Transient Temperature Measurements Research Articles

The boundary-element method for the determination of a heat source dependent on one variable

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination. In this problem, if the heat source is taken to be space-dependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is time-dependent only, then the overdetermination is the transient temperature measurement recorded by a single thermocouple installed in the interior of the heat conductor. These measurements ensure that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or the L-curve criterion for the choice of the regularization parameter. The boundary-element method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed

Noncontact transient temperature mapping of active electronic devices using the thermoreflectance method

This work presents a demonstration of the applicability and efficacy of an experimental system capable of noninvasively and nondestructively scanning the transient surface temperature of pulsed microelectronic devices with submicron spatial and sub-microsecond temporal resolutions. The article describes the features of the experimental setup, provides details of the calibration process used to map the changes in the measured surface reflectivity to absolute temperature values, and explains the data acquisition procedure used to measure the transient temperature over a given active region. This thermoreflectance thermometry system is shown to be particularly suited for directly measuring the surface temperature field of devices undergoing the fast transients that are typical of next generation microelectronic devices. To illustrate the experimental approach, both quasisteady and transient temperature measurement results are presented for standard MOSFET devices.

Measurements of electric charge associated with evaporation and condensation of water on metallic surfaces as a consequence of pressure, humidity, and temperature change

Existence of a previously unreported flow of small current to and from a metallic electrode surface during transient air pressure change is reported and described. Measurements of transient current, humidity, and temperature with transient air pressure change are presented. The flow of electrode current is shown to be not due to capacitance and input offset voltage changes, since the calculated value is on the order of 10 −16 A which is much less than the measured currents of order 10 −13 A. Measurements using air of different levels of humidity and with dry nitrogen confirm that zero moisture results in essentially zero current, and that the amplitude of the current increases with increasing humidity.

Prostate perfusion in patients with locally advanced prostate carcinoma treated with different hyperthermia techniques.

We determined prostate perfusion in 18 patients with locally advanced prostate carcinoma treated with a combination of external beam irradiation and regional (10) or interstitial (8) hyperthermia. Perfusion values were calculated from temperature elevations due to constant applied power and from transient temperature measurements after a change in applied power. Student's t test was used for comparing perfusion values with time and in the 2 groups. At the start of regional hyperthermia treatment mean estimated perfusion plus or minus standard deviation was 10 +/- 8 ml./100 gm. per minute. At the end of treatment mean perfusion was increased to 14 +/- 2 ml./100 gm. per minute (p <0.01). Achieved thermal parameters were a mean temperature of at least 40.3C +/- 0.6C in 90% of the prostate, 40.9C +/- 0.6C in 50% and a mean maximum temperature of 41.6C +/- 0.6C. At the end of interstitial hyperthermia treatment estimated mean perfusion was 47 +/- 5 ml./100 gm. per minute, which was significantly different compared with the end of regional hyperthermia (p < 0(-7) ). Mean temperature was at least 39.4C +/- 0.9C in 90% of the prostate and 41.8C +/- 1.6C in 50%, while mean maximum temperature was 53.1C +/- 6.3C. Systemic temperature increased during regional hyperthermia up to 38.6C, whereas during interstitial hyperthermia body temperature was not elevated. During interstitial hyperthermia perfusion values are higher than during regional hyperthermia. Hyperthermia causes increased prostate perfusion.

Development of a Characterization Mold to Measure the Transverse Thermal Conductivity of a Composite Material by Inverse Analysis

In the present work, the transverse thermal conductivity of a composite material is determined by inverse analysis of the heat conduction phenomenon. Knowing the evolution of boundary conditions in time, i.e., the bottom and top surface temperatures of a specific sample, the thermal conductivity can be deduced from transient temperature measurements at three given positions through the thickness of the part. Starting from an initial estimate of thermal conductivity, the inverse method begins by solving the direct problem, i.e., the heat equation. The solution gives the transient temperature field everywhere in the composite sample. Calculated temperatures are then compared with transient experimental measurements based on a criterion evaluating the integral in time of the square of the distance between the measured and predicted temperatures. Conductivity is modified iteratively so as to minimize this criterion until the desired accuracy is achieved. The inverse methodology is tested in this article for a composite part made out of unsaturated polyester resin and unidirectional glass fibers. A special multifunctional mold was designed to produce the composite test plates by the Resin Transfer Molding Process (RTM) and at the same time, measure the transverse thermal conductivity as a function of time and resin degree of polymerization. The mold has an adjustable cavity depth to accommodate various experimental configurations and allows easy testing of a series of different fiber volume contents. It is equipped with controlled heating and cooling devices. Numerical simulations were performed to determine the dimensions of the mold and to optimize the positions of temperature and pressure sensors.

