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.     

Dynamic Thermoelastic Response of a Heated Thin Composite Plate Using the Dual-Phase-Lag Heat Conduction Model

This paper investigates the dynamic thermoelastic response of a heated thin composite plate. The plate is composed of a dominant matrix domain and an insert domain. A step-function heat source is generated within the matrix domain, causing the heating of the whole plate. The dual-phase-lag heat conduction model is used to determine the thermal behavior of the plate in the form of the spatial and time variations of the temperatures in both domains. The temperature of the matrix is used to evaluate the thermoelastic behavior of the plate in the form of the induced displacements and thermal stresses. The Laplace transformation technique combined with the Rieman-sum method is used to calculate the temperatures. The finite difference method is used to solve the governing equation of plate deflection and then calculate the thermal stresses. The resulting thermal stresses are found to be compressive and follow the same behavior as that of the temperature.     

Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem

This article concerns the application of the lattice Boltzmann method (LBM) to solve the energy equation of a combined radiation and non-Fourier conduction heat transfer problem. The finite propagation speed of the thermal wave front is accounted by non-Fourier heat conduction equation. The governing energy equation is solved using the LBM. The finite-volume method (FVM) is used to compute the radiative information. The formulation is validated by taking test cases in 1-D planar absorbing, emitting, and scattering medium whose west boundary experiences a sudden rise in temperature, or, with adiabatic boundaries, the medium is subjected to a sudden localized energy source. Results are analyzed for the various values of parameters like the extinction coefficient, the scattering albedo, the conduction-radiation parameter, etc., on temperature distributions in the medium. Radiation has been found to help in facilitating faster distribution of energy in the medium. Unlike Fourier conduction, wave fronts have been found to reflect from the boundaries. The LBM-FVM combination has been found to provide accurate results.     

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.     

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.     

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.     

Analytical Solution and Numerical Simulation for One‐Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

In this article we consider a model describing the temperature profile in a longitudinal fin with rectangular, concave, triangular, and convex parabolic profiles. Both thermal conductivity and the heat transfer coefficient are assumed to be temperature‐dependent, and given by a linear function and by power laws, respectively. In addition, the effects of the thermal conductivity gradient have been investigated. Optimal homotopy analysis method (OHAM) is employed to analyze the problem. The effects of the physical applicable parameters such as thermo‐geometric fin, thermal conductivity, and heat transfer mode are analyzed. The OHAM solutions are obtained and validity of obtained solutions is verified by the Runge–Kutta fourth‐order method and numerical simulation. A very good agreement is found between analytical and numerical results. Also for investigation of lateral effects on the accuracy of results, numerical simulation (by Ansis software) is compared with the homotopy analysis method (HAM) and numerical solution (by Runge–Kutta) of the energy balance equation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21104     

Non-Fourier Heat Conduction Problems and the Use of Exponential Basis Functions

A solution method using exponential basis functions (EBFs) is proposed for transient one-/two-dimensional non-Fourier heat conduction problems having particular application in bio-heat fields. A summation of EBFs satisfying the governing differential equation is considered in time and space. The presented method uses a noniterative algorithm for the solution of direct/inverse problems. It is demonstrated that the use of extra EBFs in the form of enrichment functions significantly improves the results when some jumps are seen in the input data. Four numerical examples, including bio-heat conduction problems, are provided to investigate the accuracy and performance of the method presented.     

Establishment of Modified-One-Dimensional and Two-Dimensional Models for Two-Directional Heat Conduction in a Wet Fin Assembly

This paper deals with an analysis of two-dimensional temperature distribution within a rectangular fin assembly under wet conditions and subject to convective condition at the primary inner wall. An analytical method based upon the separation of variables was suggested to determine the two-dimensional temperature field. A modified one-dimensional model was used to more closely approximate the results of the two-dimensional model; a one-dimensional classical model was also elaborated to provide a basis for comparison, allowing the two-dimensional effect to be established in the case of wet fins. Next, wet fin efficiency was determined. To establish the merit of the present work in considering the two-dimensional effect in wet fins, the results of the two-dimensional model were compared with those obtained from the one-dimensional classical models, demonstrating a considerable difference in their results for various design and psychrometric conditions. The wet-fin analysis presented herein is equally suitable for dry-surface fins by accounting for the absence of latent heat transfer.     

