Axisymmetric Radiative Transfer Research Articles

Heat Transfer Study in Cylindrical Cavity with Heat Absorption or Generation

Lattice Boltzmann mesoscopic (LBM) is applied to solve energy equation of a transient conduction radiation heat transfer problem in a two-dimensional cylindrical participating (absorbing, emitting and scattering) medium in the presence of heat generation/absorption coefficient. Control volume finite element method (CVFEM) formulation is used to obtain the radiative information. To study the effectiveness of the LBM-CVFEM combination on unsteady conduction-radiation problems in cylindrical media, the energy equation of the problem is also solved using the finite difference method (FDM) in which the CVFEM is used to compute radiative information. The effects of heat generation/absorption coefficient on temperature distributions in the medium are studied. Results of the present work are benchmarked against those available in the literature. The hybrid numerical model’s results are also compared with those obtained by the FDM-CVFEM combination. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems .

Impact of Smoluchowski Temperature and Maxwell Velocity Slip Conditions on Axisymmetric Rotated Flow of Hybrid Nanofluid past a Porous Moving Rotating Disk.

Colloidal suspensions of regular fluids and nanoparticles are known as nanofluids. They have a variety of applications in the medical field, including cell separation, drug targeting, destruction of tumor tissue, and so on. On the other hand, the dispersion of multiple nanoparticles into a regular fluid is referred to as a hybrid nanofluid. It has a variety of innovative applications such as microfluidics, heat dissipation, dynamic sealing, damping, and so on. Because of these numerous applications of nanofluids in minds, therefore, the objective of the current exploration divulged the axisymmetric radiative flow and heat transfer induced by hybrid nanofluid impinging on a porous stretchable/shrinkable rotating disc. In addition, the impact of Smoluchowski temperature and Maxwell velocity slip boundary conditions are also invoked. The hybrid nanofluid was formed by mixing the copper (Cu) and alumina (Al2O3) nanoparticles scattered in the regular (viscous) base fluid (H2O). Similarity variables are used to procure the similarity equations, and the numerical outcomes are achieved using bvp4c in MATLAB software. According to the findings, double solutions are feasible for stretching and shrinking cases . The heat transfer rate is accelerated as the hybrid nanoparticles increases. The suction parameter enhances the friction factors as well as heat transfer rate. Moreover, the friction factor in the radial direction and heat transfer enrich for the first solution and moderate for the second outcome due to the augmentation , while the trend of the friction factor in the radial direction is changed only in the case of stretching for both branches.

Axisymmetric Radiative Transfer Models of Kilonovae

Abstract The detailed observations of GW170817 proved for the first time directly that neutron star mergers are a major production site of heavy elements. The observations could be fit by a number of simulations that qualitatively agree, but can quantitatively differ (e.g., in total r-process mass) by an order of magnitude. We categorize kilonova ejecta into several typical morphologies motivated by numerical simulations, and apply a radiative transfer Monte Carlo code to study how the geometric distribution of the ejecta shapes the emitted radiation. We find major impacts on both spectra and light curves. The peak bolometric luminosity can vary by two orders of magnitude and the timing of its peak by a factor of five. These findings provide the crucial implication that the ejecta masses inferred from observations around the peak brightness are uncertain by at least an order of magnitude. Mixed two-component models with lanthanide-rich ejecta are particularly sensitive to geometric distribution. A subset of mixed models shows very strong viewing angle dependence due to lanthanide “curtaining,” which persists even if the relative mass of lanthanide-rich component is small. The angular dependence is weak in the rest of our models, but different geometric combinations of the two components lead to a highly diverse set of light curves. We identify geometry-dependent P Cygni features in late spectra that directly map out strong lines in the simulated opacity of neodymium, which can help to constrain the ejecta geometry and to directly probe the r-process abundances.

Spectral Evolution and Radial Dust Transport in the Prototype Young Eruptive System EX Lup*

Abstract EX Lup is the prototype of a class of pre-main-sequence eruptive stars defined by their repetitive outbursts lasting several months. In 2008 January–September EX Lup underwent its historically largest outburst, brightening by about 4 mag in visual light. In previous studies we discovered ongoing silicate crystal formation in the inner disk during the outburst, but also noticed that the measured crystallinity fraction started decreasing after the source returned to the quiescent phase. Here we present new observations of the 10 μm silicate feature, obtained with the MIDI and VISIR instruments at Paranal Observatory. The observations demonstrate that within five years practically all crystalline forsterite disappeared from the surface of the inner disk. We reconstruct this process by presenting a series of parametric axisymmetric radiative transfer models of an expanding dust cloud that transports the crystals from the terrestrial zone to outer disk regions where comets are supposed to form. It is possible the early Sun also experienced similar flare-ups, and the forming planetesimals might have incorporated crystalline silicate material produced by such outbursts. Finally, we discuss how far the location of the dust cloud could be constrained by future James Webb Space Telescope observations.

