Heat Conduction System Research Articles

Exponential Boundary Control for 2-D Spatial Distributed Parameter Systems Under Boundary Collocated and Planar Linear Measurements.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

Application of the double decentralized fuzzy inference method to heat flux distribution identification in single-bubble boiling

Accurately determining the spatiotemporal distribution of boiling heat flux in a single-bubble pool is crucial for understanding the pool’s heat transfer mechanism. However, direct measurement is challenging. Utilizing an inverse heat transfer approach, where part of the temperature measurement information of the boiling wall is employed, offers an effective solution to this issue. This study explores the application of the double decentralized fuzzy inference (DDFI) method to identify the distribution of single-bubble boiling heat flux in three-dimensional heat conduction systems. Through simulation experiments, we estimate the boiling heat flux distribution of single-bubble boiling and validate the DDFI method’s effectiveness through comparative analysis. Furthermore, the measured temperature data of the single-bubble boiling process is utilized to identify the heat flux distribution on the boiling surface using the DDFI method. We reconstruct the transient temperature field of the heating wall using inversion results, and verify the reliability of the reconstruction results.

Response spatiotemporal correlation and transient temperature field direct reconstruction for heat conduction system

In this paper, according to a spatiotemporal correlation characteristic of the temperature response of a transient heat conduction system, a response spatiotemporal correlation (RSTC) model of the temperatures between measurement space and estimation space of the system is proposed. Furthermore, a RSTC based direct reconstruction (RSTC-DR) method is developed for a transient temperature field reconstruction problem of a heat conduction system with unknown heat sources. In the offline stage, firstly, mapping eigenvectors of a heat conduction system are determined by the transfer equations without specific heat source information. Then, according to the correlation degree between the mapping eigenvectors, a finite number of representative spatial points (RPs) are extracted. Meanwhile, a fuzzy membership relationship between the mapping characteristics of the RPs and that of the temperature field is determined. Namely, effective mapping characteristic coverage of the RPs to the whole temperature field is realized. Moreover, a RSTC model between the measurement spatial points (MPs) and the RPs is obtained by the step response model of the temperature field. In the online stage, based on the RSTC model, the temperature responses of the RPs are estimated by employing the time series vector of the temperature measurements of the MPs. Next, according to the fuzzy membership relationship, the temperature field can be reconstructed in real time by synthesizing the temperature estimations of the RPs. The RSTC-DR method is employed to achieve the non-destructive reconstruction of the transient temperature field of a two-dimensional heat conduction system. The temperature field is reconstructed by the numerical experiment to verify the effectiveness of the proposed method and to discuss its adaptability. Furthermore, the practical effectiveness of the method is demonstrated by applying the existing experimental data.

An Analytic Solution for 2D Heat Conduction Problems with Space–Time-Dependent Dirichlet Boundary Conditions and Heat Sources

This study proposes a closed-form solution for the two-dimensional (2D) transient heat conduction in a rectangular cross-section of an infinite bar with space–time-dependent Dirichlet boundary conditions and heat sources. The main purpose of this study is to eliminate the limitations of the previous study and add heat sources to the heat conduction system. The restriction of the previous study is that the values of the boundary conditions and initial conditions at the four corners of the rectangular region should be zero. First, the boundary value problem of 2D heat conduction system is transformed into a dimensionless form. Second, the dimensionless temperature function is transformed so that the temperatures at the four endpoints of the boundary of the rectangular region become zero. Dividing the system into two one-dimensional (1D) subsystems and solving them by combining the proposed shifting function method with the eigenfunction expansion theorem, the complete solution in series form is obtained through the superposition of the subsystem solutions. Three examples are studied to illustrate the efficiency and reliability of the method. For convenience, the space–time-dependent functions used in the examples are considered separable in the space–time domain. The linear, parabolic, and sine functions are chosen as the space-dependent functions, and the sine, cosine, and exponential functions are chosen as the time-dependent functions. The solutions in the literature are used to verify the correctness of the solutions derived using the proposed method, and the results are completely consistent. The parameter influence of the time-dependent function of the boundary conditions and heat sources on the temperature variation is also investigated. The time-dependent function includes exponential type and harmonic type. For the exponential time-dependent function, a smaller decay constant of the time-dependent function leads to a greater temperature drop. For the harmonic time-dependent function, a higher frequency of the time-dependent function leads to a more frequent fluctuation of the temperature change.

