The thermal behavior of a wafer during a Rapid Thermal Chemical Vapor Deposition (RTCVD) process depends on its spectral radiative properties, along with other factors. One of the major contributing factors is the thin film that is deposited on the wafer substrate. The presence of a thin film (of thickness anywhere above 0.1 nm) can drastically alter the radiative properties of the wafer surface, thereby leading to significantly different wafer temperatures. This article presents a model to simulate thin film effects in RTCVD processes. Radiative transfer is modeled using a Monte-Carlo ray-tracing technique. Radiative properties are calculated using fundamental Electromagnetic Wave Theory. Simulation results match remarkably well with experimental data, demonstrating the importance of thin film effects.
{"title":"Effect of Thin Films on Radiative Transport in Chemical Vapor Deposition Systems","authors":"S. Mazumder, A. Kersch","doi":"10.1115/imece1999-1057","DOIUrl":"https://doi.org/10.1115/imece1999-1057","url":null,"abstract":"\u0000 The thermal behavior of a wafer during a Rapid Thermal Chemical Vapor Deposition (RTCVD) process depends on its spectral radiative properties, along with other factors. One of the major contributing factors is the thin film that is deposited on the wafer substrate. The presence of a thin film (of thickness anywhere above 0.1 nm) can drastically alter the radiative properties of the wafer surface, thereby leading to significantly different wafer temperatures. This article presents a model to simulate thin film effects in RTCVD processes. Radiative transfer is modeled using a Monte-Carlo ray-tracing technique. Radiative properties are calculated using fundamental Electromagnetic Wave Theory. Simulation results match remarkably well with experimental data, demonstrating the importance of thin film effects.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134205342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-11-14DOI: 10.1109/TEPM.2000.895061
T. Lee, Jong-Kai Lin
The fluid field of the electroless plating bath was analyzed using a Computational Fluid Dynamics Tool. By solving continuity and momentum equations, the pressure and velocity distributions in the plating bath were predicted. The analysis was performed under various design options: flow direction, flowrate, diffuser plate design, and wafer cassette design. It was found that with the reverse flow option; it seems to deliver uniform flow as compared to the forward flow option. Flow pattern was similar among different flowrates and diffuser designs. Low velocity flow always existed at the top portion of the wafer and near the last row of the wafer cassette. With the hypothesis that slower flowrate results in higher plating rate; a qualitative agreement has been observed between the predicted flow pattern and the plated nickel height uniformity.
{"title":"Design Analysis of an Electroless Plating Bath Using CFD Technique","authors":"T. Lee, Jong-Kai Lin","doi":"10.1109/TEPM.2000.895061","DOIUrl":"https://doi.org/10.1109/TEPM.2000.895061","url":null,"abstract":"\u0000 The fluid field of the electroless plating bath was analyzed using a Computational Fluid Dynamics Tool. By solving continuity and momentum equations, the pressure and velocity distributions in the plating bath were predicted. The analysis was performed under various design options: flow direction, flowrate, diffuser plate design, and wafer cassette design. It was found that with the reverse flow option; it seems to deliver uniform flow as compared to the forward flow option. Flow pattern was similar among different flowrates and diffuser designs. Low velocity flow always existed at the top portion of the wafer and near the last row of the wafer cassette. With the hypothesis that slower flowrate results in higher plating rate; a qualitative agreement has been observed between the predicted flow pattern and the plated nickel height uniformity.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134473655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quench probes have been used to collect temperature data in controlled quenching experiments; the data is then used to deduce the heat transfer coefficients in the quenching medium. The process of determination of the heat transfer coefficient at the surface is the inverse heat conduction problem, which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching carried out to determine the surface heat flux history during a quenching process by an inverse algorithm based on an analytical solution. The algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve obtained from the analytical solution is compared with experimental results. The inverse calculation appears to produce fast, stable, but approximate results. These results can be used as the initial guess to improve the efficiency of iterative numerical solutions which are sensitive to the initial guess.
