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At least 199 records · Page 11

Truchas Overview

Truchas and Truchas-PBF are two sister codes for part-scale multi-physics modeling of manufacturing processes. Both programs are open source and made publicly available. They’re designed for efficient use of HPC resources and can be programmatically driven from Python packages. This enables automatic execution and analysis of ensembles of simulations, in some cases allowing 1000s of simulations to be evaluated in a day on HPC. Beyond just giving engineers a window into the concealed internal state of a system, the goal of Truchas is to provide a framework for developing novel manufacturing processes by understanding how the entire space of engineering inputs affects thermal state. It often is used to explore combinations of capabilities uncommon in commercial software, or to scale up analyses beyond the capabilities of commercial software.

97 MATHEMATICS AND COMPUTING↗

Regional mantle upwelling on Venus: The Beta-Atla-Themis anomaly and correlation with global tectonic patterns

The morphology and global distribution of volcanic centers and their association with other geological characteristics offers significant insight into the global patterns of geology, tectonic style, thermal state, and interior dynamics of Venus. Magellan data permit the detailed geological interpretation necessary to address questions about interior dynamics of Venus particularly as they reflect relatively physical, chemical, and thermal conditions of the interior. This paper focuses on the distribution of anomalous concentrations of volcanic centers on Venus and regional patterns of tectonic deformation as it may relate to the identification of global internal anomalies, including mantle dynamic, petrological, or thermal patterns.

Crumpler, L. S.↗

Thermally Activated Delayed Photoluminescence: Deterministic Control of Excited-State Decay

Thermally activated photophysical processes are ubiquitous in numerous organic and metal-organic molecules, leading to chromophores with excited state properties that can be considered an equilibrium mixture of the available low-lying states. Relative populations of the equilibrated states are governed by temperature. Such molecules have been devised as high quantum yield emitters in modern organic light-emitting diode technology and for deterministic excited state lifetime control to enhance chemical reactivity in solar energy conversion and photocatalytic schemes. This recent discovery of thermally activated photophysics at CdSe nanocrystal-molecule interfaces enables a new paradigm wherein molecule-quantum dot constructs are used to systematically generate material with predetermined photophysical response and excited state properties. Semiconductor nanomaterials feature size-tunable energy level engineering, which considerably expands the purview of thermally activated photophysics beyond what is possible using only molecules. This Perspective is intended to provide a non-exhaustive overview of the advances that led to the integration of semiconductor quantum dots in thermally activated delayed photoluminescence (TADPL) schemes and to identify important challenges moving into the future. The initial establishment of excited state lifetime extension utilizing triplet-triplet excited-state equilibria is detailed. Next, advances involving the rational design of molecules composed of both metal-containing and organic-based chromophores that produce the desired TADPL are described. Lastly, the recent introduction of semiconductor nanomaterials into hybrid TADPL constructs is discussed, paving the way towards the realization of fine-tuned deterministic control of excited state decay. It is envisioned that libraries of synthetically facile composites will be broadly deployed as photosensitizers and light emitters for numerous synthetic and optoelectronic applications in the near future.

14 SOLAR ENERGY↗

Preliminary thermal-structural design and analysis of an airframe-integrated hydrogen-cooled scramjet

This paper presents the salient features of a preliminary thermal-structural design and analysis study of a hydrogen-fueled, regeneratively cooled, airframe-integrated scramjet. This three-dimensional fixed geometry scramjet concept which was developed at NASA Langley Research Center is designed to operate over a flight Mach number range from 4 to 10. The thermal-structural study was focused on a scramjet application to one concept for a hypersonic research vehicle and was based on technology developed under the NASA Hypersonic Research Engine Project. State-of-the-art analytical methods consisting of lumped system and finite difference steady-state thermal analyses and a finite element structural analysis were used. The results of the study indicated that this scramjet concept is viable from both a structural mass and cooling requirement standpoint. However, advances in material and fabrication technology for hydrogen-cooled structures appear necessary for acceptable engine life for commercial application.