A two-dimensional finite volume scheme solving the axisymmetric radiative heat transfer based on general structured grids

A two-dimensional finite volume scheme solving the axisymmetric radiative heat transfer based on general structured grids

Simultaneous Spectral Energy Distribution and Near-infrared Interferometry Modeling of HD 142666

Abstract We present comprehensive models of the Herbig Ae star, HD 142666, which aim to simultaneously explain its spectral energy distribution (SED) and near-infrared (NIR) interferometry. Our new submilliarcsecond resolution CHARA (CLASSIC and CLIMB) interferometric observations, supplemented with archival shorter baseline data from VLTI/PIONIER and the Keck Interferometer, are modeled using centrosymmetric geometric models and an axisymmetric radiative transfer code. CHARA’s 330 m baselines enable us to place strong constraints on the viewing geometry, revealing a disk inclined at 58° from face-on with a 160° major axis position angle. Disk models imposing vertical hydrostatic equilibrium provide poor fits to the SED. Models accounting for disk scale height inflation, possibly induced by turbulence associated with magnetorotational instabilities, and invoking grain growth to ≳1 μm size in the disk rim are required to simultaneously reproduce the SED and measured visibility profile. However, visibility residuals for our best model fits to the SED indicate the presence of unexplained NIR emission, particularly along the apparent disk minor axis, while closure phase residuals indicate a more centrosymmetric emitting region. In addition, our inferred 58° disk inclination is inconsistent with a disk-based origin for the UX Ori-type variability exhibited by HD 142666. Additional complexity, unaccounted for in our models, is clearly present in the NIR-emitting region. We propose that the disk is likely inclined toward a more edge-on orientation and/or an optically thick outflow component also contributes to the NIR circumstellar flux.

New constraints on the disk characteristics and companion candidates around T Chamaeleontis with VLT/SPHERE

The transition disk around the T Tauri star T Cha possesses a large gap, making it a prime target for high-resolution imaging in the context of planet formation. We aim to find signs of disk evolutionary processes by studying the disk geometry and the dust grain properties at its surface, and to search for companion candidates. We analyze a set of VLT/SPHERE data at near-infrared and optical wavelengths. We performed polarimetric imaging of T Cha with IRDIS (1.6 $\mu$m) and ZIMPOL (0.5-0.9 $\mu$m), and obtained intensity images from IRDIS dual-band imaging with simultaneous spectro-imaging with IFS (0.9-1.3 $\mu$m). The disk around T Cha is detected in all observing modes and its outer disk is resolved in scattered light with unprecedented angular resolution and signal-to-noise. The images reveal a highly inclined disk with a noticeable east-west brightness asymmetry. The significant amount of non-azimuthal polarization signal in the $U_{\phi}$ images, with a $U_{\phi}$/$Q_{\phi}$ peak-to-peak value of 14%, is in accordance with theoretical studies on multiple scattering. Our optimal axisymmetric radiative transfer model considers two coplanar inner and outer disks, separated by a gap of 0.28" (~30au) in size. We derive a disk inclination of ~69 deg and PA of ~114 deg. In order to self-consistently reproduce the intensity and polarimetric images, the dust grains, responsible for the scattered light, need to be dominated by sizes of around ten microns. A point source is detected at an angular distance of 3.5" from the central star. It is, however, found not to be co-moving. We confirm that the dominant source of emission is forward scattered light from the near edge of the outer disk. Our point source analysis rules out the presence of a companion heavier than ~8.5 $M_{\mathrm{jup}}$ between 0.1" and 0.3". The detection limit decreases to ~2 $M_{\mathrm{jup}}$ for 0.3" to 4.0".

