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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Implicit-explicit Runge-Kutta for radiation hydrodynamics I: Gray diffusion

Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and nonlinear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. In conclusion, we prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3–5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dominant balance-based adaptive mesh refinement for incompressible fluid flows

This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a Gaussian mixture model (GMM) to classify grid cells into active and passive regions based on the dominant physical interactions within the equation space. By modeling truncation error probabilistically from discretized terms, the method identifies regions of high interaction where numerical accuracy is most sensitive to resolution. Unlike traditional AMR strategies, this approach does not rely on heuristic-based sensors or user-defined thresholds, providing a fully automated and problem-independent framework for AMR. Applied to the incompressible Navier-Stokes equations for steady and unsteady flow past a cylinder, the DBA-based AMR method achieves comparable accuracy to high-resolution grids while reducing computational costs by up to 70 %. The validation highlights the method’s effectiveness in capturing complex flow features while minimizing grid cells, directing computational resources toward regions with the most critical dynamics. This modular and scalable strategy is adaptable to a wide range of applications, presenting a promising tool for efficient high-fidelity simulations in CFD and other multiphysics domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

42 ENGINEERING↗
DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗
DOE OSTI2024

Mechanistic definition and prediction of the mass exchange coefficient between rivers and hyporheic zones: The $α$ of two $Ω$s

Solute transport in interconnected rivers and hyporheic zones is typically modeled through dual-domain models where first-order solute mass transfer between the two domains, Ω R and Ω HZ , is represented by a coefficient α. The transient storage model (TSM) is an example of such an approach. In practice, α is determined by fitting the tails of solute tracer breakthrough curves using a TSM. This approach has led to ambiguity regarding α’s physical meaning and transferability. Here, in this work, we investigated the physical basis for α and tested it with virtual experiments through the fully coupled multiphysics model hyporheicFoam for the Ω R – Ω HZ system. hyporheicFoam explicitly simulated coupled flow and solute transport over a kilometer with centimeter-scale resolution. Model results were analyzed to calculate α following its theoretical definition directly. Using the determined α within a TSM enables accurate reproduction of solute transport, underscoring α’s physical relevance and precision.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A concurrent irradiation-mechanics multiscale coupling model

The vast majority of our current knowledge regarding the basic mechanisms controlling irradiation effect on mechanical properties is based almost entirely on the results of post-irradiation experiments or theoretical models. However, the concurrent effects of irradiation, mechanical stress, and thermal damage on the failure phenomena of materials and components remain largely unexplored due to its internal multiscale-multiphysics coupling nature. Here, we present here a concurrent irradiation-mechanics multiscale coupling model. The concurrent evolutions of nanoscale irradiation defect clusters, microscale dislocation configurations, and mechanical responses are well captured based on coupling cluster dynamics, discrete dislocation dynamics, and the finite element methods using an effective time marching scheme. Model predictions of defect densities and size are in general agreement with experimental observations. Irradiation hardening is shown to take place also in samples undergoing concurrent irradiation-mechanical loading, similar to samples tested post-irradiation. However, the occurrence of plastic flow localization and dislocation channel formation is not accompanied with apparent yield drop (softening) under concurrent irradiation-mechanical loading conditions, which is different from the post-irradiation case.

42 ENGINEERING↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Impact of uranium oxide (UO 2 ) fuel with molybdenum (Mo) inserts on pressurized water reactor performance and safety

This work investigates nuclear reactor performance and safety characteristics of UO 2 with high thermal conductivity Mo insert structures by using multiphysics modeling techniques. Additionally, the purpose of this study is to use scoping analyses to quantify the impact of using Mo inserts from neutronic and heat transfer standpoints. Attention is given to reactor performance parameters, such as cycle length, maximum fuel temperature, temperature gradients in the fuel, and stored energy in the fuel. The finite-element code BISON and the Monte Carlo particle transport code Serpent were used to perform sensitivity analyses on the Mo insert geometry to optimize the insert design and inform larger scale modeling that required the homogenization of the UO 2 and Mo. Although BISON is often used as a fuel performance analysis tool, it is used in this context for heat transfer analysis only. Fuel performance optimization is outside the scope of the current study, but would be important for future work focused on this concept. The results showed that the insert had little impact on neutronic performance and that homogenizing the UO 2 and Mo was acceptable for reactor physics calculations. Reactivity temperature coefficients calculated using homogeneous UO 2 -Mo were shown to be relatively similar to UO 2 , but higher Mo content and 235 U enrichment can reduce the worth of soluble boron and control rods. The effect of insert geometry on heat transfer was much greater, and an approximately 15–20% difference in maximum fuel temperature was predicted between the best and worst performing heat transfer geometries. Furthermore, thermal conductivity calibration based on the finite element analysis results was performed to improve the accuracy of temperature predictions in reactor analysis models that homogenized the UO 2 -Mo fuel. Compared with UO 2 in a pressurized water reactor (PWR), the optimized UO 2 -Mo design increased the margin to fuel melt by 13–32% across the fuel cycle, but it requires the 235U enrichment to exceed 5% to match the cycle length of conventional UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

