Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction

This work presents an improved apparatus and a numerical approach to obtain the estimate of thermal diffusivity of complex materials. Transient thermal response at the axis of cylindrical sample is measured when boundary temperature is suddenly changed. Instead of assuming an ideal step temperature excitement, a measured temperature of a material boundary was employed. An iterative procedure, based on minimizing a sum of squares function with the Levenberg–Marquardt method, is used to solve the inverse problem. A graphical user interface is built to enable easy use of the inverse thermal diffusivity estimation method. The reference materials used to evaluate the method are Agar water gel, glycerol and Ottawa quartz sand.     

Thermal diffusivity of some crystalline rocks

Thermal diffusivity data at room temperature and uniaxial pressure of 1 MPa are reported for five sets of crystalline rocks—granite, granodiorite, gabbro, basalt and gneiss. Diffusivity ranges between approximately 0.6 and 1.9 mm²/s, the lower end of the range being appropriate for basic rocks and the upper end for quartz-bearing acidic rocks. The scatter in diffusivity for each data set is significantly more than that of thermal conductivity, because the diffusivity of water is typically less than 10% of the diffusivity of most common minerals, whereas water conductivity is 25–30% of the conductivity of the minerals. For a sample set of uniform mineralogy in which porosity varies, a greater variation of diffusivity than of conductivity is therefore expected. For three of the sets sufficient mineralogical data were available to permit the assessment of methods of estimating thermal diffusivity from mineral content. All models tested yielded higher mean values of diffusivity than the means of the measured values. No model was found to be able to predict diffusivity to better than approximately 20%, but if that accuracy is sufficient, a simple geometrical model, for which only quartz content must be known, is adequate. The diffusivity data have been combined with measurements of thermal conductivity and density to provide estimates of specific heat. These all tend to be higher than those reported in the literature. For some rocks, such as the basalts, this can be explained in terms of relatively high water content and the very high specific heat of water compared with that of most common minerals. For the granites and granodiorites, the new specific heat data redefine the previously published means and ranges, by increasing the data base by approximately an order of magnitude.     

Effects of Thermal Stresses on the Frequency-Temperature Behavior of Piezoelectric Resonators

The frequency-temperature behavior of a piezoelectric crystal resonator can be predicted quite accurately if the resonator is under a stress-free and steady-state uniform temperature condition. The condition is however seldom achieved practically. Most practical resonators are subjected to thermal stresses. Conventional finite element analytical tools such as ANSYS cannot provide a sufficiently accurate model for the frequency-temperature behavior of piezoelectric quartz resonators. A new dynamic frequency-temperature model which accurately predicted the frequency-temperature behavior of quartz resonators affected by transient and steady state temperature changes was presented. Lagrangean equations for small vibrational (incremental) displacements superposed on initial thermal stresses and strains were employed. The initial thermal stresses and strains were obtained from the uncoupled heat and thermoelastic equations. The constitutive equations for the incremental displacements incorporated the temperature derivatives of the material constants. Numerical results were compared with the experimental results for a 50 MHz AT-cut quartz resonator mounted on a glass package. Good comparisons between the experimental results and numerical results from our new model were found. The differences between the thermal expansion coefficients of glass and quartz gave rise to the thermal stresses that had adverse effects on the frequency stability of resonators. Different optimal crystal cut angles of quartz, and resonator geometry were found to achieve stable frequency-temperature behavior of the resonator in a glass package. The dynamic frequency-temperature model was used in the theoretical analyses and designs of high Q, 3.3 GHz, quartz thin film resonators.     