{"title":"Determination of Surface Heat Flux in Quenching","authors":"M. K. Alam, H. Pasic, K. Anagurthi, R. Zhong","doi":"10.1115/imece1999-1092","DOIUrl":"https://doi.org/10.1115/imece1999-1092","url":null,"abstract":"\u0000 Quench probes have been used to collect temperature data in controlled quenching experiments; the data is then used to deduce the heat transfer coefficients in the quenching medium. The process of determination of the heat transfer coefficient at the surface is the inverse heat conduction problem, which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching carried out to determine the surface heat flux history during a quenching process by an inverse algorithm based on an analytical solution. The algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve obtained from the analytical solution is compared with experimental results. The inverse calculation appears to produce fast, stable, but approximate results. These results can be used as the initial guess to improve the efficiency of iterative numerical solutions which are sensitive to the initial guess.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"299 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122097524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents an experimental investigation on nitrogen and helium flow in microchannels etched in silicon with hydraulic diameters of 9.7, 19.6, and 46.6 μm, and Reynolds numbers ranging from 0. 2 to 1000. The objectives of this research are (1) to measure the pressure distribution along the length of a microchannel; and (2) to determine the friction factor within the fully developed region of the microchannel. The pressure distribution is presented as absolute local pressure plotted against the distance from the microchannel inlet. The friction factor results are presented as the product of friction factor and Reynolds number plotted against Reynolds number with the outlet Knudsen number, Kn, as a curve parameter. The following conclusions have been reached in the present investigation: (1) Pressure losses at the microchannel entrance can be significant; (2) the product, f*Re, when measured sufficiently far away from the entrance and exit is a constant in the laminar flow region; and (3) the friction factor decreases as the Knudsen number increases.
{"title":"Local Pressure Measurement of Gaseous Flow Through Microchannels","authors":"S. Turner, Hongwei Sun, M. Faghri, O. Gregory","doi":"10.1115/imece1999-1064","DOIUrl":"https://doi.org/10.1115/imece1999-1064","url":null,"abstract":"\u0000 This paper presents an experimental investigation on nitrogen and helium flow in microchannels etched in silicon with hydraulic diameters of 9.7, 19.6, and 46.6 μm, and Reynolds numbers ranging from 0. 2 to 1000. The objectives of this research are (1) to measure the pressure distribution along the length of a microchannel; and (2) to determine the friction factor within the fully developed region of the microchannel. The pressure distribution is presented as absolute local pressure plotted against the distance from the microchannel inlet. The friction factor results are presented as the product of friction factor and Reynolds number plotted against Reynolds number with the outlet Knudsen number, Kn, as a curve parameter. The following conclusions have been reached in the present investigation: (1) Pressure losses at the microchannel entrance can be significant; (2) the product, f*Re, when measured sufficiently far away from the entrance and exit is a constant in the laminar flow region; and (3) the friction factor decreases as the Knudsen number increases.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124749718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The growth of silica particles in coflow diffusion flames has been studied experimentally using light scattering and local thermophoretic sampling techniques. The number densities and volume fractions of both aggregates and spherical particles have been determined calculated by a novel method of using the scattering cross section measured from 90° light scattering with the combination of particle sizes and morphology measured from the localized sampling and TEM image analysis under the assumption of monodisperse distribution of primary particles in an aggregate. Rayleigh-Debye-Gans and Mie theories have been applied to the calculations for fractal aggregates and spherical particles, respectively. Of particular interests are the effects of carrier gas flow rates on the evolution of silica particles and the roles of radial heat and H2O diffusion have been studied when using N2 or O2 as a carrier gas.