An ab initio molecular dynamics investigation of the thermophysical properties of molten NaCl-MgCl 2

Molten salts have many applications in the nuclear and solar energy industries for thermal storage and heat transfer applications. However, there is a knowledge gap in molten salt thermophysical properties which hinders the technical readiness level of molten salt applications, especially in the nuclear industry. A common method of investigating new materials is through ab initio Molecular Dynamics (AIMD) simulations which is an effective tool to investigate structural and thermophysical properties at realistic temperatures. NaCl-MgCl 2 is an inexpensive salt that is a good candidate for use as a heat transfer medium in solar power applications or in the secondary loop of a nuclear reactor. In this article, the thermophysical properties of NaCl-MgCl 2 are computed via AIMD calculations to supplement the limited experimental studies in the literature. Here a wide range of compositions and temperatures for the pseudo-binary NaCl-MgCl 2 were used to calculate the density, heat capacity, compressibility, enthalpy of mixing, and volumetric thermal expansion coefficient. AIMD is shown to accurately model the densities of molten NaCl-MgCl 2 as there is good agreement with the available literature. This work observed a transition to a monotonic increase of the density with respect to MgCl 2 composition occurring above 1100 K. The heat capacity values increase uniformly with respect to concentration of MgCl 2 at a rate of 2.85 J/mol-K per 10 mol% of MgCl 2 . Select thermophysical properties are fit to a Redlich-Kister expansion for utilization in multiphysics simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Implications of point defect accumulation on UO 2 thermal conductivity and fission gas release under accelerated fuel irradiation

Evaluation of thermal properties is a crucial factor for nuclear fuel performance. During reactor operation, the accumulation of fission products and irradiation-induced lattice defects are responsible for degradation in thermal conductivity. Consequently, it affects fuel temperature and fission gas release (FGR) among other Multiphysics processes important for economics and safety analysis. We analyze the implications of point defects (PD) accumulation described using a rate theory (RT) Model on lattice thermal conductivity of UO 2 . Here, we demonstrate that fission rate-dependent point defect concentrations have the largest impact on in-pile thermal conductivity in the periphery of light water reactor fuels below a temperature threshold governed by the migration barrier of defects. Our analysis provides a mechanistic description of this phenomena which current fuel performance codes treat empirically. The reduction of thermal conductivity in the low -temperature rim region acts as additional thermal resistance and leads to a temperature notably larger than suggested by Lucuta thermal conductivity correlation. These effects are anticipated to have notable impacts when fuels are exposed to accelerated radiation. The impact of such point defect-informed treatment of thermal conductivity on fuel performance is evaluated by a detailed analysis of fission gas behavior and its release. We consider several models capturing different stages of fission gas bubble evolution and fission gas release (FGR). Finally, a new fission rate-dependent correction to the Lucuta correlation is proposed. The results show a significant reduction in thermal conductivity at the fuels’ periphery and an increase in fuel centerline temperature specifically at low burnups. Ultimately a modified LC shows a higher FGR compared to the original LC, while the acceleration process results in a reduction in overall FGR.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Numerical investigation of thermal runaway mitigation through a passive thermal management system

Prevention of thermal runaway and its propagation remains a technical barrier to the application of lithium-ion batteries. To mitigate thermal runaway in lithium-ion battery packs, heat sinks have been designed using various materials, such as phase-change materials or metal plates. In this study, aluminum plates were assembled into battery modules as heat sinks and the effect of plate thickness on thermal runaway mitigation was numerically investigated. A three-dimensional integrated multiphysics model was validated and calibrated with experimental data. It identified the mechanism and sequence of thermal runaway propagation in detail. Thermal mass and contact resistance are found to be the key design parameters for preventing thermal runaway propagation for the studied battery module configuration. In addition, this study provides further insights into the design of aluminum heat sinks for lithium-ion battery packs.

25 ENERGY STORAGE↗
DOE OSTI2026

Gas-driven short disconnection mitigates thermal runaway in Li-ion batteries under mechanical abuse

Mechanical abuse poses a critical safety risk to Li-ion batteries by inducing internal short circuits that initiate thermal runaway. Remarkably, voltage recovery frequently emerges during thermal runaway initiation, a phenomenon that conventional theories fail to explain. Here, our study develops a new multiphysics mechanism to explain voltage recovery, termed gas-driven short disconnection, whereby internal gas pressure mechanically disengages short-circuit contacts and causes the cell voltage to rebound. This mechanism incorporates gas generation and its structural impact on the short circuit. Real-time optical and thermal imaging and X-ray computed tomography reveal fluid-structure interaction between internal gas flow and adjacent shorting contacts. We establish a mechanistic framework linking gas-driven short disconnection to cell-level voltage and temperature responses, elucidating the extension–truncation pattern of voltage recovery. Furthermore, thermal regime maps show that a voltage recovery duration exceeding 5 s correlates with limited temperature rise below 150 °C, indicating that sustained short-circuit disconnection suppresses Joule heating. Additionally, a dimensionless criterion is deduced from scaling analysis for physical plausibility of gas-driven short disconnection in mechanically abused cells. This finding inspires smart venting control, which regulates gas release to maintain the internal pressure while dissipating gas enthalpy, thereby providing a device-level strategy for thermal runaway mitigation.

