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An accurate and stable numerical method for solving a micro heat transfer model in a one-dimensional N-Carrier system in spherical coordinates / Weizhong Dai in Journal of heat transfer, Vol. 134 N° 5 (Mai 2012) 

Public ISBD [article]  in Journal of heat transfer > Vol. 134 N° 5 (Mai 2012) . - 07 p. Titre : An accurate and stable numerical method for solving a micro heat transfer model in a one-dimensional N-Carrier system in spherical coordinates Type de document : texte imprimé Auteurs : Weizhong Dai, Auteur ; Da Yu Tzou, Auteur Année de publication : 2012 Article en page(s) : 07 p. Note générale : heat transfer Langues : Anglais (eng) Mots-clés : spherical  coordinates;  micro  heat  transfer  model;  N-carriers  and  Neumann  boundary  condition;  Crank–Nicholson  scheme Index. décimale : 536 Chaleur. Thermodynamique Résumé : We consider the generalized micro heat transfer model in a 1D microsphere with N-carriers and Neumann boundary condition in spherical coordinates, which can be applied to describe nonequilibrium heating in biological cells. An accurate Crank–Nicholson type of scheme is presented for solving the generalized model, where a new second-order accurate numerical scheme for the Neumann boundary condition is developed so that the overall truncation error is second order. The scheme is proved to be unconditionally stable and convergent. The present scheme is then tested by three numerical examples. Results show that the numerical solution is much more accurate than that obtained based on the Crank–Nicholson scheme with the conventional method for the Neumann boundary condition. Furthermore, the convergence rate of the present scheme is about 1.8 with respect to the spatial variable, while the convergence rate of the Crank–Nicholson scheme with the conventional method for the Neumann boundary condition is only 1.0 with respect to the spatial variable. The scheme is ready to apply for thermal analysis in N-carrier systems. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.org/getabs/servlet/GetabsServlet?prog=normal&id=JHTRAO000134000005 [...] [article] An accurate and stable numerical method for solving a micro heat transfer model in a one-dimensional N-Carrier system in spherical coordinates [texte imprimé] / Weizhong Dai, Auteur ; Da Yu Tzou, Auteur . - 2012 . - 07 p. heat transfer Langues : Anglais (eng) in Journal of heat transfer > Vol. 134 N° 5 (Mai 2012) . - 07 p. Mots-clés : spherical  coordinates;  micro  heat  transfer  model;  N-carriers  and  Neumann  boundary  condition;  Crank–Nicholson  scheme Index. décimale : 536 Chaleur. Thermodynamique Résumé : We consider the generalized micro heat transfer model in a 1D microsphere with N-carriers and Neumann boundary condition in spherical coordinates, which can be applied to describe nonequilibrium heating in biological cells. An accurate Crank–Nicholson type of scheme is presented for solving the generalized model, where a new second-order accurate numerical scheme for the Neumann boundary condition is developed so that the overall truncation error is second order. The scheme is proved to be unconditionally stable and convergent. The present scheme is then tested by three numerical examples. Results show that the numerical solution is much more accurate than that obtained based on the Crank–Nicholson scheme with the conventional method for the Neumann boundary condition. Furthermore, the convergence rate of the present scheme is about 1.8 with respect to the spatial variable, while the convergence rate of the Crank–Nicholson scheme with the conventional method for the Neumann boundary condition is only 1.0 with respect to the spatial variable. The scheme is ready to apply for thermal analysis in N-carrier systems. DEWEY : 536 ISSN : 0022-1481 En ligne : http://asmedl.org/getabs/servlet/GetabsServlet?prog=normal&id=JHTRAO000134000005 [...]