Switching behavior of microcrystalline silicon deposited by hot-wire chemical vapor deposition

We study current-induced changes in electrical and structural properties of a p-type microcrystalline silicon (μc-Si) films sandwiched between two metal contacts. After switching, the resistance decreases from above 1MΩ to below 1kΩ. The voltage–current characteristics show a saturated voltage region where irreversible changes occur gradually. In this region, transient temperature measurements show that film temperature rises considerably. The resistance of the switched state depends strongly on device area, suggesting that structural changes responsible for switching involve a large fraction of the device area. Micro-Raman studies show that film crystallinity increases during switching. This increase in crystallinity may indicate that the electrical switching process involves the formation of percolation paths through an amorphous incubation layer formed during film growth. This switching mechanism is quite different from the metallic filament formation observed in amorphous silicon switches.

Numerical nonlinear inverse problem of determining wall heat flux

The inverse problem of determining time-variable surface heat flux in a plane wall, with constant or temperature dependent thermal properties, is numerically studied. Different kinds of incident heat flux, including rectangular waveform, are assumed. The solution is numerically solved as a function estimation problem, so that no a priori information for the functional waveforms of the unknown heat flux is needed. In all cases, a solution in the form of a piece-wise function is used to approach the incident flux. Transient temperature measurements at the boundary, from the solution of the direct problem, served as the simulated experimental data needed as input for the inverse analysis. Both direct and inverse heat conduction problems are solved using the network simulation method. The solution is obtained step-by-step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. A straight line of variable slope and length is used for each one of the stretches of the desired solution. The influence of random error, number of functional terms and the effect of sensor location are studied. In all cases, the results closely agree with the solution.

Study of rapid transient explosive boiling under short-pulsed laser heating *

Using acetone, ethanol, water and acetone-water mixture as test liquids, the rapid transient explosive boiling (RTEB) taking place under short-pulsed laser heating is observed in experiment. The behaviors of temperature variation are investigated via transient temperature measurement. The vapor bubble behaviors of RTEB are captured by high-speed photography, and the difference between RTEB and normal boiling is analyzed. The boiling heat transfer of RTEB is also discussed. It shows that the character of RTEB is far different from normal boiling.

Resolution of linear inverse forced convection problems using model reduction by the Modal Identification Method: application to turbulent flow in parallel-plate duct

Inverse Heat Convection Problems have received attention only recently. They usually involve the use of a high order model corresponding to the spatial discretization of the domain. In this numerical study, the possibility to quickly solve such a problem with a low order model is analysed. The proposed method can be applied to any forced convection problem, whatever the geometry, as far as it is linear. Starting from a Detailed Model (DM) of the system, the Modal Identification Method is applied to build a Reduced Model (RM), which can be used to solve the inverse problem. The inversion procedure is sequential and requires no iterations. The function specification method is used to stabilize the inverse problem. An illustrative application is given. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, turbulent flow of a newtonian and constant property fluid inside a parallel-plate duct. Axial conduction in the flow is neglected. Two wall heat flux densities, varying with time, are estimated from the knowledge of simulated transient temperature measurements inside the fluid. When solving the inverse problem with RM instead of DM, a drastic reduction of computing time is obtained (with a reduction factor up to 11,000 in the present study), without significant loss of accuracy. Effects of functional form of the unknowns, sensors number and position, measurement error, on the accuracy of estimates are examined.

Comparison of Two Procedures for the Estimation of Surface Temperature History Using Function Specification Method

This work presents a comparative study of two alternative procedures for the estimation of surface temperature of a heated body from transient interior temperature measurements. This Inverse Heat Conduction Problem (IHCP) is solved (in both procedures) by using the Function Specification Method. A numerical test was used in order to compare the best estimation achieved in each procedure. The influences of the time step size, the total number of measurements and the noise level in the measurement have been considered in the estimation. Two criteria (minimization of total error and residual principle [3] are used to choose the best hyper-parameter (r). The comparisons confirm that the procedures and criteria used provide similar results, nevertheless this study reveals slight differences with respect to the accurate and the CPU time.

INVERSE HEAT CONDUCTION PROBLEM OF ESTIMATING TIME-VARYING HEAT TRANSFER COEFFICIENT

An inverse heat conduction problem is solved by using Alifanov's iterative regularization method to estimate the time-varying heat transfer coefficient of forced-convective flow boiling over the outer surface of a heater tube. The estimation is based on transient temperature measurements taken by a thermocouple on the inner surface of the circular tube on which the flow boiling occurs. The inverse problem is solved as an optimization problem in which a squared residue functional is minimized with the conjugate gradient method. A sensitivity problem is solved to determine the step size in the direction of descent, and an adjoint problem is solved to determine the gradient of the functional. No prior information is used in the functional form of the heat transfer coefficient variation with time. Numerical experiments are performed to test the proposed mathematical model of the measurement of flow boiling heat transfer coefficient. Effects of the time scale of the heat transfer coefficient variation, the mea...