Gas-driven short disconnection↗
DOE OSTI2026

Material-dependent photon ionizing radiation effects in Si and GaAs PIN diodes: A numerical investigation

We present a finite-element drift-diffusion-Poisson model in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework to compare the radiation response of silicon (Si) and gallium arsenide (GaAs) PIN diodes under high-energy photon irradiation. The model solves coupled carrier continuity and Poisson’s equations with Shockley-Read-Hall recombination, and is verified against standard analytical J-V behavior. Using a simplified 1D geometry with ideal Ohmic contacts, we quantify device response under forward and reverse bias with a 100 MeV photon flux. Under forward bias, Si exhibits markedly greater radiation sensitivity than GaAs, including larger increases in current density, stronger local field and carrier-product perturbations, and higher recombination. Under reverse bias, GaAs shows larger radiation-induced photocurrent and broader current-density peaks near junctions, indicating an advantage for photodetection. Integrated steady-state recombination is consistently higher in Si across voltages. Under periodic photon pulses, GaAs produces higher-amplitude photoresponse and settles more rapidly than Si. These results highlight material-dependent trade-offs for radiation-tolerant, high-speed optoelectronics and provide guidance for selecting PIN architectures in aerospace, nuclear, and high-energy physics environments.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Pellet-clad mechanical interaction screening using VERA applied to Watts Bar Unit 1, Cycles 1–3

The Consortium for Advanced Simulation of Light Water Reactors (CASL) aims to provide high-fidelity multiphysics simulations of light water nuclear reactors. To accomplish this, CASL is developing the Virtual Environment for Reactor Applications (VERA), which is a suite of code packages for thermal hydraulics, neutron transport, fuel performance, and coolant chemistry. As VERA continues to grow and expand, there has been an increased focus on incorporating fuel performance analysis methods. One of the primary goals of CASL is to estimate local cladding failure probability through pellet-clad interaction, which consists of both pellet-clad mechanical interaction (PCMI) and stress corrosion cracking. Estimating clad failure is important to preventing release of fission products to the primary system and accurate estimates could prove useful in establishing less conservative power ramp rates or when considering load-follow operations.While this capability is being pursued through several different approaches, the procedure presented in this article focuses on running independent fuel performance calculations with BISON using a file-based one-way coupling based on multicycle output data from high fidelity, pin-resolved coupled neutron transport–thermal hydraulics simulations. This type of approach is consistent with traditional fuel performance analysis methods, which are typically separate from core simulation analyses. A more tightly coupled approach is currently being developed, which is the ultimate target application in CASL.Recent work simulating 12 cycles of Watts Bar Unit 1 with VERA core simulator are capitalized upon, and quarter-core BISON results for parameters of interest to PCMI (maximum centerline fuel temperature, maximum clad hoop stress, and minimum gap size) are presented for Cycles 1–3. In conclusion, based on these results, this capability demonstrates its value and how it could be used as a screening tool for gathering insight into PCMI, singling out limiting rods for further, more detailed analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Application of regression, variance, and density based global sensitivity methods to integrated VERA-CS and BISON simulations [Application of regression, variance, and density based global sensitivity methods to integrated VERA-CS and BISON simulations]

Uncertainty quantification (UQ) and sensitivity analyses (SA) are performed for coupled simulations between VERA-CS, a coupled pin resolved neutron transport and subchannel thermal hydraulics code, and the fuel performance code BISON. The interface between VERA-CS and BISON is performed in a multiphysics environment known as the LOCA Toolkit for U.S. light water reactors (LOTUS) currently under development at Idaho National Laboratory (INL). A focus is placed on using a variety of SA measures, including two regression based (Pearson and Spearman), one variance based (Sobol indices), and three moment independent measures (Delta moment independent measures with L 1 , L 2 , and L ∞ norms). The problem under inspection is a single assembly depletion case for three fuel cycles. The figures of merit are the minimum departure from nucleate boiling ratio (MDNBR), maximum fuel centerline temperature (MFCT), and gap conductance at peak power (GCPP). SA results show MDNBR to be linear with consistent rankings throughout the fuel cycles. MFCT is linear, but with a change in rankings at the switch from open gap to closed gap models. GCPP is nonlinear at intermediate states that coincide with the onset of contact between fuel and cladding. Furthermore, these nonlinear states allow for the showcasing of higher order SA measures over first order methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τ D ~ O 1 , the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τ D ≈ 4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio N u total / N u no - rad reaches a peak value of 1.76 at τ D = 4 and z/D = 200 , and is less than 1.1 for τ D < 0 . 1 and τ D > 60 . Under aiding-flow mixed convection, N u total / N u no - rad reaches a peak of 1.34 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 4 and τ D > 36 . Under opposing-flow mixed convection, Nu total / Nu no - rad reaches a peak of 1.81 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 2 and τ D > 50 . RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where N u total / N u no - rad is 2.26 observed at z/D = 50 . The sensitivity to wall emissivity is evaluated; in forced convection, the peak N u total / N u no - rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε = 1 (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( Gr / R e 2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