Wieting, A. R.↗

Finite-temperature tensor network study of the Hubbard model on an infinite square lattice

Here, the Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network—an infinite projected entangled pair state—evolved in imaginary time by the neighborhood tensor update algorithm working directly in the thermodynamic limit. With U⁡(1)×U⁡(1) symmetry and the bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators, unaffected by boundary effects. The spin correlators—measurable in prospective ultracold atoms experiments attempting to approach the thermodynamic limit—provide evidence of disruption of the antiferromagnetic background with mobile holes in a slightly doped Hubbard model. The charge correlators reveal the presence of hole-doublon pairs near half filling and signatures of hole-hole repulsion on doping. We also obtain specific heat in the slightly doped regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Transient thermal-structural analysis using adaptive unstructured remeshing and mesh movement

An adaptive unstructured remeshing technique is applied to transient thermal-structural analysis. The effectiveness of the technique, together with the finite element method and an error estimation technique, is evaluated by two applications which have exact solutions: (1) the steady-state thermal analysis of a plate subjected to a highly localized surface heating, and (2) the transient thermal-structural analysis of a simulated convectively cooled leading edge subjected to a translating heat source. These applications demonstrate that the remeshing technique significantly reduces the problem size as well as the analysis solution error as compared to the results produced using standard structured meshes.

Dechaumphai, Pramote↗

Thermal Analysis of the Advanced Technology Large Aperture Space Telescope (ATLAST) 8 Meter Primary Mirror

The Advanced Technology Large Aperture Space Telescope (ATLAST) preliminary design concept consists of an 8 meter diameter monolithic primary mirror enclosed in an insulated, optical tube with stray light baffles and a sunshade. ATLAST will be placed in orbit about the Sun-Earth L2 and will experience constant exposure to the sun. The insulation on the optical tube and sunshade serve to cold bias the telescope which helps to minimize thermal gradients. The primary mirror will be maintained at 280K with an active thermal control system. The geometric model of the primary mirror, optical tube, sun baffles, and sunshade was developed using Thermal Desktop(R) SINDA/FLUINT(R) was used for the thermal analysis and the radiation environment was analyzed using RADCAD(R). A XX node model was executed in order to characterize the static performance and thermal stability of the mirror during maneuvers. This is important because long exposure observations, such as extra-solar terrestrial planet finding and characterization, require a very stable observatory wave front. Steady state thermal analyses served to predict mirror temperatures for several different sun angles. Transient analyses were performed in order to predict thermal time constant of the primary mirror for a 20 degree slew or 30 degree roll maneuver. This paper describes the thermal model and provides details of the geometry, thermo-optical properties, and the environment which influences the thermal performance. All assumptions that were used in the analysis are also documented. Parametric analyses are summarized for design parameters including primary mirror coatings and sunshade configuration. Estimates of mirror heater power requirements are reported. The thermal model demonstrates results for the primary mirror heated from the back side and edges using a heater system with multiple independently controlled zones.

Hornsby, Linda↗

Liquid-Cooled Heat Sink Optimization for Thermal Imbalance Mitigation in Wide-Bandgap Power Modules

Power semiconductor die layout in substrates used in power modules is generally optimized for minimum electrical parasitics (e.g., stray inductance) by considering the minimum spacing between dies for thermal decoupling. The layout assumes sufficient heat spreading and transfer from dies to the cooling structure. For module designs using a direct substrate cooling method, the base plate is removed, leading to a steady-state thermal asymmetry in the power module due to insufficient heat spreading/transfer. This causes significant temperature differences among the devices. Such unintentional thermal asymmetries can lead to undesirable asymmetries in power conversion among semiconductor devices, which impact reliability. This article proposes a thermal imbalance mitigation method that uses evolutionary optimized liquid-cooled heat sinks to improve the thermal loading among devices.