INVERSE HEAT CONDUCTION PROBLEM OF ESTIMATING TIME-VARYING HEAT TRANSFER COEFFICIENT

An inverse heat conduction problem is solved by using Alifanov's iterative regularization method to estimate the time-varying heat transfer coefficient of forced-convective flow boiling over the outer surface of a heater tube. The estimation is based on transient temperature measurements taken by a thermocouple on the inner surface of the circular tube on which the flow boiling occurs. The inverse problem is solved as an optimization problem in which a squared residue functional is minimized with the conjugate gradient method. A sensitivity problem is solved to determine the step size in the direction of descent, and an adjoint problem is solved to determine the gradient of the functional. No prior information is used in the functional form of the heat transfer coefficient variation with time. Numerical experiments are performed to test the proposed mathematical model of the measurement of flow boiling heat transfer coefficient. Effects of the time scale of the heat transfer coefficient variation, the measurement errors, and the data acquisition rates on the inverse solution are investigated. We found that for a given experimental configuration there is a physical limitation on the time scale of the heat transfer coefficient variation that can be estimated by the inverse analysis.

Thermally induced optical effects in optical fibers by inverse methodology

A conjugate gradient method based on an inverse algorithm is applied in this study to estimate the unknown time-dependent convection heat transfer coefficient and microbending loss in carbon-coated optical fibers by reading the transient temperature measurement data at the fiber surface, when the optical fibers are subjected to transient thermal loading. No prior information is available on the functional form of the unknown convection heat transfer coefficient in the present study; thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact temperature measurements. Results show that an excellent estimation on time-dependent convection heat transfer coefficient, temperature distributions, and thermally induced microbending loss can be obtained for all the test cases considered in this study. The individual effect of the thickness, Young’s modulus, Poisson’s ratio, and thermal expansion coefficient of the carbon coating on the transient microbending loss of the optical fiber is also investigated. According to the numerical results, there exists an optimum value for the thickness of the carbon coating to reduce the transient microbending loss and to sustain the mechanical force at the same time.

Transient temperature measurements of resist heating using nanothermocouples

Resist heating is one of the major factors that causes feature size variation and pattern displacement in photomask fabrication. A number of models have been published to predict the rise in temperature during resist heating, but no transient temperature experimental results are available to verify those models. We have fabricated thin film gold/nickel thermocouples with junction areas as small as 100 nm2 on silicon and 500 nm2 on quartz. Microsecond scale transient resist heating measurements were obtained using these thermocouples. Irradiation by a 15 keV, 150 nA electron beam of 1.7 μm radius for 100 μs yielded temperature rises at the resist bottom surface of approximately 62 K on quartz substrates and of 18 K on silicon substrates. Simulation results using a multilayer Green’s function model are in reasonable agreement with these experimental data for smaller temperature rises but tend to overestimate by about 10% for larger rises in temperature. In our experiments, a 100 ms exposure is equivalent to a dose of 150 μC/cm2. Under the same electron beam conditions electron dosages of 5 and 15 μC/cm2 result in temperature rises of 25 and 40 K, respectively, on quartz substrates.

The Use of Model Reduction and Function Decomposition for Identifying Boundary Conditions of A Linear Thermal System

This numerical study deals with the identification of space and time varying inputs applied to a linear diffusive thermal system. Such an Inverse Heat Conduction Problem (IHCP) is ill-posed, its resolution is difficult for a large amount of unknowns and requires large memory size and computing time for multidimensional cases. Consequently, we propose a procedure to reduce both the number of unknowns and the model order. A 2D example is presented, with a heat flux density φ(y,t) to be identified from simulated transient temperature measurements. Starting from a Classical Detailed Model (CDM), two steps are performed. Firstly, a decomposition of the spatial distribution of φ on a functions basis leads to a small number of unknowns. Secondly, a Reduced Model (RM) is built using the Modal Identification Method. When RM is used to solve the inverse problem instead of CDM, computing time is drastically reduced (up to a factor 1000) whilst preserving accuracy. A procedure to determine the number of unknown coefficients is proposed. The inversion algorithm is sequential and requires no iterations. Future time steps with a function specification are used as a regularisation procedure. Tikhonov's regularisation is needed with CDM but not with RM.