A radiation transfer model for the Milky Way: I. Radiation fields and application to high-energy astrophysics★

We present a solution for the ultraviolet – submillimetre (submm) interstellar radiation fields (ISRFs) of the Milky Way (MW), derived from modelling COBE, IRAS and Planck maps of the all-sky emission in the near-, mid-, far-infrared and submm. The analysis uses the axisymmetric radiative transfer model that we have previously implemented to model the panchromatic spectral energy distributions (SEDs) of star-forming galaxies in the nearby universe, but with a new methodology allowing for optimization of the radial and vertical geometry of stellar emissivity and dust opacity, as deduced from the highly resolved emission seen from the vantage point of the Sun. As such, this is the first self-consistent model of the broad-band continuum emission from the MW. In this paper, we present model predictions for the spatially integrated SED of the MW as seen from the Sun, showing good agreement with the data, and give a detailed description of the solutions for the distribution of ISRFs, as well as their physical origin, throughout the volume of the galaxy. We explore how the spatial and spectral distributions of our new predictions for the ISRF in the MW affects the amplitude and spectral distributions of the gamma rays produced via inverse Compton scattering for cosmic ray (CR) electrons situated at different positions in the galaxy, as well as the attenuation of the gamma rays due to interactions of the gamma-ray photons with photons of the ISRF. We also compare and contrast our solutions for the ISRF with those incorporated in the galprop package used for modelling the high-energy emission from CR in the MW.

A Methodology to Solve 2D and Axisymmetric Radiative Transfer Problems Using a General 3D Solver

A method to solve the radiative transfer equation (RTE) for absorbing-emitting and/or scattering media for 2-D and axisymmetric geometries using a general 3-D solver with a special treatment of the boundary condition in the third direction is presented. It allows a choice of first- or second- order schemes and can be used with non-orthogonal hexahedral grids for complex domains. Two-dimensional or axisymmetric problems are treated as different special cases of a three-dimensional problem. The method is tested on axisymmetric problems with absorbing-emitting and/or scattering media and on a 2D planar problem with a transparent medium and validated by comparisons with benchmark solutions.

PHOTOEVAPORATION OF CIRCUMSTELLAR DISKS REVISITED: THE DUST-FREE CASE

Photoevaporation by stellar ionizing radiation is believed to play an important role in the dispersal of disks around young stars. The mass loss model for dust-free disks developed by Hollenbach et al. is currently regarded as a conventional one and has been used in a wide variety of studies. However, the rate in this model was derived by the crude so-called 1+1D approximation of ionizing radiation transfer, which assumes that diffuse radiation propagates in a direction vertical to the disk. In this study, we revisit the photoevaporation of dust-free disks by solving the 2D axisymmetric radiative transfer for steady-state disks. Unlike that solved by the conventional model, we determine that direct stellar radiation is more important than the diffuse field at the disk surface. The radial density distribution at the ionization boundary is represented by the single power-law with an index -3/2 in contrast to the conventional double power-law. For this distribution, the photoevaporation rate from the entire disk can be written as a function of the ionizing photon emissivity, Phi_EUV, from the central star and the disk outer radius, r_d, as follows: Mdot_PE = 5.4 x 10^-5 x (Phi_EUV/10^49 sec^-1)^1/2 x (r_d/1000 AU)^1/2 Msun/yr. This new rate depends on the outer disk radius rather than on the gravitational radius as in the conventional model, caused by the enhanced contribution to the mass loss from the outer disk annuli. In addition, we discuss its applications to present-day as well as primordial star formation.

A Spectrally Accurate Two-Dimensional Axisymmetric, Tightly Coupled Photon Monte Carlo Radiative Transfer Equation Solver for Hypersonic Entry Flows

A two-dimensional axisymmetric ray tracing photon Monte Carlo radiative transfer solver is developed. Like all ray tracing Monte Carlo codes, the ray tracing is performed in 3D, however, arrangements are made to take advantage of the 2D nature of the problem, to minimize computational time. The solver is designed to be tightly integrated into finite volume hypersonic flow solvers and is able to resolve the complex spectral properties of such flows to line-by-line (LBL) accuracy. The solver is then directly integrated into data parallel line relaxation (DPLR), a hypersonic flow solver, and closely coupled calculations are performed.

Panchromatic radiation from galaxies as a probe of galaxy formation and evolution

AbstractI review work on modelling the infrared and submillimetre SEDs of galaxies. The underlying physical assumptions are discussed and spherically symmetric, axisymmetric, and 3-dimensional radiative transfer codes are reviewed. Models for galaxies with Spitzer IRS data and for galaxies in the Herschel-Hermes survey are discussed. Searches for high redshift infrared and submillimetre galaxies, the star formation history, the evolution of dust extinction, and constraints from source-counts, are briefly discussed.

