Resolution of Unknown Heat Source Inverse Heat Conduction Problems Using Particle Swarm Optimization

The main objective of this article is to solve inverse heat conduction problems with the particle swarm optimization method. An enhanced particle swarm optimization (EPSO) algorithm is proposed to overcome the shortcoming of earlier convergence of standard PSO algorithms. The EPSO is used to estimate the unknown time-dependent heat source in complex regions. Numerical experiments indicate the validity and stability of the EPSO method.     

Inverse Transient Heat Conduction Problems of a Multilayered Functionally Graded Cylinder

Inverse transient heat conduction problems of a multilayered functionally graded (FG) cylinder are presented. The approach is based on measurement of temperature on the outer surface of the cylinder to estimate the heat flux and convection heat transfer coefficient on its inner surface. The non-Fourier heat transfer equation is employed to accurately formulate the problem. The conjugate gradient method (CGM) is used for the optimization procedure and the incremental differential quadrature method (DQM) is applied to solve the direct, sensitivity, and adjoint problems. The accuracy of the presented approach is examined by simulating the exact and noisy data through different examples. Good accuracy of the obtained results validates the presented approach.     

Improved Cuckoo Search Algorithm for Solving Inverse Geometry Heat Conduction Problems

Cuckoo Search (CS) algorithm has shortcomings of weak local search ability, slow convergence speed, and low accuracy. In order to overcome these disadvantages, an improved CS algorithm based on Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm (CS-BFGS) is proposed for solving inverse geometry heat conduction problems, and the physical field is the steady-state heat conduction. Firstly, the unknown initial boundary is evolved by Lévy flights and elimination mechanism. Then the BFGS algorithm is applied to minimize the objective function. Finally, the influences of random errors, measurement point number, and measurement point position on the inverse results are investigated. The results show that the CS-BFGS algorithm has higher accuracy and faster convergence speed than BFGS and CS algorithm. With the decrease of measurement errors, the increase of measurement point number, and measurement point position closer to the inverse boundary, the results become more accurate.     

Hessian and Fisher Matrices For Error Analysis in Inverse Heat Conduction Problems

This article deals with the evaluation of the impact of some errors on the prediction when an inverse heat conduction problem (IHCP) is solved. This evaluation is performed through an analysis of the cost function Hessian to be minimized. More precisely, this article presents a comparison between the computations of a cost function Hessian and of the related Fisher matrix. The Fisher matrix is an approximation of the Hessian matrix. It needs only the solution of the sensitivity problems. On the other hand, the computation of the exact Hessian needs the solution of the Euler equation along with the second-order adjoint problems.     

Resolving the Final Time Singularity in Gradient Methods for Inverse Heat Conduction Problems

This work investigates overall performance of the modification techniques for resolving the singularity at the final time in the gradient method for the inverse heat conduction problem. Four representative methods are selected based on the literature and analyzed for the same case. They are the regularization term method, the differential equation method, the gradient integration method, and the sequential gradient method. All four methods are reproduced and tested for the same test case. Based on the test results, a two-step method that can both alleviate the systematic bias and at the same time resolve the singularity is proposed.     

Thermocouple Data in the Inverse Heat Conduction Problem

The presence of thermocouples inside a heat-conducting body will distort the temperature field in the body and may lead to significant bias in the temperature measurement. If temperature histories obtained from thermocouples are used in the inverse heat conduction problem (IHCP), errors are propagated into the IHCP results. The bias in the thermocouple measurements can be removed through use of appropriate detailed thermocouple models to account for the dynamics of the sensor measurement. The results of these models can be used to generate correction kernels to eliminate bias in the thermocouple reading, or can be applied as sensitivity coefficients in the IHCP directly. Three-dimensional and axisymmetric models are compared and contrasted and a simple sensitivity study is conducted to evaluate the significance of thermal property selection on the temperature correction and subsequent heat flux estimation. In this paper, a high-fidelity thermocouple model is used to account for thermocouple bias in an experiment to measure heat fluxes from solidifying aluminum to a sand mold. Correction kernels are obtained that are used to demonstrate the magnitude of the temperature measurement bias created by the thermocouples. The corrected temperatures are used in the IHCP to compute the surface heat flux. A comparison to IHCP results using uncorrected temperatures shows the impact of the bias correction on the computed heat fluxes.     

锅筒截面瞬态温度场的导热正反问题耦合解法

针对外壁受热的增压锅炉锅筒,提出了求解其截面瞬态温度场的导热正反问题耦合解法.根据锅筒外壁是否受热,将其外壁划分为受热和不受热2个区域.对于不受热区域,沿外壁周向布置热电偶,根据实际测量所得温度,利用导热反问题解法求解该区域的温度场;对于受热区域,利用导热正问题解法求解其温度场;对于耦合边界区域,将不受热区域反问题解法得到的交接边界处温度赋值给受热区域正问题解法作为已知边界条件,从而实现正反问题耦合,得到整个锅筒截面的瞬态温度场.利用Ansys软件对锅炉冷态启动过程中锅筒的温度场进行了计算,并与正反问题耦合解法的计算结果进行了对比.结果表明:正反问题耦合解法具有较高的精度,在复杂边界条件下具有很好的适应性,能够满足工程应用的需要.     