Identification of fractional order non– homogeneous Hammerstein-Wiener MISO continuous systems

Aiming at the problem of difficult identification of parameters in fractional non-homogeneous Hammerstein-Wiener nonlinear MISO time-delay continuous systems, an algorithm that can simultaneously identify coupled coefficients, orders, and time-delays in nonlinear fractional-order systems is designed. In this algorithm, a fractional order fitting model is constructed by using the Legendre wavelet operation matrix, and a full-parameter partial derivative model of the time-delay nonlinear system is derived. Second, the sequential quadratic programming (SQP) method is used to simultaneously estimate the non-homogeneous order, delay parameters, and coefficient parameters of the fractional order system. Finally, the effectiveness of the proposed algorithm is demonstrated through an academic example and a two-wall heat conduction system with a nonlinear fractional order system of MISO.

A quantum algorithm for heat conduction with symmetrization

Heat conduction, driven by thermal non-equilibrium, is the transfer of internal thermal energy through physical contacts, and it exists widely in various engineering problems, such as spacecraft and state-of-the-art dilution refrigerators. The mathematical equation for heat conduction is a prototypical partial differential equation. Here we report a quantum algorithm for heat conduction (QHC) that significantly outperforms classical algorithms. We represent the original heat conduction system by a symmetric system with an ancilla qubit so that the quantum circuit complexity is polylogarithmic in the number of discretized grid points. Compared with the existing algorithms based on solving linear equations via the Harrow-Hassidim-Lloyd (HHL) algorithm, our method evolves the linear process directly without phase estimation, which involves complex quantum operations and large output error. Therefore, this algorithm is experimental-friendly and without output error after the discretization procedure. We experimentally implemented the algorithm for a one-dimensional thermal conduction process with two-edge constant temperatures and adiabatic conditions on a nuclear spin quantum processor. The spatial and temporal distributions of the temperature are accurately determined from the experimental results. Our work can be naturally applied to any physical processes that can be reduced to the heat equation.

Explosive Spalling Mechanism and Modeling of Concrete Lining Exposed to Fire.

Traditional heat transfer analysis has been adopted to predict the damage in a tunnel under fire without considering the effect of concrete spalling, which leads to underestimation of the fire damage of concrete. However, accounting for the spalling effect of concrete under high temperature in an analytical heat transfer model is difficult because of the complexity of the spalling mechanism. This study aims to establish an analytical model to estimate the influence of concrete spalling on the fire-damage depth prediction. To overcome this challenge, first, a series of fire tests were conducted in a unidirectional heating system. The spalling phenomenon and spalling characteristics were observed. Based on the experimental test results, the moisture content of concrete is one of the key factors of spalling. Obvious layered spalling characteristics of concrete samples without drying could be observed under the unidirectional heat conduction system. The critical temperature of spalling is 600 °C, and the thickness of the spalling layer is 2 cm~2.5 cm. These two parameters are critical spalling conditions. Second, a multilayer model for the heat transfer analysis considering the spalling effect of tunnel lining under fire was proposed. By using Laplace transform and the series solving method for ordinary differential equations, the time-dependent temperature and stress fields of concrete lining during tunnel fire could be obtained, which are the basis of damage evolution. The analytical results agreed with the experimental data. The spalling depth of tunnel lining related to the temperature rise of tunnel fire could be predicted by using the proposed analytical model. The results of this research can be used to provide a better damage evaluation of tunnel lining under fire.

