Estimation of thermal contact resistance and thermally induced optical effects in single-coated optical fibers

In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown time-dependent thermal contact resistance in a single-coated optical fiber, which is subjected to transient thermal loading. While knowing the temperature history at the measuring position, no prior information is needed on the functional form of the unknown contact resistance. The temperature data obtained from the direct problem are used to simulate the temperature measurement. The influence of measurement errors, initial guess values, and measurement locations upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent thermal contact resistance, temperature distributions, thermally induced microbending loss, and refractive index changes can be obtained for the case considered in this study.     

Identifying time-dependent damping and stiffness functions by a simple and yet accurate method

The inverse vibration problem is a mathematical process to determine unknown mechanical parameters from measured vibration data. In this study the data of displacement are chosen in order to identify a time-dependent function of damping or stiffness. However, when both functions are to be identified we require both the data of displacement and velocity. This is the first time that a closed-form estimation method for the inverse vibration problems of estimating time-dependent parameters has been constructed. We are able to transform the inverse vibration problem into an identification problem governed by a parabolic-type partial differential equation (PDE). Then, a one-step group-preserving scheme (GPS) for the semi-discretization of PDE is established, which can be used to derive a closed-form solution for estimating parameters. The new Lie-group estimation method has three further advantages: it does not require any prior information on the functional forms of unknown functions; no initial guesses are required; and no iterations are required. Numerical examples were examined to show that the present approach is highly accurate and efficient even for identifying discontinuous and oscillatory parameters. Against the noise is good when only one function is estimated; however, the present approach is slightly weak against the noise when both functions are identified.     

Measurement of annular air-gap using active infrared thermography

The paper discusses an infrared thermography (IRT) based procedure for quantification of annular air-gap in cylindrical geometries. Different annular air-gaps are simulated using aluminum hollow cylinders and solid stainless steel inserts of varying diameters. The specimens are externally heated using a hot air-gun and the temperature of the specimens are monitored during cooling using an infrared camera. The temperature decay during the cooling cycle follows an exponential profile in all the cases where the decay constant is air-gap dependent. The rate of temperature decay is fastest for the empty cases (without inserts) and lower for smaller air-gaps. The system is analyzed using a lumped system model by measuring the temperature over a time scale significantly higher than the transition time of the lumped system. It is observed that the Biot number of the system is less than unity, allowing analysis of the system in terms of a single time constant, neglecting internal temperature transients. It is observed that the time constant of temperature decay increases with decreasing annular air-gap. An empirical relation between the inverse of time constant of temperature decay and annular air-gaps is established. Using this calibration curve, unknown air-gaps up to 20 μm could be measured with good accuracy. Applications of this newly developed technique include detection of misalignment of concentric machineries and determination of fuel-to-clad gap of nuclear reactor fuels.     

Estimating cutting front temperature difference in disk and CO2 laser beam fusion cutting

A three-dimensional, semi-stationary, simplified thermal numerical model was developed. The average cutting front temperature difference in disk and CO₂ laser beam fusion cutting of 90MnCrV8 was estimated by computing the conductive power loss. Basing on heat affected zone extension experimentally measured and using an inverse methodology approach, the unknown thermal load on the cutting front during laser cutting was calculated. The accuracy of the numerical power loss estimation was evaluated comparing the results from simulation with the ones from analytical models. A good agreement was found for all the test cases considered in this study. The conduction losses estimation was used for justifying the lower quality of disk laser cuts due to the lower average cut front temperature. This results in the increase of viscosity of molten material and in the subsequent more difficult ejection of the melted material from the cut kerf.     

Particle Size Distribution by Combined Elastic Light Scattering and Turbidity Measurements. A Novel Method to Estimate the Required Normalization Factor

Turbidity (T) and Elastic Light Scattering (ELS) measurements can be combined to estimate the particle size distribution (PSD) of a polymer latex. To this effect a “normalization factor” must be employed to adequately scale both measurements. In a real application, such factor is a priori unknown, and it must be estimated for determining the PSD. In a previous publication, a method was proposed to simultaneously estimate the normalization factor and the PSD by solving an inverse nonlinear problem. In this work, a simpler technique is presented which estimates the normalization factor and the PSD by sequentially solving two inverse linear problems. To evaluate the proposed technique, a synthetic example based on a polystyrene latex sample with a bimodal PSD was solved. It is shown that, for slight noise measurements, the errors in the estimation of the normalization factor are quite small and have a low effect on the PSD recovery.     