Structured Multiblock Grid Solution of Two-Dimensional Transient Inverse Heat Conduction Problems in Cartesian Coordinate System

ABSTRACT

In this study a structured multiblock grid is used to solve two-dimensional transient inverse heat conduction problems. The multiblock method is implemented for geometric decomposition of the physical domain into regions with blocked interfaces. The finite-element method is employed for direct solution of the transient heat conduction equation in a Cartesian coordinate system. Inverse algorithms used in this research are iterative Levenberg-Marquardt and adjoint conjugate gradient techniques for parameter and function estimations. The measured transient temperature data needed in the inverse solution are given by exact or noisy data. Simultaneous estimation of unknown linear/nonlinear time-varying strengths of two heat sources in two joined surfaces with equal and different heights is obtained for the solution of the inverse problems, and the results of the present study for unknown heat source functions are compared to those of exact functions. This study is an attempt to challenge the goal of combining a multiblock technique with inverse analysis methods. In fact, the structured multiblock grid is capable of providing accurate solutions of inverse heat conduction problems (IHCPs) in industrial configurations, including composite structures. In addition, the multiblock IHCP solver is suitable to estimate unknown parameters and functions in these structures.     

Implementation of Geometrical Domain Decomposition Method for Solution of Axisymmetric Transient Inverse Heat Conduction Problems

The objective of this article is to study the performance of iterative parameter and function estimation techniques to solve simultaneously two unknown functions (quadratic in time, and linear in time and space) using transient inverse heat conduction method in conjunction with a geometrical domain decomposition approach, in cylindrical coordinates. For geometrical decomposition of physical domain, a multi-block method has been used. The numerical scheme for the solution of the governing partial differential equations is the finite element method. The results of the present study for a configuration composed of two joined disks with different heights are compared to those of exact heat source and temperature boundary condition using inverse analysis. Good agreement between the estimated results and exact functions has been observed for parameter estimation techniques in contrast to those of function estimation approach. In summary, the results show that the function estimation technique is sensitive to the location of measurement points, but is useful to estimate unknown functions without a priori knowledge of the functions' spatial and/or temporal distributions. However, the function estimation technique suffers from a drawback: its implementation and data extraction are less straightforward than parameter estimation method. Finally, it is shown that the use of geometrical domain decomposition offers the possibility of developing a robust inverse analysis code for general purpose heat conduction problems.     

Inverse Hyperbolic Heat Conduction in Fins with Arbitrary Profiles

This study aims to estimate unknown base temperature distribution in different non-Fourier fins. The Cattaneo–Vernotte (CV) heat model is used to predict the heat conduction behavior in these fins. This inverse problem is solved by the function-estimation version of the Adjoint conjugate gradient method (ACGM) based on boundary temperature measurements. The ACGM includes direct, sensitivity, and adjoint problems. For each of these problems, a one-dimensional general formulation of the non-Fourier model for longitudinal fins with arbitrary profile is driven and solved by an implicit finite difference method. In this study, three different profiles are considered: triangular, convex parabolic, and concave parabolic. For each of them, two different base temperature distributions are estimated using an inverse method. Moreover, the effects of sensor positions at the fin tip and a specific place in-between are considered on the base temperature estimation. A close agreement between the exact values and the estimated results is found, confirming the validity and accuracy of the proposed method. The results show that the ACGM is an accurate and stable method to determine the thermal boundary conditions in different non-Fourier fin problems.     

An Inverse Heat Conduction Problem and Improving Shielded Thermocouple Accuracy

A shielded thermocouple is a measurement device used for monitoring the temperature in chemically, or mechanically, hostile environments. The sensitive parts of the thermocouple are protected by a shielding layer. In order to improve the accuracy of the measurement device, we study an inverse heat conduction problem where the temperature on the surface of the shielding layer is sought, given measured temperatures in the interior of the thermocouple. The procedure is well suited for real-time applications where newly collected data is continuously used to compute current estimates of the surface temperature. Mathematically we can formulate the problem as a Cauchy problem for the heat equation, in cylindrical coordinates, where data is given along the line r = r ₁ and the solution is sought at r ₁ < r ≤ r ₂. The problem is ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. Thus, regularization techniques are needed. The ill–posedness of the problem is analyzed and a numerical method is proposed. Numerical experiments demonstrate that the proposed method works well.     

