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576 records · Page 16

Reliability Analysis of Single Crystal NiAl Turbine Blades

As part of a co-operative agreement with General Electric Aircraft Engines (GEAE), NASA LeRC is modifying and validating the Ceramic Analysis and Reliability Evaluation of Structures algorithm for use in design of components made of high strength NiAl based intermetallic materials. NiAl single crystal alloys are being actively investigated by GEAE as a replacement for Ni-based single crystal superalloys for use in high pressure turbine blades and vanes. The driving force for this research lies in the numerous property advantages offered by NiAl alloys over their superalloy counterparts. These include a reduction of density by as much as a third without significantly sacrificing strength, higher melting point, greater thermal conductivity, better oxidation resistance, and a better response to thermal barrier coatings. The current drawback to high strength NiAl single crystals is their limited ductility. Consequently, significant efforts including the work agreement with GEAE are underway to develop testing and design methodologies for these materials. The approach to validation and component analysis involves the following steps: determination of the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; measurement of the failure strength envelope of the material; coding of statistically based reliability models; verification of the code and model; and modeling of turbine blades and vanes for rig testing.

Joseph Palko

Electrochemical cells and methods of manufacturing the same

Electrochemical cells and methods of making electrochemical cells are described herein. In some embodiments, an apparatus includes a multi-layer sheet for encasing an electrode material for an electrochemical cell. The multi-layer sheet including an outer layer, an intermediate layer that includes a conductive substrate, and an inner layer disposed on a portion of the conductive substrate. The intermediate layer is disposed between the outer layer and the inner layer. The inner layer defines an opening through which a conductive region of the intermediate layer is exposed such that the electrode material can be electrically connected to the conductive region. Thus, the intermediate layer can serve as a current collector for the electrochemical cell.

Bazzarella, Ricardo

Pressure induced modification of electronic and magnetic properties of MnCrNbAl and MnCrTaAl

Spin-gapless semiconductor (SGS) is a new class of material that has been studied recently for potential applications in spintronics. This material behaves as an insulator for one spin channel, and as a gapless semiconductor for the opposite spin. In this work, we present results of a computational study of two quaternary Heusler alloys, MnCrNbAl and MnCrTaAl that have been recently reported to exhibit spin-gapless semiconducting electronic structure. In particular, using density functional calculations we analyze the effect of external pressure on electronic and magnetic properties of these compounds. It is shown that while these two alloys exhibit nearly SGS behavior at optimal lattice constants and at negative pressure (expansion), they are half-metals at equilibrium, and magnetic semiconductors at larger lattice constant. At the same time, reduction of the unit cell volume has a detrimental effect on electronic properties of these materials, by modifying the exchange splitting of their electronic structure and ultimately destroying their half-metallic/semiconducting behavior. Thus, our results indicate that both MnCrNbAl and MnCrTaAl may be attractive for practical device applications in spin-based electronics, but a potential compression of the unit cell volume (e.g. in thin-film applications) should be avoided.

Materials Science

A Self‐Healing System for Polydicyclopentadiene Thermosets

Self-healing offers promise for addressing structural failures, increasing lifespan, and improving durability in polymeric materials. Implementing self-healing in thermoset polymers faces significant manufacturing challenges, especially due to the elevated temperature requirements of thermoset processing. To introduce self-healing into structural thermosets, the self-healing system must be thermally stable and compatible with the thermoset chemistry. This article demonstrates a self-healing microcapsule-based system stable to frontal polymerization (FP), a rapid and energy-efficient manufacturing process with a self-propagating exothermic reaction (≈200 °C). A thermally latent Grubbs-type complex bearing two N-heterocyclic carbene ligands addresses limitations in conventional G2-based self-healing approaches. Under FP's elevated temperatures, the catalyst remains dormant until activated by a Cu(I) co-reagent, ensuring efficient polymerization of the dicyclopentadiene (DCPD) upon damage to the polyDCPD matrix. The two-part microcapsule system consists of one capsule containing the thermally latent Grubbs-type catalyst dissolved in the solvent, and another capsule containing a Cu(I) coagent blended with liquid DCPD monomer. Using the same chemistry for both matrix fabrication and healing results in strong interfaces as demonstrated by lap-shear tests. In an optimized system, the self-healing system restores the mechanical properties of the tough polyDCPD thermoset. Self-healing efficiencies greater than 90% via tapered double cantilever beam tests are observed.