Sahu, Raj↗

Time-domain theory of transient heat conduction in the local limit

Ultrafast and nanoscale heat conduction demands a unified theoretical framework that rigorously bridges macroscopic transport equations with microscopic material properties derived from statistical physics. Existing empirical generalizations of Fourier's law often lack a solid microscopic foundation, failing to connect observed non-Fourier behavior with underlying atomic-scale mechanisms. In this work, we present a time-domain theory of transient heat conduction rooted in Zwanzig's statistical theory of irreversible processes. Central to this framework is the time-domain transport function $\overleftrightarrow{𝑍}$⁡(𝑡) defined through equilibrium time-correlation functions of heat fluxes. This function generalizes the conventional concept of steady-state thermal conductivity, governing the transition of conduction dynamics from onset second sound type wave propagation at finite speeds to diffusion-dominated behavior across broad temporal and spatial scales. Unlike phonon hydrodynamic models that rely on mesoscopic constructs such as phonon drift velocity, our approach provides a quantitative and microscopic description of intrinsic memory effects in transient heat fluxes and applies universally to bulk materials at any temperature or length scale. By integrating atomistic-scale first-principles calculations with continuum-level macroscopic equations, this framework offers a robust foundation for numerical simulations of transient temperature fields. Furthermore, it facilitates the interpretation and design of transient thermal grating experiments using nanometer-scale heat sources and ultrafast laser systems in the extreme ultraviolet and x-ray wavelength ranges, advancing our understanding of heat dissipation dynamics.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Thermal inertia mapping - A promising new tool for mineral exploration

The Heat Capacity Mapping Mission (HCMM) is a NASA-sponsored program designed to acquire day visible and day and night thermal IR imagery from a satellite launched on April 26, 1978 into a near polar orbit at 620 km altitude. The data are used to produce temperature difference (12 or 36 hour interval) and apparent thermal inertia (ATI) images or numerical data sets for selected areas within much of North America, Europe, North Africa, and Australia. These data are being applied to rock type discrimination, soil moisture detection, assessment of vegetation states, thermal current monitoring in water bodies, urban heat island analysis and other multidisciplinary studies. Key geological results include (1) groups of dissimilar rock materials and some individual rock types can be separated and sometimes identified by their satellite-determined thermal inertias (dependent on their albedos, densities, and conductivities), (2) large lineaments (including some faults) are often recognized by their thermal signatures (may relate to moisture content and/or reduced bulk density), and (3) visually striking expressions of geomorphic units (types) at a regional scale are especially enhanced in the night IR imagery.

Short, N. M.↗

Impacts of Irradiation Structural Behavior on Thermal Hydraulics Safety Analysis to Support MURR LEU Conversion

The University of Missouri Research Reactor (MURR) located in Columbia, Missouri is one of six U.S. High Performance Research Reactors (USHPRR), including one critical facility, that is actively collaborating with U. S. Department of Energy (DOE) National Nuclear Security Administration (NNSA) Material Management and Minimization (M3) Office of Reactor Conversion and Uranium Supply to convert from the use of highly enriched uranium (HEU; ≥20 wt% U-235) to low-enriched uranium (LEU; <20 wt% U-235) fuel. A new type of very high-density LEU fuel based on an alloy of uranium and 10 wt% molybdenum (U-10Mo) is expected to allow the conversion to LEU of MURR, as well as four other USHPRR. MURR has been working with the Reactor Conversion Pillar at Argonne to perform fuel element design and fuel cycle performance analyses, steady-state thermal hydraulics safety analysis, and accident safety analyses in preparation for the conversion of MURR and to support a preliminary safety analysis report for conversion to LEU fuels. Subsequent analyses have also been performed, including transition cycles where all-fresh LEU fuel elements are introduced upon conversion and progressing through reactor operations the core is brought to equilibrium. Thermal hydraulics safety analyses performed as part of the above have employed an assumption on channel gap reduction due to burnup-related phenomena including fuel swelling, irradiation creep, and oxide layer buildup. Recently, a series of structural analyses have been performed on the MURR LEU fuel plates and an element due to significant differences between the plate and element designs of the MURR HEU and LEU fuels. In addition, NUREG-1537 indicates that structural phenomena are to be evaluated. Two separate types of structural analyses were performed for the MURR LEU fuel element: fluid-structure interaction (FSI) and irradiation thermo-mechanical. The FSI analysis evaluated the effects of hydraulic forces on the MURR LEU fuel element to quantify the flow-induced plate deflection, and a minimal impact to the channel gap thickness was predicted under prototypic and bounding conditions. The irradiation thermo-mechanical analysis evaluated the effects of fuel swelling, irradiation creep, and thermal expansion for the MURR LEU plates and the element for prototypic thermal and irradiation conditions based on a high-fidelity approach multiphysics approach. Overall, this thermo-mechanical analysis predicts smaller gap thickness changes in previously limiting regions. Larger changes are predicted in the middle of channels, and for end channels where power density is not typically a maximum. An additional thermo-mechanical analysis was performed for the outermost HEU fuel plate, which showed a similar magnitude of deflection as the outermost LEU plate. Due to substantial differences between the channel gap reductions assumed for the previous safety analyses and those predicted by the irradiation thermo-mechanical analysis, a need to evaluate their impact on the thermal hydraulics safety analyses arose. This report presents the results from the steady-state safety analyses for normal operation as well as the accident analyses for the two most limiting accident scenarios.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Preliminary Results of an Experimental Investigation of the Qu Superconducting Heat Pipe