Numerical and experimental verification of the single neural adaptive PID real-time inverse method for solving inverse heat conduction problems

For the problems of difficult on-line tuning of PID parameters, weak anti-interference ability and poor self-adaptive ability in the classical proportional-integral-derivative (PID) inverse method, combining single artificial neuron with PID inverse algorithm, a single neural adaptive PID (SNA-PID) inverse method is established to estimate the thermal boundary condition. Compared with the classical PID inverse method, the main difference is that SNA-PID can adaptively adjust the weights of PID parameters. In the SNA-PID inverse method, firstly, the deviation signal between the output of the direct heat conduction model and the measured temperature and its first-order difference and second-order difference are taken as three inputs of a single neuron (dendritic input signal of neuron), and the connection strength of each input signal is determined according to the updated weight of the adaptive learning algorithm, The excitation value of the boundary heat flux increment of the heat conduction system is generated according to the linear truncation function. Finally, the real-time estimation of boundary heat flux of heat conduction system is realized. The unsteady boundary heat flux of one-dimensional heat conduction object is estimated through numerical and experimental tests, which verifies the effectiveness of the proposed SNA-PID inverse method.

Highly precise and efficient solution strategy for linear heat conduction and structural dynamics

AbstractTime‐dependent parabolic and hyperbolic equations are widely encountered in practical engineering. Accurate and fast solution methods for such equations have always attracted attention. To reach this aim, this article proposes a strategy to construct highly precise and efficient time integration methods (TIMs) for linear heat conduction and structural dynamic systems. In the proposed strategy, an integrated amplification matrix of a TIM is created to precisely transfer the free responses of the previous step, and the Gauss–Legendre quadrature is employed to precisely compute the forced responses of the current step. To reduce computational cost and rounding error, a 2m algorithm and a method of storing incremental matrix are applied in the construction of the integrated matrix. Moreover, the L‐stable backward difference formula for heat conduction and the generalized trapezoidal rule for structural dynamics, which is A‐stable and has controllable dissipation, are utilized to conduct this strategy. Numerical experiments validate that compared with some existing TIMs, the TIMs generated by the proposed strategy enjoy advantages both in precision and efficiency.

A parametrized level set based topology optimization method for analysing thermal problems

This paper focuses on the utilization of local radial basis functions (LRBFs) based level set method (LSM) for topology optimization of two-dimensional thermal problems using both concentrated as well as uniformly distributed heat generation. The design domain is embedded implicitly into a higher-dimensional function, which is parametrized with the LRBFs through an explicit scheme. This novel combination of LRBFs and LSM has the capability of controlling the topological variations automatically, i.e., hole insertion, merging with each other and with the boundary. The governing equations of heat conduction system are solved with the finite element method to obtain the sensitivities at level set grid points as a velocity field for evolution of the structural geometry. The objective function is set to the heat transfer potential with the maximum material volume as the design constraint. Several experiments are conducted on benchmark test problems and the resulting optimal solutions reveals efficiency, convergence and good agreement with those reported in the literature.

Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model

The generalized Cattaneo model describes the heat conduction system in the perspective of time-nonlocality. This paper proposes an accurate and robust meshless technique for approximating the solution of the time fractional Cattaneo model applied to the heat flow in a porous medium. The fractional derivative is formulated in the Caputo sense with order 1<α<2. First, a finite difference technique of convergence order O(δt3−α) is adopted to achieve the temporal discretization. The unconditional stability of the method and its convergence are analysed using the discrete energy technique. Then, a local meshless method based on the radial basis function partition of unity collocation is employed to obtain a full discrete algorithm. The matrices produced using this localized scheme are sparse and, therefore, they are not subject to ill-conditioning and do not pose a large computational burden. Two examples illustrate in computational terms of the accuracy and effectiveness of the proposed method.

TONR: An exploration for a novel way combining neural network with topology optimization

The rapid development of deep learning has opened a new door to the exploration of topology optimization methods. The combination of deep learning and topology optimization has become one of the hottest research fields at the moment. Different from most existing work, this paper conducts an in-depth study on the method of directly using neural networks (NN) to carry out topology optimization. Inspired by the idea from the field of “Inverting Representation of Image” and “Physics-Informed Neural Network”, a topology optimization via neural reparameterization framework (TONR) that can solve various topology optimization problems is formed. The core idea of TONR is Reparameterization, which means the update of the design variables (pseudo-density) in the conventional topology optimization method is transformed into the update of the NN’s parameters. The sensitivity analysis in the conventional topology optimization method is realized by automatic differentiation technology. With the update of NN’s parameters, the density field is optimized. Some strategies for dealing with design constraints, determining NN’s initial parameters, and accelerating training are proposed in the paper. In addition, the solution of the multi-constrained topology optimization problem is also embedded in the TONR framework. Numerical examples show that TONR can stably obtain optimized structures for different optimization problems, including the stress-constrained problem, structural natural frequency optimization problems, compliant mechanism design problems, heat conduction system design problems, and the optimization problem of hyperelastic structures. Compared with the existing methods that combine deep learning with topology optimization, TONR does not need to construct a dataset in advance and does not suffer from structural disconnection. The structures obtained by TONR can be comparable to the conventional methods.