36 MATERIALS SCIENCE

Rethinking 𝛼−RuCl 3 : Parameters, models, and phase diagram

RuCl 3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44 Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form 𝛼−RuCl 3 rose to exceptional prominence. This “rediscovery” of 𝛼−RuCl 3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of 𝛼−RuCl 3 , and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the nontrivial physical properties of this material. These constraints allow one to focus on the relevant region of the multidimensional phase diagram of the 𝛼−RuCl 3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the 𝛼−RuCl 3 parameter space using quasiclassical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization-group methods, demonstrating a remarkably close quantitative accord between them on the general structure and hierarchy of the phases, with the zigzag, ferromagnetic, and incommensurate phases that are proximate to each other. As a result, one of the highlights is the detailed agreement on the nature of the incommensurate phases that realize two distinct counterrotating helical states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Mechanistic origin of solvent-dependent thermal stability in sodiated Sn anodes for sodium-ion batteries

Understanding the thermal stability of high-energy density alloy anodes is critical for the safe deployment of sodium-ion batteries (SIBs). Here, accelerating rate calorimetry (ARC), post-mortem characterizations, and density functional theory (DFT) calculations are combined to understand the thermal reactivity of fully sodiated Sn, Sn-hard carbon (HC) blends, and HC anodes in carbonate- and ether-based electrolytes. ARC measurements show that propylene carbonate (PC) causes earlier self-heating rate (SHR) onset and higher reactivity than tetraethylene glycol dimethyl ether (TEGDME), indicating inferior thermal stability. Sodiated Sn exhibits better thermal stability than sodiated HC, while Sn-HC blends show intermediate behavior that improves with increasing Sn content. Post-ARC analyses reveal desodiation of Na15Sn4 to metallic Sn with particle coalescence, whereas Sn-HC blends and HC retain finer morphologies. PC promotes Sn oxidation to SnO, while TEGDME suppresses oxide formation; NaPF6-containing electrolytes additionally form NaF. DFT calculations show that PC adsorption lowers Na extraction energy and enhances interfacial electronic interactions, facilitating Na release and reductive decomposition. These results establish a direct correlation between solvent-dependent reaction pathways and thermal stability in SIB alloy anodes.

Accelerating rate calorimetry

Evaluation of Fatigue Damage Accumulation Functions for Delamination Initiation and Propagation

The present report follows on the cohesive fatigue damage model methodology proposed in NASA-TP-2018-219838. In that report, an empirical function describing the incremental damage due to cyclic loading was used to calculate fatigue damage within a cohesive formulation. The form of the function was developed such that, when integrated at a constant stress amplitude from no damage to failure, it produces a life versus load response that is consistent with an S-N diagram. Therefore, the parameters of the damage model could be obtained by fitting the model predictions to an S-N diagram. The finite element analyses performed demonstrate that the cohesive fatigue accumulation function provides a link between the S-N diagram that describes crack initiation, and the Paris law that characterizes the rate of crack propagation. However, when the model was proposed, it was not known whether the form of the damage accumulation function associated with a desired S-N diagram is unique and, if not, if the link between S-N and the Paris law is unique and independent of the fatigue function selected. In the effort described herein, several alternative forms of the damage function that reproduce the desired features of S-N diagrams were found and evaluated. The effects of each of these functions on the predicted parameters of the Paris law and the propagation threshold are discussed. The results indicate that the predicted exponent m of the Paris law is indeed independent of the damage accumulation function. However, different functions predict different values for the pre-factor C of the Paris law. Therefore, the proper damage accumulation function must be selected by comparison with experiments. One of the new damage accumulation functions proposed herein was found to be particularly useful for analysis because of the ease with which the model parameters can be determined with a minimal amount of experimental information. The effectiveness of the proposed methodology and damage function was demonstrated by conducting analyses of a double cantilever beam test, a mixed-mode bending test, and a three-point bending test of a skin/doubler specimen. The results indicate that the same set of model parameters can provide accurate predictions of the rate of fatigue crack propagation for a variety of material interfaces, mode mixities, load levels, and stress ratios.

