heat transfer in an asymmetrically heated group of five minichannels 1 mm deep. The heated element for the cooling fluid (FC-72) flowing in the minichannels was a foil made of Haynes-230 alloy. The time-dependent temperature distribution of the outer heated foil surface was recorded as a result of infrared thermography. The test section was oriented in several spatial orientations, that is, 30°, 45°, 60° and 75° inclinations to the horizontal plane. The objective of the numerical calculations, referring to the experimental results, was to determine the time–dependent heat transfer coefficient on the wall-fluid contact surface from the Robin boundary condition. Both the foil and the fluid temperatures were the result of solving the inverse and direct two-dimensional heat transfer problem in two neighboring domains: the heated foil and flowing fluid. The problem was solved using the Trefftz method and the FEM with Trefftz type basis functions. The heat transfer coefficient obtained by two numerical methods appears to be similar. During subcooled flow boiling, at higher minichannel inclination angles, higher values of the heated foil temperature were obtained, as well as higher values of the heat transfer coefficient.

Sequential estimation of the time-dependent heat transfer coefficient using the method of fundamental solutions and particle filters

In many thermal engineering problems involving high temperatures/high pressures, the boundary conditions are not fully known since there are technical difficulties in obtaining such data in hostile conditions. To perform the task of estimating the desired parameters, inverse problem formulations are required, which entail to performing some extra measurements of certain accessible and relevant quantities. In this paper, justified also by uniqueness of solution conditions, this extra information is represented by either local or non-local boundary temperature measurements. Also, the development of numerical methods for the study of coefficient identification thermal problems is an important topic of research. In addition, in order to decrease the computational burden, meshless methods are becoming popular. In this article, we combine, for the first time, the method of fundamental solutions (MFS) with a particle filter sequential importance resampling (SIR) algorithm for estimating the time-dependent heat transfer coefficient in inverse heat conduction problems. Two different types of measurements are used. Numerical results indicate that the combination of MFS and SIR shows high performance on several test cases, which include both linear and nonlinear Robin boundary conditions, in comparison with other available methods.

Estimation of Functional Form of Time-Dependent Heat Transfer Coefficient Using an Accurate and Robust Parameter Estimation Approach: An Inverse Analysis

This paper presents a numerical method to address function estimation problems in inverse heat transfer problems using parameter estimation approach without prior information on the functional form of the variable to be estimated. Using an inverse analysis, the functional form of a time-dependent heat transfer coefficient is estimated efficiently and accurately. The functional form of the heat transfer coefficient is assumed unknown and the inverse heat transfer problem should be treated using a function estimation approach by solving sensitivity and adjoint problems during the minimization process. Based on proposing a new sensitivity matrix, however, the functional form can be estimated in an accurate and very efficient manner using a parameter estimation approach without the need for solving the sensitivity and adjoint problems and imposing extra computational cost, mathematical complexity, and implementation efforts. In the proposed sensitivity analysis scheme, all sensitivity coefficients can be computed in only one direct problem solution at each iteration. In this inverse heat transfer problem, the body shape is irregular and meshed using a body-fitted grid generation method. The direct heat conduction problem is solved using the finite-difference method. The steepest-descent method is used as a minimization algorithm to minimize the defined objective function and the termination of the minimization process is carried out based on the discrepancy principle. A test case with three different functional forms and two different measurement errors is considered to show the accuracy and efficiency of the used inverse analysis.

Transient study of a solar pond under heat extraction from non-convective and lower convective zones considering finite effectiveness of exchangers

The transient performance of a salt gradient solar pond, which experiences heat extraction from both gradient and storage regions has been studied for annual performance via accounting for the overall heat transfer coefficient across heat exchangers. The proposed method after reduced complexities is satisfactorily validated with theory and experiment-based results of pertinent literature. The novelty of the work lies in the fact that, the temperature drop across both non-convective and lower-convective zone exchanger surfaces has been accounted by using a local time and space dependent heat transfer coefficient. Here, it takes into the consideration free convection from the pond to the exchanger surface, and forced convection from the exchanger surface to flowing working fluid. Further, temperature variation of thermo-fluidic parameters of water involving, viscosity, density and thermal conductivity is considered. Detailed numerical investigation reveals that by neglecting this coefficient which is assumed in conventional studies, it can lead to significant errors in the prediction of transient temperature profiles in the pond and the exchangers. Calculations reveal an error of about +69% in the annual extraction efficiency and about −9% in entropy production if the conventional assumption is used as opposed to realistic technique presented herein. Interestingly, the present study reveals that there is an optimum radius of exchanger pipe in each of non-convective and lower convective zones that maximises the annual extraction efficiency. This work presents a useful analysis to assess multi zone extraction from solar ponds under transient state in a more practical and accurate manner.