This note on preliminary results of our evaluation of the so-called Qu Tube is prompted in part by recent concerns expressed to the authors by some researchers regarding the performance characteristics of the superconducting, solid-state heat pipe as described in the patents, or on the company's websites. Briefly, the company's claims include: a new type of heat transfer mechanism that is a form of solid state thermal superconductivity, which results in an effective thermal conductivity of the order of tens of thousands of times that of an equivalent solid silver bar, or, tens to hundreds of times that of liquid - vapor heat pipes. The company's website also refers to tests conducted by Stanford Research Institute that substantiate these claims, but the report is apparently not publicly available. We are conducting an investigation of the Qu Tube under a NASA Grant, and in general find that these claims have merit, but our study is not yet complete. We present some of our preliminary results in part to show that it would not be imprudent to conduct such studies, especially for possible future applications requiring exceptional thermal management performance capabilities. Working with HiTek Services, we originally acquired several Qu Tubes, including 17" long, 5/16" diameter copper tubes, one that is 7 7/8" long, 3/16" diameter, and one that is 4" long, 1" diameter. We subjected the smaller tubes to various exploratory tests, including a transient test with electrical band heaters, boiling water tests, and a series of steady state tests with electrical band heaters heating one end with free convective cooling along the remainder of the length. All results indicate a very high thermal conductivity, but the length of these tubes limited our ability to obtain accurate data on temperature gradients, necessary to determine the effective thermal conductivity. We then acquired nine Qu Tubes that are 10' long, 5/16" diameter, and we have recently conducted initial tests, which further support the claims of exceptional thermal conductivity.