A numerical procedure for estimation of the melt depth in laser material processing

In this study, an algorithm based on conjugate gradient method (CGM) is applied to estimate the unknown time dependent melt depth during laser material processing in liquid phase. The determination of the melt depth is treated as a one-dimensional, transient, inverse heat conduction problem (IHCP). It is assumed that no prior information is available for the functional form of the unknown melt depth, but it can be estimated by an inverse analysis with temperature measurements near the heated surface. The algorithm has been applied to aluminum, titanium and fused quartz and accurate melting depth and temperature distributions can also be returned. In addition, this methodology can also be applied to solve other problems such as calculating the cutting forces in nanomachining by atomic force microscopy (AFM), and estimating the heat sources in a X-ray lithographic process.     

Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

We investigate numerically an inverse problem related to the Boltzmann–Poisson system of equations for transport of electrons in semiconductor devices. The objective of the (ill-posed) inverse problem is to recover the doping profile of a device, presented as a source function in the mathematical model, from its current–voltage characteristics. To reduce the degree of ill-posedness of the inverse problem, we proposed to parameterize the unknown doping profile function to limit the number of unknowns in the inverse problem. We showed by numerical examples that the reconstruction of a few low moments of the doping profile is possible when relatively accurate time-dependent or time-independent measurements are available, even though the later reconstruction is less accurate than the former. We also compare reconstructions from the Boltzmann–Poisson (BP) model to those from the classical drift–diffusion-Poisson (DDP) model, assuming that measurements are generated with the BP model. We show that the two type of reconstructions can be significantly different in regimes where drift–diffusion-Poisson equation fails to model the physics accurately. However, when noise presented in measured data is high, no difference in the reconstructions can be observed.     

Painlevé Integrability of Nonlinear Schrödinger Equations with bothSpace- and Time-Dependent Coefficients

We investigate the Painlevé integrability of nonautonomous nonlinearSchrödinger (NLS) equations with both space- and time-dependent dispersion, nonlinearity, and external potentials. The Painlevé analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painlevé analyses and/or become unknown new equations.     

Xenon NMR measurements of permeability and tortuosity in reservoir rocks

In this work we present measurements of permeability, effective porosity and tortuosity on a variety of rock samples using NMR/MRI of thermal and laser-polarized gas. Permeability and effective porosity are measured simultaneously using MRI to monitor the inflow of laser-polarized xenon into the rock core. Tortuosity is determined from measurements of the time-dependent diffusion coefficient using thermal xenon in sealed samples. The initial results from a limited number of rocks indicate inverse correlations between tortuosity and both effective porosity and permeability. Further studies to widen the number of types of rocks studied may eventually aid in explaining the poorly understood connection between permeability and tortuosity of rock cores.     

Coupling of Evaporation and Thermocapillary Convection in a Liquid Layer with Mass and Heat Exchanging Interface

We propose and analyse a new model of thermocapillary convection with evaporation in a cavity subjected to horizontal temperature gradient, rather than the previously studied model without evaporation. The pure liquid layer with a top free surface in contact with its own vapour is considered in microgravity condition. The computing programme developed for simulating this model integrates the two-dimensional, time-dependent Navier-Stokes equations and energy equation by a second-order accurate projection method. We focus on the coupling of evaporation and thermocapillary convection by investigating the influence of evaporation Biot number and Marangoni number on the interracial mass and heat transfer. Three different regimes of the coupling mechanisms are found and explained from our numerical results.     

