Forward Heat Conduction Research Articles

Hyper-reduced-order model for estimating convection heat transfer coefficients of turbine rotors

Forced convection heat transfer occurs inside the steam turbine, and it is crucial for thermal and strength analysis to accurately estimate the convection heat transfer coefficients of the turbine rotor. This paper presents a hyper-reduced-order model for efficiently estimating the forced convection heat transfer coefficients of a steam turbine rotor. Unlike the full-order finite element method, the hyper-reduced-order model uses the discrete empirical interpolation method to approximate the domain integration of transient heat conduction simulations. This approach greatly reduces the degrees of freedom of numerical integration, thus substantially improving the computational efficiency of forward heat conduction problems. The hyper-reduced-order model and Levenberg–Marquardt algorithm are combined to minimize temperature errors between the numerical simulation results and remote sensor measurements and iteratively estimate the heat transfer coefficients of forced convection in the rotor. The accuracy and efficiency of the proposed model are verified through a transient heat conduction simulation. Moreover, the effects of the initial guess values and measurement errors are investigated to demonstrate the universality and robustness of the proposed approach in determining the convection heat transfer coefficient. Compared with the full-order finite element model, the proposed hyper-reduced-order model can increase the efficiency of forward heat conduction simulations of the turbine rotor by more than 10 times, and it only takes 0.87 s computer runtime in single transient step simulation, and then rapidly estimate the forced convection heat transfer coefficients. Furthermore, the performance of the proposed approach is insensitive to the initial guess values, and it exhibits great robustness under measurement error. The mean errors are 4.78 %, 2.67 % and 10.51 % when the initial values are 0.015 mW·mm−3·°C−1, 0.05 mW·mm−3·°C−1 and 0.15 mW·mm−3·°C−1 respectively. When there is no measurement error, the estimated error of the convection heat transfer coefficients is 2.67 %, and even if the measurement error reaches 5 %, and the accuracy loss is only 5.57 %. Consequently, this approach is highly suitable for estimating convection heat transfer coefficients during the dynamic operation of steam turbines, and this research provides reliable guidance for the optimization design and safe operation of steam turbines.

Application of the Conjugate Gradient Method for Predicting Unknown Heat Flux in 2D Plat under Effect of Insulation

When an anomaly is discovered during a thermal inspection of industrial equipment, the diagnosis of finding the heat source is made more difficult by the presence of heat insulation. The use of the Conjugate Gradient Method (CGM) to solve the unknown heat flux in Inverse Heat Conduction Problem (IHCP) under insulation condition has been discussed. This method is used to predict a heat flux by utilizing temperature data at any points of measurement. The study deals with the structure of 2D thin plate at steady state. A copper plate with a thickness of 1 mm is used as specimen. White glass wool is used to thermally insulate the plate on the back surface. An electrical heater is plate mounted and operated by varying the DC voltage. A datalogger with thermocouple sensors records plate temperature changes. Software for solving the IHCP based on the CGM was developed. Initially, the software was implemented using synthetic data obtained from the forward heat conduction equations with a known heat flux. Simulated measurement data are assumed to have high accuracy (± 0.1 ºC). Determination of heat flux with the CGM gives very satisfactory results with a low error below 0.12%. The CGM was then applied using experimental data. With a measurement error of ± 0.5 ºC, the computational stopping criterion can still be met satisfactorily. In real installations, equipment is sometimes partially or completely isolated. In the experiment, this phenomenon is simulated by varying the isolation area as follows: 0%, 25%, 50% and 100%. The results of the flux calculation are correlated with the real flux supplied by the electrical heater. Each type of insulation area has a similar curve. By obtaining the correlation equation, the equivalent heat flux from calculation to real and vice versa can be carried out.