Solution of the Analysis Problem of a Machine Assembly Distributed System with Time-Dependent Heat Transfer Coefficient

It is well known that temperature is a factor that significantly influences the accuracy of machine tools. Compensation enables machine errors to be reduced, even for a moderately accurate machine tool. The first step in compensation is to estimate the thermal characteristics of the machine part. Thermal models with distributed parameters provide high accuracy of estimation. In these thermal models, the environmental thermal fluctuations influencing the temperature may be taken into account as the time-dependent heat-transfer coefficient. The finite elements method facilitates simulation of the machine system geometry, but is computationally expensive. One approach is to use the simplified thermal model at an early stage of development, which allows the investigation of the temperature field and the possible influence of the environment at any point of the model. In this article, it is proposed to use the spectral method based on the expansion of the temperature function in a Fourier series to analyze the thermal model distributed along the axial coordinate presented in PDE form. To maintain the similarity of thermal processes and the model, the dimension parameters of the model should be chosen such that the Biot and Fourier coefficients would be the same for the model and the machine part. The proposed method allows the PDE to be represented as an indefinite system of linear algebraic equations for the coefficients of the Fourier series, which are the amplitudes of the space–time modes of the temperature function. The solution has the advantage of an analytical solution because it provides information about the model’s temperature at any point.

Single-phase heat transfer regimes in forced flow conditions under exponential heat inputs

We present an experimental and theoretical investigation of single-phase heat transfer under exponential power inputs. We conduct forced flow experiments with water, covering a broad range of mass fluxes (from 0 to 19,300 kg/m2/s), bulk temperatures (from 25 to 100 °C), pressures (from 0.1 to 1.2 MPa), exponential power escalation periods (from 2.5 to 200 ms), and considering two different heater and channel geometries. We use a high-speed infrared thermometry technique to measure the space- and time-dependent heat transfer coefficient between the heated surface and the coolant, building a database covering 73 different experimental conditions. We consider turbulence as a diffusive process and develop an analytic model that can predict 80% of our database within a ±10% error, and the entire database within a ±20% error. We discuss the presence of three heat transfer regimes, i.e., transient conduction, transient turbulent diffusion, and quasi-steady turbulent heat transfer, and derive analytically the two associated transition criteria. These transitions depend on the power escalation period, fluid properties, and are connected to the profile of the turbulent diffusion properties across the boundary layer.

Impact of Heat Transfer on Transient Stress Fields in Power Plant Boiler Components

In boilers operating in modern power plants, thick-walled elements of complex shapes, such as valves, superheater headers, T-pipes, Y-pipes, four-way pipes, and elbows, are especially prone to fatigue processes. Higher operation parameters and more frequent startups may speed up fatigue damage in these elements. Such damage is a local phenomenon and is caused by thermomechanical fatigue (TMF). This paper presents a method designed for predicting the behavior of components subjected to variable temperature and mechanical loading conditions. This method combines the results of measurements of operating parameters of devices under industrial conditions with those obtained using finite element modeling (FEM). Particular attention was given to the influence of the time-dependent heat transfer coefficient on the local thermomechanical stress–strain behavior of the material. It was stated that heat transfer conditions have a significant impact on local transient stresses and depend on the operation parameters of boilers. Consistency of the temperature changes as a function of time, determined in industrial conditions and calculated on the basis of the model approach, was obtained. This developed and described in the work approach enables defining the conditions of heat transfer on the surface of models of considered components.

Development of an Instrumented Test Tool for the Determination of Heat Transfer Coefficients for Die Casting Applications

In the case of casting processes with permanent molds, there is still a relatively pronounced lack of knowledge regarding the locally prevailing heat transfer between casts and mold. This in turn results in an insufficient knowledge of the microstructure and the associated material properties in the areas of the casting component close to the surface. Therefore, this work deals with the design and evaluation of a test tool with an integrated sensor system for temperature measurements, which was applied to obtain a time-dependent heat transfer coefficient (HTC) during casting solidification. For this purpose, the setup, design and computational approach are described first. Special attention is paid to the qualification of the multi-depth sensor and the calculation method. For the calculations, an inverse estimation method (nonlinear sequential function) was used to obtain the HTC profiles from the collected data. The developed sensor technology was used in a test mold to verify the usability of the sensor technology and the plausibility of the obtained calculation results under real casting conditions and associated temperature loads. Both the experimental temperature profiles and the HTC profiles showed that, in the evaluated casting series, the peak values determined were close to each other and reached values between 6000 W/(m2·K) and 8000 W/(m2·K) during solidification.