板式石蜡储热器传热的数值模拟

在相变储热器中采用强化传热技术，克服相变材料的低导热性能，是目前国内外研究的热点。应用FLUENT软件数值模拟了翅片强化板式石蜡储热器的凝固传热过程，得到随时间变化的相界面位置、总凝固时间、壁面热流、翅片温度分布等，并进一步分析了翅片对不同长宽比叫的储热器的强化传热效果。模拟结果表明，只有当ω≥1时，翅片才能对储热器起到明显的强化传热作用，研究结果可为相变储热器的优化设计提供可靠的依据。     

Efficiency and Optimization of a Straight Rectangular Fin with Combined Heat and Mass Transfer

An analysis was carried out to study the efficiency of a straight rectangular fin with a uniform cross-section area when subjected to simultaneous heat and mass transfer mechanisms. The temperature and humidity ratio differences are the driving forces for the heat and mass transfer, respectively. Numerical solutions are obtained for the temperature distribution over the fin surface when the fin surface is dry, fully wet, and partially wet. The psychrometric correlation of an air-water vapor mixture was used to simulate the relation between the temperature and humidity ratio instead of the linear approximate correlations used in the literature. The effect of atmospheric pressure on the fin efficiency was also studied, in addition to fin optimum thickness for specific operating conditions. The numerical solution was compared with those of previous studies in order to find if the linear model in the published analytical results are near to the real situation. It is found that the linear model for the relation between the humidity ratio and the temperature used by Wu and Bong is a reasonable engineering approximation for small values of the fin parameter and at low relative humidities.     

翅柱复合型冷却器表面传热性能的数值研究

提出一种用于油液冷却的新型翅柱复合型冷却器,并应用SIMPLE算法对于其二维简化模型在不同工况下的表面传热及流动阻力进行数值模拟。将模拟结果与试验和经验关联式相比较,吻合情况良好,表明此算法和所简化的模型是合理的。根据数值模拟结果研究这种传热表面的传热机理,分析翅柱位置及几何参数对流动与传热的影响,对该新型翅片的推广及优化设计有较大帮助。     

Estimation of a Location- and Time-Dependent High-Magnitude Heat Flux in a Heat Conduction Problem Using the Kalman Filter and the Approximation Error Model

This paper aims to estimate a location- and time-dependent high-magnitude heat flux in a heat conduction problem. The heat flux is applied on a small region of a surface of a flat plate, while transient temperature measurements are taken on the opposite surface. This inverse problem is solved using the Kalman filter and a reduced forward model, obtained by simplifications of a three-dimensional and nonlinear heat conduction problem. To deal with the modeling errors of this reduced model, the Approximation Error Model is used. The results show that excellent estimates can be obtained at feasible computational times.     

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.     

干熄锅炉内传热过程数学模型及其数值仿真

在详细分析了干熄锅炉内传热过程的基础上,建立了干熄锅炉内传热过程数学模型。采用现场实测数据对所建立的数学模型进行了验证。在此基础上,仿真计算了典型工况下的理论产汽量,并分析了影响干熄锅炉产汽量的诸多因素。所做工作对干熄炉一锅炉系统的计算机优化控制具有重要的指导意义。     

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.     

脉动燃烧器不同形式风冷翅片传热与流动特性的数值模拟

结合脉动燃烧器高温燃烧室和尾管部分需要风冷的实际情况,采用数值模拟方法针对几种典型翅片的传热与流动特性进行了数值计算,比较分析了不同形式翅片的表面传热系数、№数和表面摩擦系数,最终为脉动燃烧器风冷翅片选择了较为合理的翅片形式。     

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.