{"title":"A Study of Particle Growth Using Light Scattering and Local Sampling in Flame Synthesis of Nano Particles","authors":"J. Cho, Jeonghoon Lee, H. W. Kim, Mansoo Choi","doi":"10.1115/imece1999-1075","DOIUrl":"https://doi.org/10.1115/imece1999-1075","url":null,"abstract":"\u0000 The growth of silica particles in coflow diffusion flames has been studied experimentally using light scattering and local thermophoretic sampling techniques. The number densities and volume fractions of both aggregates and spherical particles have been determined calculated by a novel method of using the scattering cross section measured from 90° light scattering with the combination of particle sizes and morphology measured from the localized sampling and TEM image analysis under the assumption of monodisperse distribution of primary particles in an aggregate. Rayleigh-Debye-Gans and Mie theories have been applied to the calculations for fractal aggregates and spherical particles, respectively. Of particular interests are the effects of carrier gas flow rates on the evolution of silica particles and the roles of radial heat and H2O diffusion have been studied when using N2 or O2 as a carrier gas.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131423571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The basic problem of the impact and solidification of molten solder droplets on a flat substrate is of central importance to the novel micromanufacturing process of solder jetting, in which microscopic size solder droplets are dispensed for the attachment of microelectronic components. Under certain conditions, “frozen ripples” appear on the surface of solidified solder microbumps deposited using the solder jetting technology (Waldvogel et al. 1996). The mechanism for the formation of these “frozen ripples” was later explained and quantified in a theoretical study by Waldvogel and Poulikakos (1997) as a consequence of the dynamic competition between flow oscillations and rapid solidification. However, no analogous experimental results for the transient impact process have been reported to date to the best of our knowledge. Such a study is reported in this paper. Eutectic solder (63Sn37Pb) was melted to a preset superheat and used in a specially designed droplet generator to produce droplets with diameters in the range 50–100 μm. The size, temperature, and impacting speed of the molten droplets were maintained constant. The primary variable is the temperature of the substrate that was controlled in the range from 48 °C to 135 °C. The dynamics of molten solder microdroplet impact and solidification on the substrate was investigated using a flash microscopy technique. The duration of flash used in the study was 1 μs. The time for the completion of solidification from the moment of a solder droplet impact on the substrate varies between 150 μs and 350 μs. The dynamic interaction between the oscillation in the liquid region and the rapid advance of solidification front was visualized, quantified and presented in this paper. To the best of our knowledge, this study presents the first published experimental results on the transient fluid dynamics and solidification of molten microdroplets impacting on a substrate at the above mentioned time and length scales that are directly relevant to the novel solder jetting technology. Existing results on this problem pertain to time and length scales at least one order of magnitude higher (Jonas et al. 1997; Pasandideh-Fard et al. 1998; Zhao et al. 1996). The visualization results on the oscillatory motion and rapid solidification shed light on a host of interesting phenomena and also support the frozen ripple formation theory presented by Waldvogel and Poulikakos (1997).
焊锡液滴在平面基板上的冲击和凝固的基本问题是新型微制造工艺的核心问题，在这种工艺中，微观尺寸的焊锡液滴被分配用于微电子元件的附着。在一定条件下，使用焊料喷射技术沉积的固化焊料微凸点表面出现“冻结波纹”(Waldvogel et al. 1996)。后来，Waldvogel和Poulikakos(1997)在一项理论研究中解释并量化了这些“冻结波纹”的形成机制，认为这是流动振荡和快速凝固之间动态竞争的结果。然而，据我们所知，到目前为止还没有报道过瞬态撞击过程的类似实验结果。本文报道了这一研究。将共晶焊料(63Sn37Pb)熔化至预先设定的过热度，并在专门设计的液滴发生器中产生直径在50-100 μm范围内的液滴。熔滴的尺寸、温度和冲击速度保持不变。主要变量是衬底的温度，控制在48°C到135°C的范围内。利用闪光显微技术研究了熔融焊料微滴在基体上的冲击和凝固动力学。实验中使用的闪光时间为1 μs。从钎料液滴撞击基体的瞬间开始，凝固完成的时间在150 ~ 350 μs之间。本文对液相区振荡与凝固锋快速推进之间的动态相互作用进行了可视化、定量分析。据我们所知，这项研究首次发表了在上述时间和长度尺度上影响基板的瞬态流体动力学和熔融微滴凝固的实验结果，这与新型焊喷技术直接相关。关于这个问题的现有结果涉及至少高一个数量级的时间和长度尺度(Jonas et al. 1997;Pasandideh-Fard et al. 1998;Zhao et al. 1996)。振荡运动和快速凝固的可视化结果揭示了许多有趣的现象，也支持了Waldvogel和Poulikakos(1997)提出的冻结纹波形成理论。