The energy saving performance of the thermal diode composite wall in different climate regions

The effective management of energy consumption during building operations continues to be of utmost importance. The role of a building's envelope in regulating energy consumption is critical. However, traditional building insulation systems often struggle to maintain optimal indoor temperatures in the face of fluctuating external temperatures. Solar energy, for instance, can easily penetrate a room through windows during the cooling season, leading to increased energy consumption. Similarly, heat dissipates easily during the heating season. To address these challenges, thermal diode composite walls with unidirectional heat transfer offer a groundbreaking approach to simplifying the design of thermal management systems. The thermal diode composite wall effectively controls heat conduction, convection, and radiation through the implementation of different functional layers. By regulating the heat flux through the building envelope, this technology significantly reduces energy consumption during building operations while maintaining a stable indoor temperature. To evaluate the performance of an adaptable thermal diode composite wall, we designed, implemented, and conducted tests on a thermal diode composite wall building. The results of the study demonstrate substantial energy savings, ranging from 3.5% to 69.3% for annual operation in various regions, with better performance observed in colder regions. In the forward heat conduction mode, the temperature difference between the inside and outside wall surfaces reached a maximum of 20.99 K, while in the reverse mode, it reached −35.67 K. These findings highlight the remarkable potential of thermal diode composite walls in significantly improving the energy efficiency and comfort of buildings. Consequently, the adoption of thermal diode composite walls presents numerous opportunities for the development of low-carbon buildings.

Analytic series solutions of 2D forward and backward heat conduction problems in rectangles and a new regularization

In the paper, we solve a non-homogeneous heat conduction equation with non-homogeneous boundary conditions in a 2D rectangle. First, we derive the domain/boundary integral equations for both the forward and backward heat conduction problems. Then, by using the technique of homogenization, inserting the adjoint Trefftz test functions into the derived integral equations and expanding the solutions in terms of eigenfunctions, we can obtain the expansion coefficients in closed form. Hence, the analytic series solutions of forward heat conduction problems (FHCPs) and backward heat conduction problems (BHCPs) are available. For the FHCPs, only a few terms in the series render very high-order accurate solutions at any time, with errors of the order . For the BHCPs, we require to modify the closed-form series solutions via a new spring-damping regularization technique. Numerical tests for the BHCPs in a large space-time domain reveal that the present analytic series solution is very accurate to recover the initial temperature with an error of the order , although the measured final time temperature is very small when is large up to 100 and is even polluted by a large relative noise up to the level .

Inverse estimation of heat flux using linear artificial neural networks

A modified approach is presented for estimating heat flux from an interiorly embedded thermocouple junction in the context of linear dynamical systems. Owing to the similarity of the convolution expressions describing one-dimensional feedforward heat conduction and the impulse response truncation (IRT) filter, the response of a fixed-length, linear forward heat conduction model is mathematically given based on an IRT filter. Motivated by the calibration methods proposed by Stefan Löhle, Majid Keyhani, and Jay I. Frankel et al., an alternative method is proposed for identification of the finite impulse response based on linear artificial neural networks (ANN) and calibration data from experiments. The heat flux is estimated based on the weights of the linear ANN and Beck's future-time regularization method without the knowledge of the thermophysical properties of the material, depth and inertia of the thermocouple junction, and heat losses of the sensor. Results of tests performed for validation using the short arc Xenon lamp calibration system show that, in general, the heat flux estimated based on the proposed method agree well with the known calibrated values.

AN INVERSE HEAT CONDUCTION MODEL FOR DETERMINING THE CASTING/CHILL INTERFACIAL HEAT TRANSFER COEFFICIENT

The interfacial heat transfer coefficient (IHTC) is required for accurate simulation of the casting process. However, it cannot be easily obtained simply by using either experimental or theoretical methods. Using measured temperature data, an inverse method can be used to predict the IHTC. However, the latent heat released during the solidification of a molten metal complicates the associated temperature and IHTC calculations. To overcome this difficulty, an equivalent specific heat method is applied in this study to calculate the IHTC for the casting process. It is found that the identified IHTC varies with time during castings solidification. The IHTC values calculated for an aluminum alloy casting of simple geometry cast on a steel chill vary from 1200 to 3500 W·m−2·K−1. Application of the indentified IHTC in the forward heat conduction model with the same boundary condition allows comparison between numerically calculated and experimentally obtained results for validation of the method. The results show that the numerically calculated temperatures are in good agreement with those measured experimentally. This confirms that the proposed method is a feasible and effective tool for determining the casting-mold IHTC. Additionally, the characteristics of the time−varying IHTC have also been discussed.