Numerical Simulation of Heat Conduction Problems by a New Fast Multipole Hybrid Boundary-Node Method

The fast multipole method (FMM) is an effective technique to reduce the computational cost in solving large-scale problems. In this article, a new fast multipole hybrid boundary-node method (FM-HBNM) is presented to solve three-dimensional heat conduction problems. In the new FM-HBNM, a diagonal form for translation operators is used and the computational cost of the multipole to local (M2L) translation is further reduced. Formulations for the new FM-HBNM are derived. The computational costs for the original and new FM-HBNM are estimated. The numerical results show that a speed-up about 2–3 times can be achieved by the new FM-HBNM.     

Application of Wavelet in Highly Ill-Posed Inverse Heat Conduction Problem

In this work, the prefiltering of the sensor data is taken into consideration when solving an inverse heat conduction problem. The temperature data obtained from each sensor is considered as a discrete signal, and discrete wavelet transform in a multi-resolution filter bank structure is utilized for the signal analysis, after which wavelet denoising algorithm is applied to remove noise from data signal. Subsequently, noisy and denoised temperatures are separately used as input data to an inverse heat conduction problem for comparison. The inverse heat conduction problem considered in this article is an inverse volumetric heat source problem, and it is solved using the conjugate gradient method along with the associated adjoint problem used to obtain the gradient of the objective function. Three sets of results in two case studies are compared (i.e., the result obtained from non-noisy data, noisy data, and denoised data). In the case of noisy data, iterative regularization is used to regularize the solution. The root mean square error of the estimated heat source from denoised data is reduced approximately by a factor of seven to nine as compared to those obtained from noisy data.     

A Crank–Nicolson Scheme with ADI to Compute Heat Conduction in Laser Surface Hardening

In this article, a two‐dimensional (2D) numerical model of a Crank–Nicolson scheme with alternating‐direction implicit (ADI) is developed for a heat conduction model in the laser surface hardening process. A numerical solution is compared to the analytical solution and shows a better suitability. Numerical experiment of the repetitive heating is carried out using the present model in order to investigate influences of processing parameters on temperature profiles. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 522–541, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21085     

Temperature-Constrained Topology Optimization of Transient Heat Conduction Problems

A regional temperature measure model is constructed to obtain a small number of temperature constraints for local transient temperature control. The temperature sensitivity is derived using the adjoint variable method. The multiple temperature criteria and three-phase topology optimization are further investigated for transient heat conduction design. The material layout design of transient heat conduction is replaced by a static optimization problem, which is subsequently solved by the method of moving asymptotes. Finally, several numerical examples are provided to demonstrate the feasibility and validity of the proposed topology optimization for transient heat conduction problems.     

The Estimation of Fluid Temperatures Through an Inverse Heat Conduction Technique

Transient, internal temperatures within an instrumented probe are considered as part of an inverse heat conduction problem (IHCP) to compute the temperature of the surrounding fluid. A linear scheme is used where the exchange coefficients are treated as known parameters.Input data to the IHCP have been generated numerically. When these are uncorrupted, the inverse algorithm works well without stabilization. However, in practice the algorithm must be stabilized, as it is shown that noise is amplified substantially. It becomes necessary both to parameterize spatial variations in the fluid temperature and to utilize a functional specification method to address the noncausal solution.     

Equivalence Principle for Analyzing Steady-State Heat Conduction Problems

This article presents the concept of equivalence principle in the analysis of steady-state heat conduction problems. A surface integral equation formulation is established for homogeneous thermal media and a volume integral equation formulation for inhomogeneous isotropic/anisotropic thermal media. These formulations are analogous to those commonly used in electromagnetic scattering problems and can be solved with the same numerical algorithms used for electromagnetic analysis. This feature makes the proposed theory useful for simultaneous analysis of electromagnetic fields and heat conduction in an electronic system.     

Numerical Simulation of Dual-Phase-Lag Model and Inverse Fractional Single-Phase-Lag Problem for the Non-Fourier Heat Conduction in a Straight Fin

In recent years, many studies have been done on heat transfer in the fin under unsteady boundary conditions using Fourier and non-Fourier models. In this paper, unsteady non-Fourier heat transfer in a straight fin having an internal heat source under periodic temperature at the base was investigated by solving numerically Dual-Phase-Lag and Fractional Single-Phase-Lag models. In this way, the governing equations of these models were presented for heat conduction analysis in the fin, and their re...     

Solution of an Inverse Heat Conduction Problem in a Bi-Layered Spherical Tissue

This work attempts to estimate the phase lag times of a tissue based on the dual-phase-lag model from the experimental data. The inverse dual-phase-lag bioheat transfer problem in the bilayered spherical tissue is studied. The difference between two layers in the thermophysical parameters, geometry effects, and measurement errors of the input data make it hard to be solved. To solve the present problem, a hybrid scheme based on the Laplace transform, change of variables, and the least-squares scheme is proposed. In order to evidence the validity and accuracy of the estimated results, the comparison of the history of temperature increase between the calculated results and the experimental data is made for various measurement locations. The effect of measurement location on the estimated results is also investigated.