Estimation of surface condition from the theory of dynamic thermal stresses

The present study applies a hybrid numerical algorithm of the Laplace transform technique and the finite-difference method with a sequential-in-time concept and the least-squares scheme to predict the unknown surface condition from the theory of dynamic thermal stresses. The unknown surface condition is not given a priori and is assumed to be the function of time before performing the inverse calculation. The whole time domain is divided into several analysis sub-time intervals and then the unknown surface condition on each analysis interval can be estimated from the transient displacement measurements or the transient temperature measurements. In order to show the efficiency and accuracy of the present inverse scheme, the comparison between the present estimates, the exact solution and the previous estimated results is demonstrated. The results show that a good estimation on the unknown surface condition can be obtained only at one selected location even for the case with the measurement error. The effect of the measurement location and the measurement error will also be investigated.

Characteristics of vortex flow in a low speed air jet impinging onto a heated disk in a vertical cylindrical chamber

An experiment combining flow visualization and transient temperature measurement is carried out to investigate the characteristics of the mixed convective vortex flow resulting from a low speed air jet impinging onto a heated horizontal circular disk confined in a vertical adiabatic cylindrical chamber. Attention is focused on the conditions leading to the onset of the inertia and buoyancy driven vortex rolls and the effects of governing nondimensional groups on the steady and time dependent vortex flow. More specifically, experiments are conducted for the jet Reynolds number varied from 0 to 1082 and Rayleigh number from 0 to 18,790 for two different injection pipes. The results show that typically the steady vortex flow in the processing chamber consists of two inertia-driven and one buoyancy-driven circular vortex rolls. The secondary inertia-driven roll only appears at high jet Reynolds numbers. At low buoyancy-to-inertia ratio Gr/ Re j 2 the vortex rolls are steady and axisymmetric. But at certain high Gr/ Re j 2 the vortex flow becomes unstable and the vortex rolls are somewhat deformed. Besides, new vortex rolls can be induced by the additional thermal rising from the heated disk and the splitting of the primary inertia-driven roll. The temporal characteristics of the time periodic vortex flows are examined in detail. In the region dominated by the new rolls the flow oscillates significantly. Finally, empirical equations are proposed to correlate the oscillation frequency of the time periodic flow, and the size and location of the vortex rolls. Furthermore, the conditions for the onset of the buoyancy driven rolls are given. A flow regime map is provided to delineate the temporal state of the vortex flow.

An inverse problem of parameter estimation for heat and mass transfer in capillary porous media

This work deals with the solution of an inverse problem of parameter estimation involving heat and mass transfer in capillary porous media, as described by the dimensionless linear Luikov’s equations. The physical problem under picture involves the drying of a moist porous one-dimensional medium. The main objective of this paper is to simultaneously estimate the dimensionless parameters appearing in the formulation of the physical problem by using transient temperature and moisture content measurements taken inside the medium. The inverse problem is solved by using the Levenberg–Marquardt method of minimization of the least-squares norm with simulated measurements.

E132 強制対流熱伝達問題における未知熱的境界条件の推定

An inverse approach to estimate unknown steady thermal boundary conditions with spacewise variation for forced convection field is proposed. The estimation is based on adjoint formulation using transient temperature measurements taken with single sensor. Least squares method is applied to the extimation process to overcome the ill-posed behavior associated with inverse problems. A numerical example determining the unknown wall heaf flux for the parallel plate model is shown to demonstrate the possibility of this method.

Transient Temperature Measurement of Unburned Gas Using Optical Heterodyne Interferometry.

This paper demonstrates an application of the optical heterodyne interferometry, a laser-based technique for measuring the temperature history of gas in combustion devices, such as internal combustion engines. The technique is based on refractive index measurements using laser interferometry along a line of sight. The temperature history of gas can be determined from the pressure history in the combustion chamber, the gas composition, and the laser interference intensity. A polarization-preserving fiber was used to deliver the test beam to and from the test section to improve the feasibility of the system as a sensor probe. The temperature of the unburned mixture in the end-gas region of a constant volume combustion chamber and in an engine cylinder were measured during flame propagation. The accuracy of the measurement and the feasibility of this system are discussed. The measurement accuracy of our system was sufficient to be applied to temperature history measurement of an unburned gas compressed by flame propagation in an engine cylinder. The uncertainty of this method is within ±10K. The resolution of the temperature measurement was approximately 0.5 K, and was dependent upon both the sampling clock speed of the A/D converter and the length of the test section. This optical heterodyne interferometry system may also be used for other applications that require a fast response time to measure the density and pressure of a gas, and thereby obtain a transient temperature record.