Heat Transfer in Semitransparent Solids

Viskanta, R.; Anderson, Edward E.

doi:10.1016/s0065-2717(08)70077-7

Cited by 125 publications

(70 citation statements)

References 131 publications

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“…These include (1) transient and steady-state heat conduction without radiation [20], (2) absorbing but non-scattering gray slab with black surfaces subjected to diffuse or collimated incident radiation without heat conduction [18], (3) steady-state combined 1D conduction and radiation in a slab between black surfaces at different temperatures [46]. Further validation was performed by comparing results for the full simulations with those for the lump system approach.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Radiative heat transfer in enhanced hydrogen outgassing of glass

Kitamura

Pilon

2009

International Journal of Hydrogen Energy

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This paper explores the physical mechanisms responsible for experimental observations that led to the definition of "photo-induced hydrogen outgassing of glass". Doped borosilicate glass samples were placed inside an evacuated silica tube and heated in a furnace or by an incandescent lamp. It was observed that hydrogen release from the glass sample was faster and stronger when heated by an incandescent lamp than within furnace. Here, sample and silica tube were modeled as planeparallel slabs exposed to furnace or to lamp thermal radiation. Combined conduction, radiation, and mass transfer were accounted for by solving the one-dimensional transient mass and energy conservation equations along with the steady-state radiative transfer equation. All properties were found in the literature. The experimental observations can be qualitatively explained based on conventional thermally activated gas diffusion and by carefully accounting for the participation of the silica tube to radiation transfer along with the spectral properties of the silica tube and the glass samples. In brief, the radiation emitted by the incandescent lamp is concentrated between 0.5 and 3.0 µm and reaches directly the sample since the silica tube is nearly transparent up to 3.5 µm. On the contrary, for furnace heating at 400 o C, the silica tube absorbs a large fraction of the incident radiation which reduces the heating rate and the H 2 release rate. However, between 0.8 and 3.2 µm undoped borosilicate does not absorb significantly. Coincidentally, Fe 3 O 4 doping increases the absorption coefficient and also reacts with H 2 to form ferrous ions which increase the absorption coefficient of the sample by two orders of magnitude. Thus, doped and reacted 1 samples heat up much faster when exposed to the heating lamp resulting in the observed faster response time and larger H 2 release rate.Keywords: hydrogen storage, photo-induced gas diffusion, hollow glass microspheres, outgassing NOMENCLATURE c p Specific heat at constant pressure (J/kg.K)

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Section: Methods Of Solutionmentioning

confidence: 99%

Radiative heat transfer in enhanced hydrogen outgassing of glass

Kitamura

Pilon

2009

International Journal of Hydrogen Energy

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“…There is a vast literature dealing with numerical methods for the radiative transfer equations, see for example [22,27] for a survey. These equations have been the key to understand the thermal radiation distribution on many semitransparent materials.…”

Section: Introductionmentioning

confidence: 99%

“…In (2.3), s = s − 2(n · s)n is the specular reflection of s on ∂Ω, and ρ ∈ [0, 1] is the reflectivity obtained according to the Fresnel and Snell laws [27]. Thus, for an incident angle θ m given by cos θ m = |n · s| and Snell's law…”

Section: Introductionmentioning

confidence: 99%

“…Note that many physical assumptions have to be taken into account to derive well-posed models for radiative transfer equations in non-grey diffusive semitransparent media. For more details on these assumptions, we refer to [22,27] among others. In what follows, we briefly recast the SP N approximations for the radiative transfer equations (2.6).…”

Section: Introductionmentioning

confidence: 99%

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hp-adaptive discontinuous Galerkin methods for simplified PN
Giani
¹
,
Seaı̈d
²

2016
Computer Methods in Applied Mechanics and Engineering
11
0
0
0
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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe investigate the performance of a class of hp-adaptive discontinuous Galerkin methods for the numerical solution of simplified P N approximations of radiative transfer in non-grey semitransparent media. By introducing an optical scale and using asymptotic expansions in the radiative transfer equation we formulate the simplified P N approximations. The optical spectrum is decomposed in frequency bands and the simplified P N equations are solved for each frequency band. As a numerical solver for the simplified P N equations we consider a high-order discontinuous Galerkin method. The solver belongs to a class of finite element methods whose approximate solutions are discontinuous across inter-element boundaries; this property renders the method ideally suited for the hp-adaptivity. An error estimator is shown to provide reliable and practically useful upper bounds for the numerical errors independent of the optical scales used in the simulations. The proposed method is simple, fast and highly accurate. The performance of the method is analyzed on several applications in frequency-dependent radiative transfer. The aim of such a method compared to the conventional finite element methods is to solve the simplified P N equations efficiently and with a high level of accuracy on unstructured meshes with different elements. The obtained results demonstrate the ability of the proposed method to capture the main radiative features.

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“…General details on physical and mathematical descriptions of these models have been addressed in a number of books and papers [22,21,19,30] among others. Despite the equation governing the transient radiative transfer is linear, computing its numerical solution is not trivial due to:…”

Section: Introductionmentioning

confidence: 99%

A Frequency-Domain Approach for the $$\hbox {P}_1$$ P 1 Approximation of Time-Dependent Radiative Transfer

2014

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(2015) 'A frequency-domain approach for the P1 approximation of time-dependent radiative transfer.', Journal of scientic computing., 62 (3). pp. 623-651. Further information on publisher's website:http://dx.doi.org/10.1007/s10915-014-9870-9Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s10915-014-9870-9Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe propose a new frequency-domain method to solve the simplified P 1 approximation of timedependent radiative transfer equations. The method employs the Fourier transform and consists of two stages. In the first stage the equations are transformed into an elliptic problem for the frequency variables. The numerical solutions of this problem are approximated using a Galerkin projection method based on the tensor-product B-spline interpolants. In the second stage a Gauss-Hermite quadrature procedure is proposed for the computation of the inverse Fourier transform to recover the numerical solutions of the original simplified P 1 problem. The method avoids the discretization of the time variable in the considered system and it accurately resolves all time scales in radiative transfer regimes. Several test examples are used to verify high accuracy, effectiveness and good resolution properties for smooth and discontinuous solutions.

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Heat Transfer in Semitransparent Solids

Cited by 125 publications

References 131 publications

Radiative heat transfer in enhanced hydrogen outgassing of glass

Radiative heat transfer in enhanced hydrogen outgassing of glass

hp-adaptive discontinuous Galerkin methods for simplified PN
Giani
¹
,
Seaı̈d
²

2016
Computer Methods in Applied Mechanics and Engineering
11
0
0
0
View full text Add to dashboard Cite

A Frequency-Domain Approach for the $$\hbox {P}_1$$ P 1 Approximation of Time-Dependent Radiative Transfer

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Heat Transfer in Semitransparent Solids

Cited by 125 publications

References 131 publications

Radiative heat transfer in enhanced hydrogen outgassing of glass

Radiative heat transfer in enhanced hydrogen outgassing of glass

hp-adaptive discontinuous Galerkin methods for simplified PNGiani1, Seaı̈d2 2016Computer Methods in Applied Mechanics and Engineering11000View full textAdd to dashboardCite

A Frequency-Domain Approach for the $$\hbox {P}_1$$ P 1 Approximation of Time-Dependent Radiative Transfer

Contact Info

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About

hp-adaptive discontinuous Galerkin methods for simplified PN
Giani
¹
,
Seaı̈d
²

2016
Computer Methods in Applied Mechanics and Engineering
11
0
0
0
View full text Add to dashboard Cite