Blackmon, James B.↗

Scatterometer-Calibrated Stability Verification Method

The requirement for scatterometer-combined transmit-receive gain variation knowledge is typically addressed by sampling a portion of the transmit signal, attenuating it with a known-stable attenuation, and coupling it into the receiver chain. This way, the gain variations of the transmit and receive chains are represented by this loop-back calibration signal, and can be subtracted from the received remote radar echo. Certain challenges are presented by this process, such as transmit and receive components that are outside of this loop-back path and are not included in this calibration, as well as the impracticality for measuring the transmit and receive chains stability and post fabrication separately, without the resulting measurement errors from the test set up exceeding the requirement for the flight instrument. To cover the RF stability design challenge, the portions of the scatterometer that are not calibrated by the loop-back, (e.g., attenuators, switches, diplexers, couplers, and coaxial cables) are tightly thermally controlled, and have been characterized over temperature to contribute less than 0.05 dB of calibration error over worst-case thermal variation. To address the verification challenge, including the components that are not calibrated by the loop-back, a stable fiber optic delay line (FODL) was used to delay the transmitted pulse, and to route it into the receiver. In this way, the internal loopback signal amplitude variations can be compared to the full transmit/receive external path, while the flight hardware is in the worst-case thermal environment. The practical delay for implementing the FODL is 100 s. The scatterometer pulse width is 1 ms so a test mode was incorporated early in the design phase to scale the 1 ms pulse at 100-Hz pulse repetition interval (PRI), by a factor of 18, to be a 55 s pulse with 556 s PRI. This scaling maintains the duty cycle, thus maintaining a representative thermal state for the RF components. The FODL consists of an RF-modulated fiber-optic transmitter, 20 km SMF- 28 standard single-mode fiber, and a photodetector. Thermoelectric cooling and insulating packaging are used to achieve high thermal stability of the FODL components. The chassis was insulated with 1-in. (.2.5-cm) thermal isolation foam. Nylon rods support the Micarta plate, onto which are mounted four 5-km fiber spool boxes. A copper plate heat sink was mounted on top of the fiber boxes (with thermal grease layer) and screwed onto the thermoelectric cooler plate. Another thermal isolation layer in the middle separates the fiberoptics chamber from the RF electronics components, which are also mounted on a copper plate that is screwed onto another thermoelectric cooler. The scatterometer subsystem fs overall stability was successfully verified to be calibratable to within 0.1 dB error in thermal vacuum (TVAC) testing with the fiber-optic delay line, while the scatterometer temperature was ramped from 10 to 30 C, which is a much larger temperature range than the worst-case expected seasonal variations.

McWatters, Dalia A.↗

Heat transport with a twist

Despite the desirability of polymers for use in many products due to their flexibility, light weight, and durability, their status as thermal insulators has precluded their use in applications where thermal conductors are required. However, recent results suggest that the thermal conductance of polymers can be enhanced and that their heat transport behaviors may be highly sensitive to nanoscale control. Here we use non-equilibrium molecular dynamics simulations to study the effect of mechanical twist on the steady-state thermal conductance across multi-stranded polyethylene wires. We find that a highly twisted double-helical polyethylene wire can display a thermal conductance up to three times that of its untwisted form, an effect which can be attributed to a structural transition in the strands of the double helix. We also find that in thicker wires composed of many parallel strands, adding just one twist can increase its thermal conductance by over 30%. However, we find that unlike stretching a polymer wire, which causes a monotonic increase in thermal conductance, the effect of twist is highly non-monotonic, and certain amounts of twist can actually decrease the thermal conductance. Finally, we apply the Continuous Chirality Measure (CCM) in an attempt to explore the correlation between heat conductance and chirality. The CCM is found to correlate with twist as expected, but we attribute the observed heat transport behaviors to structural factors other than chirality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High Modulus and High T(sub g) Thermally Stable Polymers from p-Ethynyl-Terminated Rigid-Rod Monomers

Novel p-ethynyl-substituted rigid rod monomers were studied by pressure Differential Scanning Calorimetry (DSC), ThermoGravimetric Analysis (TGA), IsothermoGravimetric Analysis (IGA), and TGA-IR. These monomers, 4,4'-bis(((4-ethynylphenyl)carbonyl)oxy)biphenyl, designated 1, 1,5-bis-(((4-ethynylphenyl)carbonyl)oxy)naphthalene, designated 2, and bis(4-ethynylphenyl)pyromellitimide, designated 3, were polymerized in the solid state. Thermal polymerization in N2 or air produced highly cross-linked resins with polymerization exotherms centered between 212 and 276 C. The (delta)H's of polymerization of these resins in air were found to be double those in N2. When monomers 1 and 2 were heated in air from 23 to 750 C at 10 C/min, the main decomposition product was carbon dioxide, evolving at a maximum rate between 500 and 600 C; water was also detected as a decomposition product. Void-free neat resin moldings, designated lp to 3p, were made by compression molding the monomers and then heating them. The resulting polymers were highly cross-linked, and their glass transition temperatures (T(sub g)) were much higher than their polymerization temperatures. Using ThermoMechanical Analysis (TMA), we found that polymers lp to 3p had T(sub g)'s of 422, 329, and 380 C, respectively. The thermal and thermooxidative stabilities improved when lp to 3p were postcured in N2 (the postcured polymers were designated 1pp to 3pp). The Linear Thermal Expansions (LTE) for lp and 3p were 1% between 23 and 420 C. Using rheological analysis, we could not clearly detect the T(sub g)'s of lp to 3p because their moduli dropped only slightly between 23 and 490 C and the changes in tan beta were very low. Because of high cross-link density, their moduli changed little as the resins went from a glassy to a rubbery state. Their shear storage moduli in air ranged from 0.82 (3p, 3pp) to 1.6 GPa (lpp) at 23 C, from 0.16 (2p) to 0.7GPa(lpp) at 380 C, and from 0.18(lpp)to 0.6GPa(2p) at 490 C. Finally, these novel-p-ethynyl polymers exhibited an excellent combination of high T(sub g), low LTE, and high thermooxidative stability. Most notably, 3pp lost only 3% of its initial weight when it was aged for 500 h at 288 C in air.