光学热带法测量固态材料热物性研究

针对接触式瞬态热带法测量导热系数时,加热丝和样品间接触热阻,会影响实验测量结果以及对固体样品形状大小要求较高的现状,根据瞬态热带法原理,本文提出了一种光学瞬态热带法来测量固体材料的导热系数。采用连续激光为加热源,通过透镜将光斑放大并聚焦照射在样品表面,实现样品非接触式测量。构建二维导热模型,采用红外热像仪记录样品表面温升随时间的变化关系,根据导热理论模型求出待测样品的热扩散系数及导热系数。以K9和石英玻璃为样品对本套测量方法进行验证,制备并测量了纯石蜡、0.5%和1%石墨烯-石蜡的固态复合相变材料的导热系数,探讨了影响实验结果的潜在因素。     

Thermal Dissolution of a Spherical Particle with a Moving Boundary

A numerical problem for mass and energy transport considering thermodynamic equilibrium is solved around a spherical particle in the absence of hydrodynamic effects in a binary solution. The analysis includes the radial convective term generated due to the differences on density between the solid and liquid phases. Because the transport of mass and energy compete in the process, how the rate of dissolution is affected by compositional diffusivity or thermal diffusivity is distinguished. The partial differential equations are discretized with the finite difference method in space, and the resulting set of ordinary differential equations in time is solved by the method of lines. The numerical solution for the thermal dissolution of a spherical particle in a binary melt is compared with heat-balance integral method for small times of the process. The solutions are found to agree for conditions close to the dissolution regime.     

Thermal diffusivity measurement of glass at high temperature by using flash method

A measurement of the thermal diffusivity of a semi-transparent material (glass) by means of the "Flash Method" is investigated in the present work. By taking into account the heat losses on the two faces of the sample, and using a new experimental technique design, an improvement of the determination of the thermal diffusivity of the semi-transparent material (glass) at high temperature is realized. The experimental design presented here is an original technical concept that enables a significant reduction in heat loss during the experiments. A very simple model based on the quadrupole method is used to theoretically determine the thermal diffusivity of the semi-transparent material by taking into account both conduction and radiation. Theoretical results clarify the effect of the absorption coefficient and the thickness of the sample on the heat transfer in the semi-transparent medium.     

The Lock-in Heating-Cooling Method for the Measurement of the Thermal Diffusivity of Solid Materials

A new test method is presented for the on-field nondestructive measurement of the thermal diffusivity of solid materials. A periodic thermal disturbance is supplied to the inspected material by a thermoelectric source based on the Peltier effect. This can alternate heating and cooling stages and provide, if properly controlled, a harmonic disturbance with null net heat flux. A steady-periodic temperature field can thus be induced within the specimen. The diffusivity of the material is then estimated by monitoring the propagation of the temperature cycles along the optically accessible surface of the specimen, adjacent to the thermal input surface area. A camera for infrared thermography is used for nonintrusive surface temperature measurement. At the current stage of development, the focus is on the accurate reproduction of the theoretical model on which the method is based. Ease of operation and portability of the test equipment are also pursued. However, tests on thin specimens of materials with known properties give measurements in encouraging agreement with the nominal values.     

Thermal Fracture of an Interpenetrating Phase Composite: Effects of Local Thermal Nonequilibrium

When subjected to thermal shocks, an interpenetrating phase composite may undergo significant, long range temperature difference between the constituent phases due to the interconnected microstructural networks, which facilitate faster heat transfer in the phase of higher thermal diffusivity. This temperature differential may alter the macroscopic temperature field thereby inducing additional thermal stresses in the composite. This work presents a local thermal nonequilibrium (LTNE) thermoelasticity theory for interpenetrating phase composites. In the LTNE thermoelasticity theory, the temperatures of the constituent phases are governed by the LTNE heat conduction equations based on the continuum theory of mixtures. A weighted average of temperatures for the constituents is employed in the thermoelastic constitutive equations of the homogenized composite. The model is subsequently applied to an infinite composite strip with an edge crack subjected to a thermal shock. Asymptotic solutions of temperature, thermal stress, and thermal stress intensity factor are obtained using the Laplace transform technique. The numerical results for an interpenetrating Al₂O₃/Al composite show that the temperature and thermal stress fields of the LTNE theory deviate from those of the classical theory. More importantly, the thermal stress intensity factor is reduced by considering the LTNE effect, which indicates that interpenetrating networks enhance the thermal fracture resistance of ceramic-metal composites.     