An Experimental Investigation into the Onset of Smearing Damage in Nonconformal Contacts with Application to Roller Bearings

The onset of smearing damage was studied under controlled conditions in a custom test rig that simulates the passage of a rolling element through loaded and unloaded zones of a rolling bearing. The setup includes a spherical roller that is intermittently loaded between two bearing raceways driven at a prescribed speed. The roller is free to accelerate during the loading phase. Contact load, roller speed and acceleration, and electrical contact resistance are recorded during the test. Contact shear stress, friction coefficient, frictional power intensity, and elastohydrodynamic film thickness are calculated from the recorded kinematics data. Results suggest that the first onset of smearing occurs early in the loading phase where the roller is near stationary and the frictional power intensity is high. The raceway speed at the onset of damage decreases with increasing load and increasing lubricant supply temperature. The maximum frictional power intensity is found to be relatively constant at all contact conditions that led to smearing. An existing thermomechanical contact model is used to estimate the contact temperature distribution under smearing conditions and the potential for elastohydrodynamic lubrication (EHL) film thickness reduction due to forward heat conduction.

Determination of heat transfer coefficients at metal/chill interface in the casting solidification process

The present work focuses on the determination of interfacial heat transfer coefficients (IHTCs) between the casting and metal chill during casting solidification. The proposed method is established based on the least-squares technique and sequential function specification method and can be applied to calculate heat fluxes and IHTCs for other alloys. The accuracy and stability of the method has been investigated by using a typical profile of heat fluxes simulating the practical conditions of casting solidification. In the test process, the effects of various calculation parameters in the inverse algorithm are also analyzed. Moreover, numerically calculated and experimental results are compared by applying the determined IHTCs into the forward heat conduction model with the same boundary conditions. The results show that the numerically calculated temperatures are in good agreement with those measured experimentally. This confirms that the proposed method is a feasible and effective tool for determination of the casting-mold IHTCs.

Estimation of heat flux at metal-mold interface during solidification of cylindrical casting

For modeling solidification process of casting accurately, the correct information about the heat flux boundary condition is required. In this study, an inverse heat conduction model is established to determine the interfacial heat flux at metal-mold in the process of casting with a cylindrical geometry. The numerically calculated temperature is compared with the exact solution and simulation solution obtained by commercial software ProCAST to investigate the accuracy of forward heat conduction model. The analysis of calculated heat flux indicates that the inverse model may be taken as a feasible and effective tool for the estimation of the metal-mold interfacial heat flux during solidification of cylindrical casting.

Study on Thermal Conductivity of Personal Computer Aluminum-Magnesium Alloy Casing

With the rapid development of computer technology, micro-state atoms by simulating the movement of material to analyze the nature of the macro-state have become an important subject. Materials, especially aluminium-magnesium alloy materials, often used in personal computer case, this article puts forward heat conduction model of the material, and numerical methods of heat transfer performance of the material.