AN UNCONDITIONALLY STABLE METHOD FOR TRANSIENT HEAT CONDUCTION

Time-dependent transient heat conduction problems are widely encountered in aerospace, civil engineering, metallurgical engineering, etc., and for such problems, accurate and fast numerical approaches have always attracted attention in the past decades. To achieve this goal, this paper proposes an unconditionally stable single-step time integration method for general transient heat conduction systems. In the proposed method, the temperature vector and its time derivative are formulated independently by the Langrage interpolation function, and then the relation between the temperature vector and its time derivative is defined with the weighted residual method. Theoretical analysis, including convergence rate and amplification factor, illustrates that the proposed method is strictly second-order accurate for the temperature vector and its time derivative, and it has the strong algorithmic dissipation (L-dissipation), meaning that it can quickly filter out the unwanted numerical oscillations in the high-frequency range. At present, most existing time integration methods, such as the Crank-Nicolson method and the Galerkin method, are unconditionally stable for linear transient heat conduction systems, but they are conditionally stable for nonlinear ones. To this end, this work improved the stability analysis theory for nonlinear transient heat conduction systems proposed by Hughes and used the improved stability analysis theory to design the free parameters of the proposed method. Because of this reason, the proposed method is unconditionally stable for both linear and nonlinear transient heat conduction problems. Due to the desirable algorithmic stability, the proposed method can still provide accurate and stable predictions for nonlinear transient heat conduction problems where the excellent Crank-Nicolson method fails. Some linear and nonlinear transient heat conduction problems are solved in this paper, and the results of these problems show that compared to the currently popular time integration methods, such as the Crank-Nicolson method and the backward difference formula, the proposed method enjoys noticeable advantages in accuracy, dissipation and stability.

Level-set topology optimization for effective control of transient conductive heat response using eigenvalue

Designing thermally efficient devices for an instantaneous heating condition is a challenging task, since a structure that simultaneously satisfies a lower peak temperature as well as a slower thermal response time must be achieved. In order to design a structure for both of the requirements, a transient analysis-based structural topology optimization method can be usually employed. However, the overall thermal response time of a heat conduction system can be modelled simply via the fundamental thermal eigenvalue, which is a physical quantity. This suggests that a thermal eigenvalue analysis can be adopted instead of transient analysis for an effective design of the structure controlling its thermal response time. In this study, we aim at developing a level-set topology optimization method to effectively optimize the overall response time of heat conduction systems using the thermal eigenvalue. The proposed level-set thermal eigenvalue topology optimization updates the structural boundary based on the common fixed grid approach, and the adjoint variable method is applied to compute shape sensitivity. Numerical examples clearly show the controllability of overall heat response time through the thermal eigenvalue, and especially, it is demonstrated that the proposed method is useful in designing an effective cooling structure for an instantaneous heating.

Development of Geothermal Power Generation Device using Heat Conduction System and Class Practice on Renewable Energy

Development of Geothermal Power Generation Device using Heat Conduction System and Class Practice on Renewable Energy

Proposal of Improved Method for Heat Conduction Inverse Problem Analysis

In a one-dimensional unsteady heat conduction system of a one-layer solid, there is a heat conduction inverse problem analysis method that evaluates the heat transfer characteristics of the surface from the temperature history of two places inside the solid. The method can be applied to several other conditions. However, when the surface has a different layer such as an oxide film, the heat transfer characteristics of the different layer surface cannot be evaluated. Therefore, based on the existing inverse problem analysis method, we propose a method to evaluate the heat transfer characteristics of the surface of the different layer from the temperature history of two places inside the solid having the different layer on the surface. In this method, the different layer surface temperature is assumed from the different layer backside temperature and heat flux obtained by the existing method. The surface heat transfer characteristics are evaluated by gradually correcting the assumed surface temperature using the backside heat flux obtained by the heat transfer direct problem. As a result, when the interface temperature and heat flux of the two-layer solid with different layers are known, it was confirmed that the different layer surface heat transfer characteristics can be sufficiently evaluated by this proposed method.