DKIN/Stiffener Debonding

Electrochemical Behavior of Cerium at an Indium Tin-Doped Oxide Electrode in Acidic Media

The redox behavior and speciation of cerium at mesoporous thin films composed of nanoparticles of indium tin-doped oxide (nITO) electrodes were characterized in pH 4.8, 0.1 M acetate buffer and both 0.1 and 1 M HNO 3 using electrochemical techniques and X-ray photoelectron spectroscopy. Anodic deposition of ceria species from Ce(III) to the nITO electrode was achieved under all solvent conditions via spontaneous condensation of electrochemically generated ceric hydroxide species. In 1 M nitric acid, the rate of CeO 2 dissolution is on the same order as CeO 2 deposition, resulting in negligible amounts of CeO 2 electrodeposited at the nITO surface. The cathodic stripping of CeO 2 from the nITO substrate deposited in 0.1 M nitric acid or pH 4.8 acetate buffer follows a 2-step process where Ce(IV)-oxide is initially reduced to an unstable Ce(III)-oxide species that rapidly undergoes acid catalyzed dissolution to yield soluble Ce(III) (aq) . These findings provide a foundation for the pH and anodic potential controlled deposition of CeO 2 thin films to ITO substrates, which can aid in the development of materials composed of ceria. As a result, they can also be used to infer likely analogous actinide redox behavior and speciation at these electrodes.

Cerium

Vapor-phase pillarization of MXenes for engineering hierarchical interlayer porosity

MXenes, a family of two-dimensional (2D) multilamellar materials, possess excellent thermal and electronic properties for a range of applications. Their use in heterogeneous catalysis, however, is limited by the low surface area resulting from stacked layers. Pillarization with inorganic oxides can create more open, mesoporous MXene structures, improving accessibility for guest species to diffuse, reside or react in the space between 2D layers. A previous liquid-phase pillarization method, however, involves excessive use of solvent-based precursors and multiple processing steps. Here, we report a vapor-phase pillarization (VPP) strategy to introduce pillars, exemplified by silica pillars, with high pillar precursor usage efficiency and a simplified processing workflow. The resulting silica-pillared mesoporous MXene exhibits significantly increased surface area and porosity. These textural properties can be easily tuned by the VPP synthesis conditions. When applied as a ruthenium (Ru) catalyst support for the hydrogenolysis of low-density polyethylene (LDPE), the silica-pillared MXene enabled high Ru dispersion and catalytic activity. This study highlights the potential of the VPP method for engineering mesoporous, 2D MXene materials and demonstrates the effectiveness of mesoporous MXene as a catalyst support in overcoming mass transport and active-site accessibility challenges in heterogeneous catalysis involving bulky substances, such as plastics upcycling.

Luo, Song [University of Delaware, Newark, DE (Uni

Novel PtNi single-atom–nanocluster (SA–NC) ensembles promote Tafel kinetics and ampere-class AEM hydrogen evolution