Sequential particle filter estimation of a time-dependent heat transfer coefficient in a multidimensional nonlinear inverse heat conduction problem

In the applied mathematical modelling of heat transfer systems, the heat transfer coefficient (HTC) is one of the most important parameters. This paper proposes a combination of the Method of Fundamental Solutions (MFS) with particle filter Sequential Importance Resampling (PF-SIR) to estimate the time-dependent HTC in two-dimensional transient inverse heat conduction problems from non-standard boundary integral measurements. These measurements ensure the unique solvability of the boundary coefficient identification problem. Numerical results show high performance on several test cases with both linear and nonlinear Robin boundary conditions, supporting the synergy between the MFS and simulation-based particle filter sequential analysis methods.

Estimation of time-dependent heat transfer coefficient in unidirectional casting using a numerical model coupled with solidification analysis and data assimilation

We have recently developed a method to estimate the heat transfer coefficient based on data assimilation. To understand its usefulness for estimating the time-dependent heat transfer coefficient, herein we performed unidirectional casting experiments of Al-1mass%Si alloy and obtained the cooling curves during solidification. The experimental data were then used to validate the estimated time-dependent heat transfer coefficient. Consequently, the measured cooling curves could be accurately simulated, and the average errors between measured and simulated cooling curves were below 0.8%. The estimated time-dependent heat transfer coefficient was 29461.5 Wm−2K−1 at the initial stage of cooling, which rapidly decreased to about 6000 Wm−2K−1 and then gradually decreased to about 1000 Wm−2K−1. These values are reasonable as the heat transfer coefficients for castings of Al base alloys. Additionally, the effect of the setting parameters of the data assimilation were evaluated. It was found that the position of the cooling curve(s) used in the estimation was the most important factor and a cooling curve measured at the position near the surface of the mold should be utilized. This method allows the reasonable estimation of the time-dependent heat transfer coefficient between the mold and molten alloy for unidirectional castings without using trial and error, and experimentally measured cooling curves can be accurately reproduced by solidification analysis.

Experimental estimation of temporal and spatial resolution of coefficient of heat transfer in a channel using inverse heat transfer method

In this research, a novel method to investigate the transient heat transfer coefficient in a channel is proposed, in which the water flow, itself, is considered both single-phase and two-phase. The experiments were designed to predict the temporal and spatial resolution of the Nusselt number. The inverse technique method is non-intrusive, in which time history of temperature is measured, using some thermocouples within the wall to provide input data for the inverse algorithm. The Tikhonov method is used as an inverse method. Error for estimation heat flux is around 0.06q mean. The temporal and spatial changes of heat flux, Nusselt number, vapor quality, convection number, and boiling number have all been estimated, showing that the estimated local Nusselt numbers of flow for without and with phase change are close to those predicted previously. This study suggests that the extended inverse technique can be successfully utilized to calculate the local time-dependent heat transfer coefficient of boiling flow.

Parameter estimation for heat transfer analysis during casting processes based on ensemble Kalman filter

It is very important for production of casts with high quality to predict and control the solidification processes of the alloy. Heat transfer analysis has been utilized for understanding solidification processes. However, it is often difficult to obtain values of all input parameters such as thermal conductivity and heat transfer coefficient precisely. In this study, a parameter estimation method in heat transfer analysis is developed based on data assimilation. In the authors’ previous study, the particle filter, a method of data assimilation, was applied to estimation of thermal conductivity and heat transfer coefficient in heat transfer analysis for mold casting, and its applicability was systematically investigated. It was shown that the particle filter is very effective in estimating these parameters. However, the particle filter suffers from a shortcoming called sample degeneracy which often prevents accurate estimation of parameters in phenomena of interest. The present study focuses on a different method of data assimilation called the ensemble Kalman filter and its applicability to the estimation of heat transfer coefficient and thermal conductivity is investigated based on twin experiments. It is shown that thermal conductivity and constant or time-dependent heat transfer coefficient can be accurately estimated independently with three and two cooling curves, respectively. Furthermore, the thermal conductivity and time-dependent heat transfer coefficient can be estimated simultaneously with high accuracy.