Effects of signal corrections on measurements of temperature and OH concentrations using laser-induced fluorescence

Temperature and OH concentrations derived from OH laser-induced fluorescence (LIF) are known to be susceptible to effects such as collisional quenching, laser absorption, and fluorescence trapping. In this paper, a set of analytical and easy-to-implement methods is presented for treating these effects. The significance of these signal corrections on inferred temperature and absolute OH concentration is demonstrated in an atmospheric-pressure, near-stoichiometric CH₄-air flame stabilized on a Hencken burner, for laser excitation of both the A²Σ⁺←X²Π (0,0) and (1,0) bands. It is found that the combined effect of laser attenuation and fluorescence trapping can cause considerable error in the OH number density and temperature if not accounted for, even with A–X(1,0) excitation. The validity of the assumptions used in signal correction (that the excited-state distribution is either thermalized or frozen) is examined using time-dependent modeling of the ro-vibronic states during and after laser excitation. These assumptions are shown to provide good bounding approximations for treating transition-dependent issues in OH LIF, especially for an unknown collisional environment, and it is noted that the proposed methods are generally applicable to LIF-based measurements.     

Model predictive inverse method for recovering boundary conditions of two-dimensional ablation

A model predictive inverse method (MPIM) is presented to estimate the time- and space-dependent heat flux onthe ablated boundary and the ablation velocity of the two-dimensional ablation system. For the method, first of all, therelationship between the heat flux and the temperatures of the measurement points inside the ablation material is establishedby the predictive model based on an influence relationship matrix. Meanwhile, the estimation task is formulated as aninverse heat transfer problem (IHTP) with consideration of ablation, which is described by an objective function of thetemperatures at the measurement point. Then, the rolling optimization is used to solve the IHTP to online estimate theunknown heat flux on the ablated boundary. Furthermore, the movement law of the ablated boundary is reconstructedaccording to the estimation of the boundary heat flux. The effects of the temperature measurement errors, the numberof future time steps, and the arrangement of the measurement points on the estimation results are analyzed in numericalexperiments. On the basis of the numerical results, the effectiveness of the presented method is clarified.     

Infrared thermography applied to the resolution of inverse heat conduction problems: recovery of heat line sources and boundary conditions

In this paper we present an application of infrared thermography for inverse heat conduction problems resolution. The approach described in the paper is based on a Boundary Element Method formulation of the transient heat diffusion equation. The inverse problems under investigation concern the time and space reconstruction of unknown boundary conditions or heat line source strength. As there is a lack of information in the system, some additional measurements are necessary to solve the problem. In the examples proposed in this paper the extra information is provided by an infrared scanner. The measurements contained in the infrared pictures are used in the model as a Dirichlet boundary condition or as a special boundary condition prescribing both temperature and heat flux density on the scanned boundary. We present some experimental results concerning line source strength identification and the reconstruction of unknown heat fluxes applied on an out of reach boundary. All the examples presented in this paper are related to 2D transient diffusion. As the inverse problem is ill-posed, time and space regularization techniques are used to stabilize the solution and reduce the sensitivity of the latter to measurement errors.     

Experimental Design and Methodology for Estimation of Local Heat Transfer Coefficient in Jet Impingement Using Transient Inverse Heat Conduction Problem

Abstract

This article aims to employ a two-dimensional inverse heat conduction technique in designing an experiment for accurately estimating the local convective heat transfer coefficient in slot jet impingement, given temperature measurements at some interior locations in the target plate. The method uses a sequential procedure together with the Beck function specification approach. Solution accuracy and experimental errors are examined using simulated temperature data. It is concluded that a good estimation of the space variable heat transfer coefficient can be made from the knowledge of the transient temperature recordings. The technique is used in a series of numerical experiments to provide the optimum experimental design for a slot jet impingement heat transfer investigation.     

Vacuum pair-production in a classical electric field and an electromagnetic wave

Using semiclassical WKB-methods, we calculate the rate of electron–positron pair-production from the vacuum in the presence of two external fields, a strong (space- or time-dependent) classical field and a monochromatic electromagnetic wave. We discuss the possible medium effects on the rate in the presence of thermal electrons, bosons, and neutral plasma of electrons and protons at a given temperature and chemical potential. Using our rate formula, we calculate the rate enhancement due to a laser beam, and discuss the possibility that a significant enhancement may appear in a plasma of electrons and protons with self-focusing properties.     