The development of efficient, durable, and low-PGM electrocatalysts for the hydrogen evolution reaction (HER) in alkaline media is critical for next-generation electrolysis technologies. We report a facile two-step synthesis of highly dispersed PtNi and PtNi-nitride nanoclusters (NCs) (~2.3 nm) with ultralow Pt content (0.5 at.%) anchored on N-doped Vulcan carbon. Structural and compositional characterization via XAS, XPS, HAADF-STEM, HRTEM, and EDS mapping established key structure–activity relationships across varying Pt/Ni ratios and pyrolysis temperatures. The Pt0.5Ni0.5/C-750 catalyst, an ensemble of PtNi M-N-C type single-atom (SA) moieties with neighboring PtNi nanoclusters (NC), exhibited superior HER performance in alkaline media, achieving overpotentials of 30, 115, and 210 mV at 10, 100, and 500 mA cm−2, respectively. Despite at a lower Pt content, this novel SA–NC ensemble outperformed commercial Pt/C by ~36%. A standardized literature comparison with contemporary Pt- and Ru-doped analogues reveals the as-prepared Pt0.5Ni0.5/C-750 to sit at the apex of Tafel-limited kinetics and low overpotential at 100 mA cm−2. Tafel-limited Tafel slopes in both alkaline and acidic regimes confirm favorable proton recombination kinetics. Mass activities at 200 mV reached 13.8 and 18.84 A mgPt−1 in alkaline and acidic media, respectively. However, excessive nitridation (e.g., at 650 °C) adversely altered Pt electronic structure and HER kinetics. While Ni enhanced alkaline HER, acidic HER favored Ni-free analogues. Pt0.5Ni0.5/C-750 also demonstrated robust temperature responsiveness and 300-h operational stability at high current densities (0.5–1.0 A cm−2) in MEA tests. This work presents a scalable strategy for designing thermally responsive, durable, and compositionally tunable NC catalysts with neighboring SA moieties for alkaline electrolysis.

AEMWE

An Investigation Regarding the Effects of Volume Dynamics on Gas Turbine Engine Performance and Operability

This work explores the impact of adding volume dynamics to an electrified turbofan engine model. The zero-dimensional single-input single-output volume elements capture the physics of fluid compressibility of flow in the engine core gas path turbomachinery during transient operation with greater fidelity. Some background regarding the motivation for this effort is provided. A model of the volume element is developed from first principles. The baseline engine model is described and an explanation is given of the modifications made to incorporate the volume elements into the new model. Details of the simulated inputs, designed to elicit exaggerated dynamic responses and to facilitate comparison between the baseline and modified engine models, are explicated. The results of these simulations are presented and discussed, demonstrating that the transient performance and operability of the modified engine model, measured by parameters such as shaft speeds, thrust, and high-pressure compressor (HPC) stall margin, are impacted by the additional dynamics. Commentary is provided regarding potential explanations for the differences in behavior exhibited by the two models. Finally, suggestions are offered for future work that might improve the volume models developed in this effort and leverage the improved fidelity enabled by the modeling of turbomachinery volume dynamics.

Volume dynamics

Laboratory Development of a Pot Calcination Process for Converting Liquid Wastes to Solids

Simulated Darex, Purex, Thorex, and TBP-25 wastes were batch-evaporated and calcined to solids. The weight of residue was decreased to ~ 8% of the original waste for Darex, to ~ 4% for Purex, to ~ 2% for Thorex, and ~ 7% for TBP-25 by calcination to 1200°C. Semicontinuous evaporation and calcination to solids at 900°C of Darex and Purex wastes gave volume reduction factors of ~ 8 and 7 to 10, respectively. The nitrate contents of the residues from batch calcination to 800°C were from ~ 0.07 to 0.5 wt % while the nitrate contents of the residues from semicontinuous calcination to 900°C were from ~ 0.1 to 0.7 wt %. Sodium, calcium, and magnesium additives to Purex waste decreased the percent of sulfate volatilized into the condensate from ~ 30% to <0.5%. Replacement of the atmosphere above the waste with nitric oxide decreased ruthenium volatility from 50 to 60% of that originally present in Purex waste to 0.5 to 3.5%. The thermal conductivities for the calcined wastes, measured in situ, were all >0.1 Btu/hr ft °F at ~ 400°F and increased almost linearly with increasing temperature to >0.3 Btu/hr ft °F at ~ 1600°F in all cases studied.