The impact of the casting thickness on the interfacial heat transfer and solidification of the casting during permanent mold casting of an A356 alloy

Many important quality indicators for components manufactured using permanent mould casting, such as the presence of shrinkage porosity, microstructure features, dimensional stability, cycle time and filling mechanisms are controlled directly or indirectly by the heat transfer mechanisms linking the casting to the mould. While interfacial heat transfer in permanent mould casting has been significantly investigated and widely reported in the literature, the geometrical dependence of heat transfer parameters has not been studied or reported in detail. Understanding this dependency is very important as the same cast component most often is constituted by different sections and geometrical variations. In this paper, experimental methods and analytical correlations have been developed and presented that enable an accurate determination of the time dependent interfacial heat flux density and heat transfer coefficient at the casting-mould interface. The variation of these parameters is investigated and analysed for three different casting sections and two types of thermal barrier coatings.

An investigation of uncertainties in determining convective heat transfer during immersion frying using the general uncertainty management framework

Although extensively studied (and of large importance for food processing) there is still no general consensus on the time-dependent convective heat transfer coefficient (h) in immersion frying – reported values differ by orders of magnitude (4–7000 W m−2 K−1). Moreover, none of the many methods suggested have become a generally agreed upon standard.This study uses the general uncertainty management (GUM) framework to analyze the standard uncertainties in four commonly used methods to measure h in immersion frying. It is concluded that the uncertainties (when including all sources of uncertainty in a systematic manner using the GUM) are often substantially larger than previously reported (up to 100% relative uncertainty), i.e., some methods used in previous studies are very sensitive to measurement uncertainties. This can help explain the large variation in previously reported h-values. Comparisons between methods suggest that evaporation rate based methods (with numerical differentiation) provide the highest reliability.

Optimal control of multiphase steel production

An optimal control problem for the production of multiphase steel is investigated that takes into account phase transformations in the steel slab. The state equations are a semilinear heat equation coupled with an ordinary differential equation, that describes the evolution of the steel microstructure. The time-dependent heat transfer coefficient serves as a control function. Necessary and sufficient optimality conditions for the control problem are derived. For the numerical solution of the control problem, a reduced sequential quadratic programming method with a primal-dual active set strategy is developed. The numerical results are presented for the optimal control of a cooling line in the production of hot-rolled Mo–Mn dual phase steel.

Time-dependent study of boiling heat transfer coefficient in a vertical minichannel

Purpose The purpose of this paper is to determine the time-dependent heat transfer coefficient during FC-72 flow boiling in a 1.7-mm-deep vertical and asymmetrically heated minichannel. Design/methodology/approach The temperature of the minichannel heated wall was recorded continuously with the use of thermocouples. The heat transfer coefficients for the subcooled and saturated boiling regions at the heated wall–fluid contact surface were calculated from the Robin boundary condition. Both the wall and fluid temperatures were obtained from the solution of the inverse nonstationary problems in two adjacent domains: the heated wall and flowing fluid. The FEM with Trefftz-type basis functions was applied to solve the inverse problem. Findings The obtained time-dependent heat transfer coefficient in subcooled boiling achieved rather low values, whereas in saturated boiling, the coefficient was the highest at the channel inlet. The boiling curves were plotted to illustrate the results. Practical implications The results of experiments are the best source of information for the design of minichannel cooling systems used for thermoregulation of components and heat exchangers. High-tech minichannel heat exchangers are applied in various industrial applications as microelectronics devices, gas turbines, internal combustion engines, nuclear reactors, X-ray sources and organic rankine cycle (ORC) modules. Originality/value In the study, the Trefftz functions for the nonstationary Fourier–Kirchhoff equation with the factor describing void fraction were determined and then used to construct the time-dependent basis functions in FEM.

Heat Transfer Coefficient at Cast-Mold Interface During Centrifugal Casting: Calculation of Air Gap

During centrifugal casting, the thermal resistance at the cast-mold interface represents a main blockage mechanism for heat transfer. In addition to the refractory coating, an air gap begins to form due to the shrinkage of the casting and the mold expansion, under the continuous influence of strong centrifugal forces. Here, the heat transfer coefficient at the cast-mold interface h has been determined from calculations of the air gap thickness da based on a plane stress model taking into account thermoelastic stresses, centrifugal forces, plastic deformations, and a temperature-dependent Young’s modulus. The numerical approach proposed here is rather novel and tries to offer an alternative to the empirical formulas usually used in numerical simulations for a description of a time-dependent heat transfer coefficient h. Several numerical tests were performed for different coating thicknesses dC, rotation rates Ω, and temperatures of solidus Tsol. Results demonstrated that the scenario at the interface is unique for each set of parameters, hindering the possibility of employing empirical formulas without a preceding experiment being performed. Initial values of h are simply equivalent to the ratio of the coating thermal conductivity and its thickness (~ 1000 Wm−2 K−1). Later, when the air gap is formed, h drops exponentially to values at least one order of magnitude smaller (~ 100 Wm−2 K−1).