Unstructured Polygonal Finite-Volume Solutions of Radiative Heat Transfer in a Complex Axisymmetric Enclosure

Radiative heat transfer in a complex axisymmetric enclosure with participating medium is investigated by using the finite-volume method (FVM). In particular, an implementation of the unstructured polygonal meshes is adopted by connecting each center point of the unstructured triangular meshes rather than joining the centroids of the triangular elements to the midpoints of the corresponding sides to form a polygonal element. Also, typical considerations regarding application of the present polygonal mesh system to axisymmetric radiation are discussed. After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, the final discretization equation is introduced with the conventional finite-volume approach by using the directional weights. For validation and comparison, three test examples with complex axisymmetric geometries have been accomplished. The present study shows that not only is the method flexible in treating radiative problems with complex geometries, it is also accurate and efficient for the analysis of axisymmetric radiative heat transfer.

Young stars and protostellar cores near NGC 2023

We investigate the young (proto)stellar population in NGC 2023 and the L 1630 molecular cloud bordering the HII region IC 434, using Spitzer IRAC and MIPS archive data, JCMT SCUBA imaging and spectroscopy as well as targeted BIMA observations of one of the Class 0 protostars, NGC 2023 MM1. We have performed photometry of all IRAC and MIPS images, and used color-color diagrams to identify and classify all young stars seen within a 22'x26' field along the boundary between IC 434 and L 1630. For some stars, which have sufficient optical, IR, and/or sub-millimeter data we have also used the online SED fitting tool for a large 2D archive of axisymmetric radiative transfer models to perform more detailed modeling of the observed SEDs. We identify 5 sub-millimeter cores in our 850 and 450 micron SCUBA images, two of which have embedded class 0 or I protostars. Observations with BIMA are used to refine the position and characteristics of the Class 0 source NGC 2023 MM 1. These observations show that it is embedded in a very cold cloud core, which is strongly enhanced in NH2D. We find that HD 37903 is the most massive member of a cluster with 20 -- 30 PMS stars. We also find smaller groups of PMS stars formed from the Horsehead nebula and another elephant trunk structure to the north of the Horsehead. We refine the spectral classification of HD 37903 to B2 Ve. Our study shows that the expansion of the IC 434 HII region has triggered star formation in some of the dense elephant trunk structures and compressed gas inside the L 1630 molecular cloud. This pre-shock region is seen as a sub-millimeter ridge in which stars have already formed. The cluster associated with NGC 2023 is very young, and has a large fraction of Class I sources.

Resolved 24.5 micron emission from massive young stellar objects

Context. Massive young stellar objects (MYSO) are surrounded by massive dusty envelopes, whose physical structure and geometry are determined by the star formation process. Aims. Our principal aim is to establish the density structure of MYSO envelopes on scales of ∼1000 AU. This constitutes an increase of a factor ∼10 in angular resolution compared to similar studies performed in the (sub)mm. Methods. We have obtained diffraction-limited (0.6 �� ) 24.5 μm images (field of view of 40 �� × 30 �� ) of 14 well-known massive star formation regions with the COMICS instrument mounted on the 8.2 m Subaru telescope. We construct azimuthally averaged intensity profiles of the resolved MYSO envelopes and build spectral energy distributions (SEDs) from archival data and the COMICS 24.5 μm flux density. The SEDs range from near-infrared to millimeter wavelengths. Self-consistent 1-D radiative transfer models described by a density dependence of the form n(r) ∝ r −p are used to simultaneously compare the intensity profiles and SEDs to model predictions. Results. The images reveal the presence of discrete MYSO sources which are resolved on arcsecond scales, and, to first-order, the observed emission is circular on the sky. For many sources, the spherical models are capable of satisfactorily reproducing the 24.5 μm intensity profile, the 24.5 μm flux density, the 9.7 μm silicate absorption feature, and the submm emission. They are described by density distributions with p = 1.0 ± 0.25. Such distributions are shallower than those found on larger scales probed with single-dish (sub)mm studies. Other sources have density laws that are shallower/steeper than p = 1.0 and there is evidence that these are viewed near edge-on or near face-on respectively. In these cases spherical models fail to provide good fits to the data. The images also reveal a diffuse component tracing somewhat larger scale structures, particularly visible in the regions S 140, AFGL 2136, IRAS 20126+4104, Mon R2, and Cep A. Conclusions. We find a flattening of the MYSO density law going from scales probed with single-dish submm observations down to scales of ∼1000 AU probed with the observations presented here. We propose that this may be evidence of rotational support of the envelope. This finding will be explored further in a future paper using 2-D axisymmetric radiative transfer models.