Applying Neural Networks to the Solution of the Inverse Heat Conduction Problem in a Gun Barrel

The primary cause of gun barrel erosion is the heat generated by the shell as its travels along the barrel. Therefore, calculating the heat flux input to the gun bore is very important when investigating wear problems in the gun barrel and examining its thermomechanical properties. This paper employs the continuous-time analog Hopfield neural network (CHNN) to compute the temperature distribution in various forward heat conduction problems. An efficient technique is then proposed for the solution of inverse heat conduction problems using a three-layered backpropagation neural network (BPN). The weak generalization capacity of BPN networks when applied to the solution of nonlinear function approximations is improved by employing the Bayesian regularization algorithm. The CHNN scheme is used to calculate the temperature in a 155mm gun barrel and the trained BPN is then used to estimate the heat flux of the inner surface of the barrel. The results show that the proposed neural network analysis method successfully solves forward heat conduction problems and is capable of predicting the unknown parameters in inverse problems with an acceptable error.

Applying neural networks to the solution of forward and inverse heat conduction problems

This paper employs the continuous-time analogue Hopfield neural network to compute the temperature distribution in forward heat conduction problems and solves inverse heat conduction problems by using a back propagation neural (BPN) network to identify the unknown boundary conditions. The weak generalization capacity of BPN networks is improved by employing the Bayesian regularization algorithm. The feasibility of the proposed method is examined in a series of numerical simulations. The results show that the proposed neural network analysis method successfully solves forward heat conduction problems and is capable of predicting the unknown parameters in inverse problems with an acceptable error.

Methodology for estimation of time-dependent surface heat flux due to cryogen spray cooling.

Cryogen spray cooling (CSC) is an effective technique to protect the epidermis during cutaneous laser therapies. Spraying a cryogen onto the skin surface creates a time-varying heat flux, effectively cooling the skin during and following the cryogen spurt. In previous studies mathematical models were developed to predict the human skin temperature profiles during the cryogen spraying time. However, no studies have accounted for the additional cooling due to residual cryogen left on the skin surface following the spurt termination. We formulate and solve an inverse heat conduction (IHC) problem to predict the time-varying surface heat flux both during and following a cryogen spurt. The IHC formulation uses measured temperature profiles from within a medium to estimate the surface heat flux. We implement a one-dimensional sequential function specification method (SFSM) to estimate the surface heat flux from internal temperatures measured within an in vitro model in response to a cryogen spurt. Solution accuracy and experimental errors are examined using simulated temperature data. Heat flux following spurt termination appears substantial; however, it is less than that during the spraying time. The estimated time-varying heat flux can subsequently be used in forward heat conduction models to estimate temperature profiles in skin during and following a cryogen spurt and predict appropriate timing for onset of the laser pulse.

Laminar flame spread over PMMA surfaces

A study is made of the mechanisms by which laminar flames spread over flat surfaces of polymethylmethacrylate, in directions ranging from downward to horizontal. Measurements of spread rates, temperature fields and velocity fields are reported. Techniques employed include thermocouple probing, photography, interferometry, radiometer measurements, sampling followed by gas chromatography, and particle-track photography. A simplified theoretical model of the spread process is developed, involving forward heat conduction through the solid as the major mode of the energy transfer and thermal runaway of a gas-phase ignition reaction of methylmethacrylate vapor in a boundary layer just upstream from the point of flame attachment. The extent to which this physical model applies to other materials will depend on the thermal and chemical-kinetic properties of those materials.

A Critical Discussion of Theories of Flame Spread across Solid and Liquid Fuels

Mathematical descriptions of flames spreading over liquid and solid fuels are obtained, using basic assumptions derived from observations or physical reasoning. A review of existing theories shows that they are incomplete in that they either treat an uncoupled problem of the condensed phase where the spreading rate and heat flux at the surface are given, or they merely determine the spreading rate in terms of a new vaguely defined eigenvalue. An important difference between the liquid and solid cases, due to convection, is pointed out, and it is shown that solid-fuel flame-spread theories which claim to apply to the liquid case, in reality do not apply to it. A mathematical formulation and a method of solution are presented for the phenomenon of flame spread over solid fuels with forward heat conduction in both the solid and the gas. The method uses an energy integral over the field to determine the spreading rate in terms of the basic properties of the fuel and air.