Thermal wave propagation in a bi-layered composite sphere due to a sudden temperature change on the outer surface

The dynamic thermal behavior of a bi-layered composite sphere due to a sudden temperature change on the outer surface is investigated. The analytical–numerical technique, which is based on the Laplace transformation and the Riemann-sum approximation, is employed to predict the temperature and heat flux histories in the composite sphere. The effects of different parameters such as the relaxation time, the thermal diffusivity ratio, the thermal conductivity ratio, the relaxation time ratio, and the radius ratio of the inner and outer layers of the composite sphere are studied and presented.     

Numerical simulation of thermal runaway phenomena in silicon semiconductor devices

A mathematical model for heat production due to thermal excitation of conductive electrons and positive holes in a semiconductor pn junction is derived and discussed. The model is applied to simulate the thermal runaway phenomena in power electronics semiconductor devices. Our discussion focuses especially on the modeling of unexpected huge currents due to an excessive temperature increase. Calculated dynamics of temperature distributions of a silicon wafer while cooling performance decreases proved it is possible for a silicon wafer to be heated over its melting point in a few milliseconds. Our results indicate that if a local hot spot arises in a wafer, the thermal intrinsic excitation carries an increased diffusion current of minor carriers and a recombination current in the depletion layer of a pn junction. Also it appears to be important that cooling performance should be uniform on the wafer to avoid the growth of hot spots and thermal‐runaway itself. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(6): 438–455, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10044     

水蒸气环境下金属表面温度红外测量的试验研究

分析了在高温蒸汽环境的条件下,通过红外辐射方式对转子表面温度进行测量的可行性及影响测量精度的各种因素。同时通过试验方式研究了高温蒸汽及石英视窗玻璃对单色、双色及宽波段红外测温精度的影响。研究表明,以红外辐射方式对高温蒸汽环境中的物体(转子)进行表面红外测温是基本可行的,其响应速度能满足热应力分析的需求;单/双波段测温方式各有其优缺点;红外石英视窗玻璃对红外能量透射的干扰可控制在能接受范围内。上述结论为利用红外测温技术对汽轮机转子表面进行直接温度测量奠定基础。     

基于热辨识技术的硅基防热材料高温热导率测量

硅基防热材料是高超声速飞行器防热系统用重要材料之一,但由于硅基防热材料在高温条件下存在着复杂的物理化学变化,使得高温热导率的获取变得困难,这已成为飞行器防热系统精细化设计的主要制约瓶颈。基于热导率辨识方法,设计了一种能够实现硅基防热材料高温热导率测量的试验测量装置,对硅基防热材料在常温~800℃热导率进行了测量,并将测得的热导率外推应用到其他试验状态。结果表明,测得的硅基防热材料高温热导率合理可靠,具有很高的工程精度。该试验测量装置可实现不同温度下热导率的同步测量,测量成本低,效率高,这对其他防热材料的高温热导率测量具有重要的参考价值。     

Development and Characterization of Thermal Enhancement Structures for Single-Phase Liquid Cooling in Microelectronics Systems

In this paper, the development and characterization of thermal enhancement structures for single-phase liquid cooling in microelectronics systems are presented. Miniature heat sinks with three different types of thermal enhancement structures were examined. The first type was a metallic microchannel heat sink (MMCHS) made of aluminum with the channel dimensions of 15 mm (length) × 0.2 mm (width) × 2 mm (height). The second type was the silicon microchannel heat sinks (SMCHS) made through the deep reactive ion etching technique on a 6 inch wafer, with identical channel height of 0.45 mm and average channel widths of 66.6 μ m and 46.6 μ m, respectively. The last type was the metallic foam heat sinks (MFHSs), which were formed by brazing porous foam materials of high pore density onto copper base plates. All three types of heat sinks were fabricated and experimentally characterized by incorporating into electronic packages in standard flip chip ball grid array format. Characterization results indicate that, given a thermal window of 50°C, both the MMCHS and MFHSs can achieve an equivalent package heat dissipation above 100 W/cm² at moderate pressure drops and the SMCHS above 200 W/cm² at larger pressure drops. A comparison of thermal enhancement and manufacturability of the three types of heat sinks is also presented.     