Spectral Energy Distributions of High-Mass Protostellar Objects: Evidence of High Accretion Rates

The spectral energy distributions (SEDs), spanning the mid-infrared to millimeter wavelengths, of a sample of 13 high-mass protostellar objects (HMPOs) were studied using a large archive of 2D axisymmetric radiative transfer models. Measurements from the Spitzer GLIMPSE and MIPSGAL surveys and the MSX survey were used in addition to our own surveys at millimeter and submillimeter wavelengths to construct the SEDs, which were then fit to the archive of models. These models assumed that stars of all masses form via accretion and allowed us to make estimates for the masses, luminosities, and envelope accretion rates for the HMPOs. The models fit the observed SEDs well. The implied envelope accretion rates are high, ≈10−2.5 M☉ yr−1, consistent with the accretion-based scenario of massive star formation. With the fitted accretion rates and with mass estimates of up to ~20 M☉ for these objects, it appears plausible that stars with stellar masses M* > 20 M☉ can form via accretion.

Assessment of the axisymmetric radiative heat transfer in a cylindrical enclosure with the finite volume method

The radiative heat transfer in an axisymmetric enclosure containing an absorbing, emitting, and scattering gray medium is investigated by using the finite volume method (FVM). Especially, formulations with the cylindrical base vectors are introduced and its characteristics is discussed by comparing with other solution methods in the finite volume category. By considering the three-dimensional procedure, the angular redistribution term, which appears in such curvilinear coordinates as axisymmetric and spherically symmetric ones, can be treated efficiently without any artifice usually introduced in the conventional discrete ordinates method (DOM). After a mathematical formulation and corresponding discretization equation for the radiative transfer equation (RTE) are derived, final discretization equation is introduced by using the directional weight, which is the key parameter in the FVM since it represents the inflow or outflow of radiant energy across the control volume faces depending on its sign. The present approach is then validated by comparing the present results with those of previous works. All the results presented in this work show that the present method is accurate and valuable for the analysis of cylindrically axisymmetric radiative heat transfer problems.

A Discontinuous Finite-Element Formulation for Radiative Transfer in Axisymmetric Finite Cylindrical Enclosures and Coupling with Other Mode Heat Transfer

ABSTRACT This article presents a discontinuous finite-element formulation for numerical solution of internal thermal radiative transfer problems in axisymmetric cylindrical enclosures. While the computation of axisymmetric radiative transfer is essentially three-dimensional, an appropriate mapping procedure entailing the use of the axisymmetric and periodic conditions associated with the enclosures may be used to make it possible to compute the problem over a 2-D mesh only. This will result in a significant reduction in both computing time and memory storage requirement. Mathematical formulation and numerical implementation using the discontinuous Galerkin method for axisymmetric internal radiation heat transfer calculations are given. The procedures for incorporating the mapping in the discontinuous formulation to convert an essentially 3-D calculation into a 2-D calculation are discussed in detail. The computed results are given and compare well with the solutions reported in the literature using other methods. Examples include both nonscattering and scattering cases. The effects of both solid-angular and spatial discretization are discussed, and both the theory and results show that an even discretization of solid angle is important to ensure adequate numerical accuracy. The coupling of the discontinuous and conventional finite-element methods for mixed-mode heat transfer calculations, including swirling flow, conduction, natural convection, and thermal radiation in participating media, is illustrated in the last example.

A TWO-DIMENSIONAL SCHEME FOR AXISYMMETRIC RADIATIVE HEAT TRANSFER USING THE FINITE-VOLUME METHOD

ABSTRACT A two-dimensional scheme using the finite-volume method is proposed to solve the radiative transfer equation for axisymmetric radiative transfer. The directions of intensity are determined relative to Cartesian-based vectors. The final discretized equations are based on a two-dimensional mesh in the spatial domain, similar to meshes used for convective and conductive heat transfer in computational fluid dynamics analysis. The control-angle overlap problem caused by misalignment of solid angles with control-volume faces in the angular direction is eliminated in the current scheme. Error caused by the control-volume face curvature is also eliminated. A comparison study using demonstration cases with participating media in axisymmetrical cylindrical enclosures shows satisfactory results.

A numerical scheme for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular boundaries

This paper presents a new numerical scheme of the discrete ordinates method for the solution of axisymmetric radiative transfer problems in irregular domains filled by media with opaque and transparent diffuse and specular (Fresnel) boundaries and interfaces. New test problems of radiative transfer, which describe radiative transfer in domains with Fresnel interfaces, are proposed in this paper. These problems admit analytic solutions and can be used as benchmark ones. The proposed scheme is applied to the solution of the problems. Numerical results show that the presence of Fresnel interfaces leads to an appreciably larger error in numerical solution. This is connected with the “discontinuity” of the Fresnel reflectivity, which, through numerical diffusion, leads to the distortion of numerical solution. Modification of the scheme allows to reduce the numerical error.