Melissaris, Anastasios P.↗

Multi-Dimensional, Non-Pyrolyzing Ablation Test Problems

Non-pyrolyzingcarbonaceous materials represent a class of candidate material for hypersonic vehicle components providing both structural and thermal protection system capabilities. Two problems relevant to this technology are presented. The first considers the one-dimensional ablation of a carbon material subject to convective heating. The second considers two-dimensional conduction in a rectangular block subject to radiative heating. Surface thermochemistry for both problems includes finite-rate surface kinetics at low temperatures, diffusion limited ablation at intermediate temperatures, and vaporization at high temperatures. The first problem requires the solution of both the steady-state thermal profile with respect to the ablating surface and the transient thermal history for a one-dimensional ablating planar slab with temperature-dependent material properties. The slab front face is convectively heated and also reradiates to a room temperature environment. The back face is adiabatic. The steady-state temperature profile and steady-state mass loss rate should be predicted. Time-dependent front and back face temperature, surface recession and recession rate along with the final temperature profile should be predicted for the time-dependent solution. The second problem requires the solution for the transient temperature history for an ablating, two-dimensional rectangular solid with anisotropic, temperature-dependent thermal properties. The front face is radiatively heated, convectively cooled, and also reradiates to a room temperature environment. The back face and sidewalls are adiabatic. The solution should include the following 9 items: final surface recession profile, time-dependent temperature history of both the front face and back face at both the centerline and sidewall, as well as the time-dependent surface recession and recession rate on the front face at both the centerline and sidewall. The results of the problems from all submitters will be collected, summarized, and presented at a later conference.

Ablation↗

The Schwinger-Keldysh coset construction

The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S-matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermal Edge-Effects Model for Automated Tape Placement of Thermoplastic Composites

Two-dimensional thermal models for automated tape placement (ATP) of thermoplastic composites neglect the diffusive heat transport that occurs between the newly placed tape and the cool substrate beside it. Such lateral transport can cool the tape edges prematurely and weaken the bond. The three-dimensional, steady state, thermal transport equation is solved by the Green's function method for a tape of finite width being placed on an infinitely wide substrate. The isotherm for the glass transition temperature on the weld interface is used to determine the distance inward from the tape edge that is prematurely cooled, called the cooling incursion Delta a. For the Langley ATP robot, Delta a = 0.4 mm for a unidirectional lay-up of PEEK/carbon fiber composite, and Delta a = 1.2 mm for an isotropic lay-up. A formula for Delta a is developed and applied to a wide range of operating conditions. A surprise finding is that Delta a need not decrease as the Peclet number Pe becomes very large, where Pe is the dimensionless ratio of inertial to diffusive heat transport. Conformable rollers that increase the consolidation length would also increase Delta a, unless other changes are made, such as proportionally increasing the material speed. To compensate for premature edge cooling, the thermal input could be extended past the tape edges by the amount Delta a. This method should help achieve uniform weld strength and crystallinity across the width of the tape.

Costen, Robert C.↗