Investigation on measurement accuracy of the periodic hot-wire method by means of numerical temperature field calculations

The periodic hot-wire method is an appropriate means for the determination of the thermal diffusivity a and thermal conductivity λ. A thin platinum wire in a sample is heated by a sinusoidal alternating current. The resulting thermal waves penetrate into the surrounding sample. The thermal diffusivity a and the thermal conductivity λ of the sample can be calculated by analysing the amplitudes and the phase-lags of the waves and applying the Fourier equation. In order to derive the evaluation procedure for a and λ the temperature field in the sample is calculated analytically under the assumption, that the platinum wire represents a perfect, infinitly extended line heat source. This assumption can only be approached and thus measurements must deviate from theory. These deviations were determined by numerical calculations of the temperature field considering the real geometry of the platinum wire. The measurement accuracy and the optimum frequency range of the periodic hot-wire method has been obtained by comparing the numerically and analytically calculated temperature fields.     

SIMULATION OF RAPID THERMAL PROCESSING IN A DISTRIBUTED COMPUTING ENVIRONMENT

Rapid thermal processing (RTP) has become a key technology in the fabrication of advanced semiconductor devices. As wafers get larger and chip dimensions become smaller, the understanding of the highly coupled physics, such as radiative heat transfer, transient fluid flow, heat transfer, and chemical reactions through numerical modeling using high-performance computing, is the key to the design, optimization, and control of RTP reactors. In this study, an accurate and efficient simulation tool for RTP in a distributed computing environment is developed by implementing various new models and algorithms. Thegoverning equations for highly coupled and transient transport phenomena inRTP are solved by anunstructured finite volume method (FVM). Surface radiative heat transfer is the most dominant mode of heat transfer in RTP and it is modeled by the modified discrete transfer method (MDTM). The radiative properties on the patterned wafer are quite different from those on the bare silicon and they are predicted by the matrix method. To enhance thecomputationefficiency, anefficient parallelalgorithmis implemented in the solution procedure. Data communication among the processors is carried out by the Parallel Virtual Machine (PVM). To evaluate the present simulation tool, an actual commercial RTP reactor is investigated under various conditions. The accuracy of the present model is validated through the comparisons of wafer temperature profile between different models for steady state andtransient flow andheat transfer cases. To demonstrate the importance of the pattern effects in RTP systems, a transient case containing the patterned wafer is investigated. The temperature profile and its uniformity for the patterned wafer are found to be quite different from those for the unpatterned wafer. To examine the performance on parallel computation, the previous transient case is studied with different processor numbers. As the processor number increases, the computationtime is seen to reduce; however, the parallel performance is seen to degrade A larger solution iteration number and higher communication overhead are believed to be the major reasons for the degradation of the parallel performance. The present case studies indicate that the simulation tool developed in this study can be used to systematically investigate various effects in RTP systems because of its high accuracy and efficiency.     

离心铸造太阳电池硅片液态成形机制的研究

为了将离心铸造技术成功地移植到低成本超薄多晶太阳电池硅片的成形工艺上，提出了ＥＬＣＣ技术的硅片液态成形方法，即将铸模型腔预热至硅熔点以上温度，过热的硅液被浇注到型腔后，在离心力的作用下始终保持液态充型。这种成形机制易于实现厚度小于１ｍｍ的硅片的完整成形，而且对模具转速、硅液过热度等要求较低。采用该方法，硅片的成形与结晶不会同时发生，可以在硅片液态成形后，采用定向凝固的方法获得粗大的定向柱晶组织，提高硅片的光伏性能。采用理论分析、计算机模拟与工艺实验相结合的方法，对ＥＬＣＣ技术硅片液态成形机制进行了研究，为进一步对硅片凝固过程组织控制的研究奠定基础。     