{"title":"Visualization and Measurements of Picoliter-Size Molten Droplet Impact Dynamics and Solidification on a Surface","authors":"Daniel Attinger, Z. Zhao, D. Poulikakos","doi":"10.1115/imece1999-1074","DOIUrl":"https://doi.org/10.1115/imece1999-1074","url":null,"abstract":"\u0000 The basic problem of the impact and solidification of molten solder droplets on a flat substrate is of central importance to the novel micromanufacturing process of solder jetting, in which microscopic size solder droplets are dispensed for the attachment of microelectronic components. Under certain conditions, “frozen ripples” appear on the surface of solidified solder microbumps deposited using the solder jetting technology (Waldvogel et al. 1996). The mechanism for the formation of these “frozen ripples” was later explained and quantified in a theoretical study by Waldvogel and Poulikakos (1997) as a consequence of the dynamic competition between flow oscillations and rapid solidification. However, no analogous experimental results for the transient impact process have been reported to date to the best of our knowledge. Such a study is reported in this paper. Eutectic solder (63Sn37Pb) was melted to a preset superheat and used in a specially designed droplet generator to produce droplets with diameters in the range 50–100 μm. The size, temperature, and impacting speed of the molten droplets were maintained constant. The primary variable is the temperature of the substrate that was controlled in the range from 48 °C to 135 °C. The dynamics of molten solder microdroplet impact and solidification on the substrate was investigated using a flash microscopy technique. The duration of flash used in the study was 1 μs. The time for the completion of solidification from the moment of a solder droplet impact on the substrate varies between 150 μs and 350 μs. The dynamic interaction between the oscillation in the liquid region and the rapid advance of solidification front was visualized, quantified and presented in this paper. To the best of our knowledge, this study presents the first published experimental results on the transient fluid dynamics and solidification of molten microdroplets impacting on a substrate at the above mentioned time and length scales that are directly relevant to the novel solder jetting technology. Existing results on this problem pertain to time and length scales at least one order of magnitude higher (Jonas et al. 1997; Pasandideh-Fard et al. 1998; Zhao et al. 1996). The visualization results on the oscillatory motion and rapid solidification shed light on a host of interesting phenomena and also support the frozen ripple formation theory presented by Waldvogel and Poulikakos (1997).","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127920618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pulsed laser deposition (PLD) of thin films has evolved into a well-recognized technique for a wide range of materials and in a variety of devices. There is great interest in the energy characterization of the ablated plume because this is a key parameter in determining the quality of the deposited film. Spectroscopic techniques, such as optical time-of-flight (TOF,) emission spectroscopy, and laser-induced-fluorescence (LIF) are excellent methods for this purpose since they offer temporal and spatial resolution as well as the capability of distinguishing different species. The effects of laser fluence and background gas pressure on the kinetic energies of the ablated species were found by the optical time-of flight technique and by emission imaging. Furthermore, laser-induced-fluorescence was employed for spectrally resolved imaging. The results provide additional data on the kinetic energy and the distribution of neutral titanium. The axial velocity of neutral titanium was found to be as high as 2 × 104 m/s. The distribution of species within the plume was also determined.
