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Finite-volume formulation and solution of the P3 equations of radiative transfer on unstructured meshes / Mahesh Ravishankar in Journal of heat transfer, Vol. 132 N° 2 (n° spécial) (Fevrier 2010) 

Public ISBD [article]  in Journal of heat transfer > Vol. 132 N° 2 (n° spécial) (Fevrier 2010) . - pp. [023402-1/14] Titre : Finite-volume formulation and solution of the P3 equations of radiative transfer on unstructured meshes Type de document : texte imprimé Auteurs : Mahesh Ravishankar, Auteur ; Sandip Mazumder, Auteur ; Ankan Kumar, Auteur Article en page(s) : pp. [023402-1/14] Note générale : Physique Langues : Anglais (eng) Mots-clés : Radiation  Participating  media  P3  RTE  solver  Finite-volume  Unstructured Index. décimale : 536 Chaleur. Thermodynamique Résumé : The method of spherical harmonics (or PN) is a popular method for approximate solution of the radiative transfer equation (RTE) in participating media. A rigorous conservative finite-volume (FV) procedure is presented for discretization of the P3 equations of radiative transfer in two-dimensional geometry—a set of four coupled, second-order partial differential equations. The FV procedure presented here is applicable to any arbitrary unstructured mesh topology. The resulting coupled set of discrete algebraic equations are solved implicitly using a coupled solver that involves decomposition of the computational domain into groups of geometrically contiguous cells using the binary spatial partitioning algorithm, followed by fully implicit coupled solution within each cell group using a preconditioned generalized minimum residual solver. The RTE solver is first verified by comparing predicted results with published Monte Carlo (MC) results for two benchmark problems. For completeness, results using the P1 approximation are also presented. As expected, results agree well with MC results for large/intermediate optical thicknesses, and the discrepancy between MC and P3 results increase as the optical thickness is decreased. The P3 approximation is found to be more accurate than the P1 approximation for optically thick cases. Finally, the new RTE solver is coupled to a reacting flow code and demonstrated for a laminar flame calculation using an unstructured mesh. It is found that the solution of the four P3 equations requires 14.5% additional CPU time, while the solution of the single P1 equation requires 9.3% additional CPU time over the case without radiation. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.aip.org/vsearch/servlet/VerityServlet?KEY=JHTRAO&ONLINE=YES&smode= [...] [article] Finite-volume formulation and solution of the P3 equations of radiative transfer on unstructured meshes [texte imprimé] / Mahesh Ravishankar, Auteur ; Sandip Mazumder, Auteur ; Ankan Kumar, Auteur . - pp. [023402-1/14]. Physique Langues : Anglais (eng) in Journal of heat transfer > Vol. 132 N° 2 (n° spécial) (Fevrier 2010) . - pp. [023402-1/14] Mots-clés : Radiation  Participating  media  P3  RTE  solver  Finite-volume  Unstructured Index. décimale : 536 Chaleur. Thermodynamique Résumé : The method of spherical harmonics (or PN) is a popular method for approximate solution of the radiative transfer equation (RTE) in participating media. A rigorous conservative finite-volume (FV) procedure is presented for discretization of the P3 equations of radiative transfer in two-dimensional geometry—a set of four coupled, second-order partial differential equations. The FV procedure presented here is applicable to any arbitrary unstructured mesh topology. The resulting coupled set of discrete algebraic equations are solved implicitly using a coupled solver that involves decomposition of the computational domain into groups of geometrically contiguous cells using the binary spatial partitioning algorithm, followed by fully implicit coupled solution within each cell group using a preconditioned generalized minimum residual solver. The RTE solver is first verified by comparing predicted results with published Monte Carlo (MC) results for two benchmark problems. For completeness, results using the P1 approximation are also presented. As expected, results agree well with MC results for large/intermediate optical thicknesses, and the discrepancy between MC and P3 results increase as the optical thickness is decreased. The P3 approximation is found to be more accurate than the P1 approximation for optically thick cases. Finally, the new RTE solver is coupled to a reacting flow code and demonstrated for a laminar flame calculation using an unstructured mesh. It is found that the solution of the four P3 equations requires 14.5% additional CPU time, while the solution of the single P1 equation requires 9.3% additional CPU time over the case without radiation. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.aip.org/vsearch/servlet/VerityServlet?KEY=JHTRAO&ONLINE=YES&smode= [...]

Monte Carlo study of phonon heat conduction in silicon thin films including contributions of optical phonons / Arpit Mittal in Journal of heat transfer, Vol. 132 N° 5 (Mai 2010) 

Public ISBD [article]  in Journal of heat transfer > Vol. 132 N° 5 (Mai 2010) . - pp. [052402-1/11] Titre : Monte Carlo study of phonon heat conduction in silicon thin films including contributions of optical phonons Type de document : texte imprimé Auteurs : Arpit Mittal, Auteur ; Sandip Mazumder, Auteur Article en page(s) : pp. [052402-1/11] Note générale : Physique Langues : Anglais (eng) Mots-clés : Monte  Carlo  Boltzmann  transport  equation  Thin  film  Thermal  conductivity  Optical  phonon  Silicon Index. décimale : 536 Chaleur. Thermodynamique Résumé : The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T>200 K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.aip.org/vsearch/servlet/VerityServlet?KEY=JHTRAO&smode=strresults& [...] [article] Monte Carlo study of phonon heat conduction in silicon thin films including contributions of optical phonons [texte imprimé] / Arpit Mittal, Auteur ; Sandip Mazumder, Auteur . - pp. [052402-1/11]. Physique Langues : Anglais (eng) in Journal of heat transfer > Vol. 132 N° 5 (Mai 2010) . - pp. [052402-1/11] Mots-clés : Monte  Carlo  Boltzmann  transport  equation  Thin  film  Thermal  conductivity  Optical  phonon  Silicon Index. décimale : 536 Chaleur. Thermodynamique Résumé : The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T>200 K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.aip.org/vsearch/servlet/VerityServlet?KEY=JHTRAO&smode=strresults& [...]