基于最大熵估计Alpha谱缩放与平移量的温度与发射率分离算法

在热红外波段, 为了使温度与发射率分离过程不依赖数据库提供的经验信息, 并且实现更高的反演精度和更快的计算速度, 研究了一种新的温度与发射率分离算法. 首先, 在维恩近似原理的基础上, 求解了Alpha谱分布, 并利用Alpha谱描述光谱发射率的形状信息. 其次, 改进了最大熵温度与发射率分离算法: 应用最大熵估计模型对Alpha谱缩放与平移量进行估计, 减少了待估计参数的数量, 大幅简化了求解过程. 最后, 进行了算法的数值仿真实验: 求解了典型地物目标的温度与光谱发射率, 并且分析了算法对系统噪声的鲁棒性. 仿真数据表明: 发射率估计的最大RMSE为0.017, 温度估计的最大绝对误差的绝对值为0.62 K; 对系统添加测量信噪比为11的高斯白噪声, 发射率估计的相对RMSE为2.67%, 温度估计的相对误差为1.26%. 结果表明: 本文所述算法求解精度高, 计算速度快, 具备良好的鲁棒性.     

An inverse analysis of a transient 2-D conduction-radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm

This article deals with the simultaneous estimation of parameters in a 2-D transient conduction-radiation heat transfer problem. The homogeneous medium is assumed to be absorbing, emitting and scattering. The boundaries of the enclosure are diffuse gray. Three parameters, viz. the scattering albedo, the conduction-radiation parameter and the boundary emissivity, are simultaneously estimated by the inverse method involving the lattice Boltzmann method (LBM) and the finite volume method (FVM) in conjunction with the genetic algorithm (GA). In the direct method, the FVM is used for computing the radiative information while the LBM is used to solve the energy equation. The temperature field obtained in the direct method is used in the inverse method for simultaneous estimation of unknown parameters using the LBM-FVM and the GA. The LBM-FVM-GA combination has been found to accurately predict the unknown parameters.     

Effect of heat generation on transient flow of micropolar fluid in a porous vertical channel

The present work is performed to study the effect of heat generation on fully developed flow and heat transfer of micropolar fluid between two parallel vertical plates. The rigid plates are assumed to exchange heat with an external fluid by convection. The governing equations are solved by using Crank–Nicolson implicit finite difference method. The effects of governing parameters such as transient, heat generation, micropolar parameter, Prandtl number, Biot number, and Reynolds number on the velocity and temperature profiles are discussed. It is found that the presence of heat generation enhances the velocity and temperature of the micropolar fluid at the middle of the channel.     

Inverse estimation of the pulse parameters of a time-varying laser pulse to obtain desired temperature at the material surface

A proper selection of the pulse parameters is essential to achieve desired temperature at the material surface. This leads to obtain the required metallurgical changes in the surface vicinity when a time-varying laser pulse is used in a heating process such as surface modification. In this paper, the conjugate gradient method (CGM) for parameter estimation is successfully applied to estimate the unknown laser pulse parameters for those purposes during laser heating process. The determination of the pulse parameters is treated as a one-dimensional, transient, non-linear inverse heat conduction problem (IHCP). Based on a sensitivity analysis, the inverse problem is solved as an optimization problem comparing a desired temperature at the surface and a calculated one where the objective function is minimized by CGM. The method has been applied to a test case of a heating process on steel, appropriate pulse parameters and desired temperature distribution can also be returned.     

Modelling of the solid–liquid interface during laser processing using an inverse methodology

This study presents a methodology for estimating the melt depth during laser processing of solid materials. The determination of the melt depth is treated as an inverse heat conduction problem, which includes the solid and liquid phases. The conjugate gradient method is applied to treat the inverse problem using the available temperature measurements. Without the inverse methodology the melt depth is very difficult to obtain with precision. The proposed method can also be applied during microthermal machining to determine the location of the solid–liquid interface and the temperature distributions of the two phases by using scanning thermal microscopy.