{"title":"Emission and Laser-Induced Fluorescence Spectroscopy of Laser-Ablated Titanium Plume","authors":"S. Chu, C. Grigoropoulos","doi":"10.1115/imece1999-1080","DOIUrl":"https://doi.org/10.1115/imece1999-1080","url":null,"abstract":"\u0000 Pulsed laser deposition (PLD) of thin films has evolved into a well-recognized technique for a wide range of materials and in a variety of devices. There is great interest in the energy characterization of the ablated plume because this is a key parameter in determining the quality of the deposited film. Spectroscopic techniques, such as optical time-of-flight (TOF,) emission spectroscopy, and laser-induced-fluorescence (LIF) are excellent methods for this purpose since they offer temporal and spatial resolution as well as the capability of distinguishing different species. The effects of laser fluence and background gas pressure on the kinetic energies of the ablated species were found by the optical time-of flight technique and by emission imaging. Furthermore, laser-induced-fluorescence was employed for spectrally resolved imaging. The results provide additional data on the kinetic energy and the distribution of neutral titanium. The axial velocity of neutral titanium was found to be as high as 2 × 104 m/s. The distribution of species within the plume was also determined.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116513403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
T. Borca-Tasciuc, Jianlin Liu, T. Zeng, Weili Liu, D. Song, C. Moore, Gang Chen, Kang L. Wang, M. Goorsky, T. Radetić, R. Gronsky
Experimental evidence for a significant thermal conductivity reduction has been reported in recent years for GaAs/AlAs, Si/Ge, and Bi2Te3/Sb2Te3 superlattices. Previously reported experimental studies on Si/Ge superlattices are based on samples grown by metal oxide chemical vapor deposition (MOCVD) on GaAs substrates with Ge buffers. In this work, we present experimental results on the temperature dependent thermal conductivity of symmetrically strained Si/Ge superlattices grown by molecular beam epitaxy (MBE) as a function of the superlattice period and the growth temperature. Thermal conductivity measurements are performed using a differential 3ω method. In this technique, the temperature drop across the superlattice film is experimentally determined and used to estimate the thermal conductivity of the film. Transmission electron microscopy (TEM) is employed to study the quality of the superlattice and the influence of the growth temperature on the superlattice structure. For all the superlattices studied, the measured thermal conductivity values are lower than that of the Si0.5Ge0.5 alloy. Furthermore, the measured thermal conductivity of a 40Å period Si/Ge superlattice with high dislocation density is comparable to the calculated minimum thermal conductivity of the constituent bulk materials.
{"title":"Temperature Dependent Thermal Conductivity of Symmetrically Strained Si/Ge Superlattices","authors":"T. Borca-Tasciuc, Jianlin Liu, T. Zeng, Weili Liu, D. Song, C. Moore, Gang Chen, Kang L. Wang, M. Goorsky, T. Radetić, R. Gronsky","doi":"10.1115/imece1999-1069","DOIUrl":"https://doi.org/10.1115/imece1999-1069","url":null,"abstract":"\u0000 Experimental evidence for a significant thermal conductivity reduction has been reported in recent years for GaAs/AlAs, Si/Ge, and Bi2Te3/Sb2Te3 superlattices. Previously reported experimental studies on Si/Ge superlattices are based on samples grown by metal oxide chemical vapor deposition (MOCVD) on GaAs substrates with Ge buffers. In this work, we present experimental results on the temperature dependent thermal conductivity of symmetrically strained Si/Ge superlattices grown by molecular beam epitaxy (MBE) as a function of the superlattice period and the growth temperature. Thermal conductivity measurements are performed using a differential 3ω method. In this technique, the temperature drop across the superlattice film is experimentally determined and used to estimate the thermal conductivity of the film. Transmission electron microscopy (TEM) is employed to study the quality of the superlattice and the influence of the growth temperature on the superlattice structure. For all the superlattices studied, the measured thermal conductivity values are lower than that of the Si0.5Ge0.5 alloy. Furthermore, the measured thermal conductivity of a 40Å period Si/Ge superlattice with high dislocation density is comparable to the calculated minimum thermal conductivity of the constituent bulk materials.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134638827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two methods for solving heat transfer problems using wavelets are reviewed and discussed, namely the so-called “Fictitious Boundary” and “Fictitious Domain/Penalty” methods. Evaluation of the two methods is performed by solving simple two-dimensional heat conduction problems using fixed scale expansion of the unknowns. A discussion on the implemention of the boundary conditions and the ease of solving the resulting system of equations is presented. For each problem the error is computed so that the accuracy of the solution can be evaluated. It is found that the Fictitious Domain/Penalty method shows better agreement with the exact solutions than the Fictitious Boundary method as it introduces less computational errors due the methodology used to implement the boundary conditions in the extended domain.