052001* -- Nuclear Fuels-- Waste Processing

Conclusions of a Cryogenic Motor Configuration Study for Aircraft Propulsion

Cryogenic electric machines are a promising technology for multi megawatt electric aircraft drivetrains. Superconducting stators that make use of low AC loss superconducting wires are considered to be a key component for these cryogenic machines. This paper shares the lessons learned from a design study that evaluated several configurations of a 5 MW cryogenic motor for this application. The lessons are drawn from a qualitative study of 16 configurations and a quantitative study of 8 down selected configurations. The quantitative study involved using analytical calculations (electromagnetic, thermofluid, mechanical, and motor sizing) to determine each configuration’s Pareto front of total efficiency and total specific power. The conclusions from a preliminary assessment of different stator conductors (superconductors and cryogenic metals) are also presented. One motor configuration is down selected for future detailed design and demonstration at the multi megawatt level.

Electrified aircraft propulsion

Entropy-defect synergy for dual luminescence mechanism in spinel: Time-resolved anti-counterfeiting and fingerprint visualization

Multimodal luminescent materials, while promising for anti-counterfeiting, often lack dynamic time-dependent responses and controllable spatial distribution, limiting their encryption capabilities in the spatiotemporal dimension. Here, this work presents a coordinated control strategy based on entropy and defect engineering, and uses a backpropagation (BP) neural network for material screening to successfully prepare spinel Mg 0.8 (Fe 0.04 Co 0.04 Ni 0.04 Cu 0.04 Zn 0.04 )Cr 2 O 4 (MgA 5 CO) phosphors with time-dependent dynamic luminescence behavior. This phosphor simultaneously activated the d-d transition luminescence (∼618 nm) derived from Co 2+ /Cr 3+ and the defect luminescence (∼398 nm) related to zinc vacancies (V Zn ) in a single-phase solid solution. The phosphor exhibits a time-dependent color evolution from pink to purple under fixed-wavelength excitation, due to the different excited-state dynamics and decay lifetimes associated with the d-d transition and defect luminescence. Structural characterization and spectral analysis confirmed the existence of V Zn and its significant role in defect luminescence process. The fluorescent and dynamic luminescent properties of entropy-based spinel oxide enable its use in advanced anti-counterfeiting applications like fingerprint recognition and color-changing dedicated anti-counterfeiting mark, showing promise in high-end and time-dynamic anti-counterfeiting fields. This research not only developed a new type of fluorescent dynamic anti-counterfeiting material, but also provided a new idea for constructing advanced optical functional materials with multiple luminescence mechanisms.

Defect project

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy

Summary of Research Report

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Isaac Elishakoff

Implementation of A Self-Controlling Heater

Temperature control of radiation sensors, targets, and other critical components is a common requirement in modern scientific instruments. Conventional control systems use a heater and a temperature sensor mounted on the body to be controlled. For proportional control, the sensor provides feedback to circuitry which drives the heater with an amount of power proportional to the temperature error. It is impractical or undesirable to mount both a heater and a sensor on certain components such as ultra-small parts or thin filaments. In principle, a variable current through the element is used for heating, and the change in voltage drop due to the element's temperature coefficient is separated and used to monitor or control its own temperature. Since there are no thermal propagation delays between heater and sensor, such control systems are exceptionally stable.

Maxwell G Strange

A Probabilistic Model of a Porous Heat Exchanger

This paper presents a probabilistic one-dimensional finite element model for heat transfer processes in porous heat exchangers. The Galerkin approach is used to develop the finite element matrices. Some of the submatrices are asymmetric due to the presence of the flow term. The Neumann expansion is used to write the temperature distribution as a series of random variables, and the expectation operator is applied to obtain the mean and deviation statistics. To demonstrate the feasibility of the formulation, a one-dimensional model of heat transfer phenomenon in superfluid flow through a porous media is considered. Results of this formulation agree well with the Monte-Carlo simulations and the analytical solutions. Although the numerical experiments are confined to parametric random variables, a formulation is presented to account for the random spatial variations.

O P Agrawal