A resilient framework for sensor-based attacks on cyber–physical systems using trust-based consensus and self-triggered control

In networked Cyber–Physical Systems, fidelity of sensor data is critical for the safe operation of the physical plant. Misrepresentation of the data fed back by a primary sensor may cause service disruption or damage to the wider plant through interconnected physical processes. A framework for the recovery of control after an attack has been detected is developed with the following key concepts: (I) a collection of secure secondary sensors that measure energy emissions from components of the system to provide an assessment of the primary sensors’ trust status; (II) a trust-weighted consensus algorithm that fuses estimates from observers of interconnected processes with information from the secondary sensors to accurately reconstruct the state of the attacked process; and (III) a communication-aware self-triggered control protocol that regulates the attacked process using the consented estimate in the absence of reliable data from its primary sensor. The framework is physically tested on a two-dimensional heat conduction system with two kinds of secondary sensors.

Real-time estimation of thermal boundary of unsteady heat conduction system using PID algorithm

Based on the principle of the proportional-integral-derivative (PID) control in feedback control theory, an inverse method for unsteady heat conduction process is established in this paper. The inverse problems of unsteady heat conduction are transformed into a kind of PID control problem, and the PID parameters are tuned by the complex optimization method. The deviation signal between the output of the direct heat conduction model and the measured temperature is used to drive the PID controller, and the boundary heat flux of the heat conduction system is estimated in real time through the PID control law. The numerical simulation results and experiment results show that the inverse algorithm has strong anti-interference ability.

Interactive α-satisfactory method for multi-objective optimization with fuzzy parameters and linguistic preference

An interactive α-satisfactory method via relaxed order of desirable α-satisfactory degrees is proposed for multi-objective optimization with fuzzy parameters and linguistic preference in this paper. Fuzzy parameters existing in objectives and constraints of multi-objective optimization are defined as fuzzy numbers and α-level set is used to build the feasible domain of parameters. On the basis, the original problem with fuzzy parameters is transformed into multi-objective optimization with fuzzy goals. Linguistic preference of decision-maker is modelled by the relaxed order of desirable α-satisfactory degrees of all the objectives. In order to achieve a compromise between optimization and preference, the multi-objective optimization problem is divided into two single-objective sub-problems: the preliminary optimization and the linguistic preference optimization. A preferred solution can be found by parameter adjustment of inner-outer loop. The minimum stable relaxation algorithm of parameter is developed for calculating the relaxation bound of maximum desirable satisfaction difference. The M-α-Pareto optimality of solution is guaranteed by the test model. The effectiveness, flexibility and sensitivity of the proposed method are well demonstrated by numerical example and application example to heat conduction system.

A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 1: Basic algorithm

The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. Part 1 of this two-part articles presents the process and characteristics of basic algorithms, including POD explicit and implicit time-marching methods. The accuracy and efficiency are verified by several numerical examples with various boundary conditions and element types. The results show that the POD-based reduced order model (ROM) can provide high quality temperature prediction of the transient nonlinear heat conduction problems when using implicit method. However, the computational time of implicit method is much longer than that of explicit one. The acceleration effect of POD-based ROM on the calculation of the transient nonlinear heat conduction problems is one order of magnitude lower than that of the corresponding transient linear heat conduction problems. The improvement of computational efficiency is not pronounced. Further studies of the more efficient advanced algorithms to deal with POD-based ROM for transient nonlinear heat conduction problems will be presented in Part 2. Additionally, an approximate POD-based ROM for transient nonlinear heat conduction problem is proposed, which can be constructed quickly by using POD modes obtained from the corresponding transient linear heat conduction system. It is confirmed to be feasible for allowing nonlinear behavior to be modeled at an acceptable level of accuracy. It has significant application potential of solving practical engineering problems.