Thermal performance of a combined packed bed–solar pond system—a numerical study

Solar ponds have recently become an important source of energy that is used in many different applications. The technology of the solar pond is based on storing solar energy in salt-gradient stratified zones. Many experimental and numerical investigations concerning the optimum operational conditions and economical feasibility of solar ponds have been published in the last few decades. In the present study a modified solar pond with a rock bed inserted at the bottom is suggested and investigated. In order to conduct this study and predict the thermal performance of the combined system, a one-dimensional transient numerical model is developed. The boundary conditions are based on measured ambient and ground temperatures at Kuwait city. The model is validated for standard plain salt-gradient solar ponds and is then used to examine the thermal performance of the combined storage system for different rock material and bed geometry. It has been shown that the storage temperature is remarkably increased when low thermal diffusivity rocks (such as Bakelite) are used in the packed bed. Meanwhile, when high conductive rocks are used, the thermal storage temperature considerably deteriorates and the temperature variations amplitudes are almost flattened out. The bed geometry also plays a significant role in the storage process. As expected, an appreciable gain in the storage temperature was obtained for thicker rock beds. Low porosity rock beds, as well, produce higher storage temperatures in the storage zone.     

Real Time Dynamic Programming Control of Rapid Thermal Processing Furnaces

In the rapid thermal processing of a semi-conductor wafer, the temperature of the latter has to follow a preset time evolution profile while keeping spatial uniformity. A model-based open loop control strategy is presented in all its steps. A global and sufficiently accurate thermal model, based on the component interaction network, is used for the prediction of the required instantaneous heat flux distribution gained by the wafer. The same model is used to calculate the distribution of the net heat flux gainedby the wafer for each radiant emitter. The optimal combination of input powers to the radiant emitters is then determined using real time dynamic programming. It consists in minimizing the maximum difference between the required heat flux distribution and the one corresponding to the tested combination of input powers at each time step. The objective function is corrected according to the preceding time step errors, in a way to avoid cumulative temperature deviation. The solution algorithm is described, step by step, and a test case is treated. The results show good temperature tracking and uniformity.     

Simultaneous Measurement of Thermal Conductivity,Thermal Diffusivity,and Specific Heat of Nanofluids

Effective thermal conductivity, effective thermal diffusivity, and effective specific heat of nanofluids were simultaneously measured by using a transient double hot-wire technique. Several types of nanofluids were prepared by suspending different volume percentages (1 to 5%) of titanium dioxide (TiO₂), aluminum oxide (Al₂O₃), and aluminum (Al) nanoparticles in ethylene glycol and engine oil. While effective specific heats of these nanofluids decrease substantially with nanoparticle volume fraction, the enhanced effective thermal conductivity and effective thermal diffusivity were found to increase significantly with increasing volumetric loading of these nanoparticles. The increments of the effective thermal diffusivity of nanofluids were slightly larger than their effective thermal conductivity values. Predictions of the effective specific heats of nanofluids by the volume fraction mixture rule-based model showed fairly good agreement (within 7%) with the experimental results. Besides particle volume fraction, particle material, particle shape and the type of base fluid were identified to have influence on these properties of nanofluids. Both the calibration results of the base fluids (system accurate to ≤2.7%) and uncertainty analysis (uncertainty ≤2.1%) indicate high accuracy of using the double hot-wire method to simultaneously measure the effective thermal conductivity, effective thermal diffusivity, and specific heat of nanofluids.     

THERMAL BOUNDARY RESISTANCE MEASUREMENTS USING A TRANSIENT THERMOREFLECTANCE TECHNIQUE

A transient thermoreflectance technique, using a 200-fs laser pulse, is demonstrated as a nondestructive method for measuring the thermal boundary resistance between a thin metallic film and dielectric substrate. Experimental results are presented for Au deposited on silicon and silicon dioxide substrates taken at room temperature and compared to a thermal model. The relevant thermal properties of the metal film and the substrate are known, leaving the thermal boundary resistance as the only free parameter in the least-squares fitting routine. It is shown that the sensitivity of this technique is related directly to the thermal diffusivity of the substrate. A comparison between the diffuse mismatch model, the phonon radiation limit, and the experimental results indicates that the phonon dispersion relations of the materials can be utilized to give a qualitative prediction of the thermal boundary resistance.