Chebyshev collocation spectral approach for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index

Sun, Yasong; Li, Ben-Wen

doi:10.1016/j.ijheatmasstransfer.2009.11.047

Cited by 32 publications

(3 citation statements)

References 29 publications

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“…where T ref in this case is equal to 1000 K. It can be clearly seen that our results match accurately with those of the Sun and Li (2010), which very much confirms the eligibility of the model to treat radiation problems which are coupled with conduction mode of heat transfer.…”

Section: Coupled Conduction-radiation Problemsupporting

confidence: 83%

Investigation of heat transfer in one-dimensional models of polymeric foams by using a ray-splitting and tracing technique

Chhabra

Talukdar

2019

HFF

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Purpose This paper aims to develop a numerical model to investigate coupled conduction radiation heat transfer in a multilayer semi-transparent polymeric foam. Design/methodology/approach The model uses a multi-phase approach in which the radiative transfer is determined by solving the radiative transfer equation explicitly in the whole medium incorporating an interface condition valid in the geometric optics rgime. This is executed by using a combination of ray splitting and a discrete curved ray tracing technique. Both partial photon reflection and total internal reflection at the interface are considered in the present investigation. Findings The directional distribution of intensity within the whole medium can be determined, which is used to obtain the detailed temperature profile inside the domain. The performance of the proposed methodology has been tested by simulating the modelled foam at ambient conditions. The results obtained from the simulations are in good agreement with the published results and shows that there is a global non-linearity in the temperature profile in problems where conduction to radiation parameter is small. Originality/value Specular nature of radiative transfer at the interface is accounted for in the present analysis. Instead of working with direction integrated quantities (as in the case of P1 approximation), each bundle of rays is treated separately within the whole medium. This model serves as a starting point for a detailed spatially three dimensional study of heat transfer in foams and the mathematical nature of the formulation is such that it may result in an implementation to three-dimensions.

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Section: Coupled Conduction-radiation Problemsupporting

confidence: 83%

Investigation of heat transfer in one-dimensional models of polymeric foams by using a ray-splitting and tracing technique

Chhabra

Talukdar

2019

HFF

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“…The 2D transient conduction-radiation problem with an anisotropically scattering medium was analyzed by a hybrid of LBM and control volume finite element method [10]. Li et al also computed conduction-radiation combination problems using CSM in concentric spherical participating media [11], in a graded index plane [12], in a transient 1D planar or 2D rectangular geometry [13], in a transient anisotropic scattering but graded index medium [14], or even in a transient 3D system [15].…”

Section: Introductionmentioning

confidence: 99%

“…In our former works [11][12][13][14][15], the CSM was used to compute different problems of conduction-radiation combinations, from 1D to 3D, and steady or transient. The high accuracy due to exponential convergence and the high efficiency due to direct solution of CSM were illustrated.…”

Section: Introductionmentioning

confidence: 99%

Collocation Spectral Method for the Transient Conduction–Radiation Heat Transfer With Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure

2015

Journal of Heat Transfer

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The collocation spectral method (CSM) is further developed to solve the transient conduction-radiation heat transfer in a two-dimensional (2D) rectangular enclosure with variable thermal conductivity. The energy equation and the radiative transfer equation (RTE) are all discretized by Chebyshev-Gauss-Lobatto collocation points in space after the discrete ordinates method (DOM) discretization of RTE in angular domain. The treatment of variable thermal conductivity is executed using the array multiplication. The present method can deal with different boundary conditions with high accuracy, the Dirichlet one and mixed one, for example. Based on our new method, the effects of several parameters on heat transfer processes are analyzed.

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Linear stability analysis of Rayleigh-Bénard convection of cold water near its density maximum in a vertically heated annular container

Zhang

2017

J Mech Sci Technol

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Chebyshev collocation spectral approach for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index

Cited by 32 publications

References 29 publications

Investigation of heat transfer in one-dimensional models of polymeric foams by using a ray-splitting and tracing technique

Investigation of heat transfer in one-dimensional models of polymeric foams by using a ray-splitting and tracing technique

Collocation Spectral Method for the Transient Conduction–Radiation Heat Transfer With Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure

Linear stability analysis of Rayleigh-Bénard convection of cold water near its density maximum in a vertically heated annular container

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