{"title":"Wavelets and the Numerical Solution of Heat Transfer Problems: A Discussion of Two Methods","authors":"A. Sowayan, A. Benard, A. Diaz","doi":"10.1115/imece1999-1091","DOIUrl":"https://doi.org/10.1115/imece1999-1091","url":null,"abstract":"\u0000 Two methods for solving heat transfer problems using wavelets are reviewed and discussed, namely the so-called “Fictitious Boundary” and “Fictitious Domain/Penalty” methods. Evaluation of the two methods is performed by solving simple two-dimensional heat conduction problems using fixed scale expansion of the unknowns. A discussion on the implemention of the boundary conditions and the ease of solving the resulting system of equations is presented. For each problem the error is computed so that the accuracy of the solution can be evaluated. It is found that the Fictitious Domain/Penalty method shows better agreement with the exact solutions than the Fictitious Boundary method as it introduces less computational errors due the methodology used to implement the boundary conditions in the extended domain.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131829879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A three-dimensional, unsteady heat transfer model has been developed for predicting the temperature field in partially stabilized zirconia (PSZ) undergoing laser-assisted machining (LAM). PSZ is a semi-transparent ceramic which volumetrically absorbs, emits and scatters radiation across a spectral region extending from approximately 0.5 to 8 μm. As a first approximation, it is treated as optically thick within this spectral band, and the high density of scattering centers, as well as the random orientation of grain boundaries, permits the assumption of isotropic scattering. Accordingly, the Rosseland diffusion approximation is used to model internal radiative transfer. Since most of the CO2 laser radiation (λ = 10.6 μm) is absorbed in the first layer of control volumes adjacent to the surface, incident laser radiation is treated as a surface phenomenon. The equivalent radiation conductivity of PSZ is strongly temperature dependent and enhances thermal energy transfer within regions of the workpiece which are close to the location of laser irradiation. However, the effective thermal conductivity of PSZ remains relatively low, even at the highest temperatures achieved during LAM, and is responsible for large temperature gradients near the irradiated surface of the workpiece. For representative operating conditions, comparative calculations are performed with and without the radiation model to assess the influence of volumetric radiation effects on the temperature field. Numerical simulations are also performed to consider the effect of operating conditions, such as the laser power, laser/tool feed and depth-of-cut, on thermal conditions in close proximity to the material removal zone. The results are contrasted with those for silicon nitride, which is an opaque ceramic that exhibits quasi-plastic deformation when its temperature is raised above a threshold value at the depth-of-cut and can therefore be machined with a cutting tool.
{"title":"Transient, Three-Dimensional Heat Transfer Model for Partially Stabilized Zirconia Undergoing Laser-Assisted Machining","authors":"F. Pfefferkorn, F. Incropera, Y. Shin","doi":"10.1115/imece1999-1078","DOIUrl":"https://doi.org/10.1115/imece1999-1078","url":null,"abstract":"\u0000 A three-dimensional, unsteady heat transfer model has been developed for predicting the temperature field in partially stabilized zirconia (PSZ) undergoing laser-assisted machining (LAM). PSZ is a semi-transparent ceramic which volumetrically absorbs, emits and scatters radiation across a spectral region extending from approximately 0.5 to 8 μm. As a first approximation, it is treated as optically thick within this spectral band, and the high density of scattering centers, as well as the random orientation of grain boundaries, permits the assumption of isotropic scattering. Accordingly, the Rosseland diffusion approximation is used to model internal radiative transfer. Since most of the CO2 laser radiation (λ = 10.6 μm) is absorbed in the first layer of control volumes adjacent to the surface, incident laser radiation is treated as a surface phenomenon.\u0000 The equivalent radiation conductivity of PSZ is strongly temperature dependent and enhances thermal energy transfer within regions of the workpiece which are close to the location of laser irradiation. However, the effective thermal conductivity of PSZ remains relatively low, even at the highest temperatures achieved during LAM, and is responsible for large temperature gradients near the irradiated surface of the workpiece. For representative operating conditions, comparative calculations are performed with and without the radiation model to assess the influence of volumetric radiation effects on the temperature field. Numerical simulations are also performed to consider the effect of operating conditions, such as the laser power, laser/tool feed and depth-of-cut, on thermal conditions in close proximity to the material removal zone. The results are contrasted with those for silicon nitride, which is an opaque ceramic that exhibits quasi-plastic deformation when its temperature is raised above a threshold value at the depth-of-cut and can therefore be machined with a cutting tool.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126801808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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