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A Temperature Total Fourier Series Solution For a Hollow Sphere

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@article{IJASEIT112,
   author = {Mehdi Mahmudi Mehrizi},
   title = {A Temperature Total Fourier Series Solution For a Hollow Sphere},
   journal = {International Journal on Advanced Science, Engineering and Information Technology},
   volume = {1},
   number = {5},
   year = {2011},
   pages = {554--559},
   keywords = {Hollow Sphere; Fourier Series; conduction},
   abstract = {In the following pages, we exhibit an analytical solution of a two-dimensional temperature field in a hollow sphere under total periodic boundary condition. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Till now periodic boundary condition was derived with a harmonic vibration, whereas there is a noticeable difference in the practical conditions with harmonic vibration. In this essay, by means of Fourier analysis, we imagine the outside total periodic boundary condition, as aggregate of harmonic vibrations . To solve the problem, first we imagine the boundary condition as constant values and with separation of variables; we can obtain temperature distribution in the  sphere. Then Duhamel's theorem is used to calculate temperature field under fully periodic boundary condition. For confirmation of accurate solution, we can compare the result for a harmonic vibration and those reported by others. Also, solutions for a hollow sphere were compared with other present references. At last we can obtain thermal stresses which is caused by temperature field in the hollow sphere.},
   issn = {2088-5334},
   publisher = {INSIGHT - Indonesian Society for Knowledge and Human Development},
   url = {http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=112},
   doi = {10.18517/ijaseit.1.5.112}
}

EndNote

%A Mehrizi, Mehdi Mahmudi
%D 2011
%T A Temperature Total Fourier Series Solution For a Hollow Sphere
%B 2011
%9 Hollow Sphere; Fourier Series; conduction
%! A Temperature Total Fourier Series Solution For a Hollow Sphere
%K Hollow Sphere; Fourier Series; conduction
%X In the following pages, we exhibit an analytical solution of a two-dimensional temperature field in a hollow sphere under total periodic boundary condition. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Till now periodic boundary condition was derived with a harmonic vibration, whereas there is a noticeable difference in the practical conditions with harmonic vibration. In this essay, by means of Fourier analysis, we imagine the outside total periodic boundary condition, as aggregate of harmonic vibrations . To solve the problem, first we imagine the boundary condition as constant values and with separation of variables; we can obtain temperature distribution in the  sphere. Then Duhamel's theorem is used to calculate temperature field under fully periodic boundary condition. For confirmation of accurate solution, we can compare the result for a harmonic vibration and those reported by others. Also, solutions for a hollow sphere were compared with other present references. At last we can obtain thermal stresses which is caused by temperature field in the hollow sphere.
%U http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=112
%R doi:10.18517/ijaseit.1.5.112
%J International Journal on Advanced Science, Engineering and Information Technology
%V 1
%N 5
%@ 2088-5334

IEEE

Mehdi Mahmudi Mehrizi,"A Temperature Total Fourier Series Solution For a Hollow Sphere," International Journal on Advanced Science, Engineering and Information Technology, vol. 1, no. 5, pp. 554-559, 2011. [Online]. Available: http://dx.doi.org/10.18517/ijaseit.1.5.112.

RefMan/ProCite (RIS)

TY  - JOUR
AU  - Mehrizi, Mehdi Mahmudi
PY  - 2011
TI  - A Temperature Total Fourier Series Solution For a Hollow Sphere
JF  - International Journal on Advanced Science, Engineering and Information Technology; Vol. 1 (2011) No. 5
Y2  - 2011
SP  - 554
EP  - 559
SN  - 2088-5334
PB  - INSIGHT - Indonesian Society for Knowledge and Human Development
KW  - Hollow Sphere; Fourier Series; conduction
N2  - In the following pages, we exhibit an analytical solution of a two-dimensional temperature field in a hollow sphere under total periodic boundary condition. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Till now periodic boundary condition was derived with a harmonic vibration, whereas there is a noticeable difference in the practical conditions with harmonic vibration. In this essay, by means of Fourier analysis, we imagine the outside total periodic boundary condition, as aggregate of harmonic vibrations . To solve the problem, first we imagine the boundary condition as constant values and with separation of variables; we can obtain temperature distribution in the  sphere. Then Duhamel's theorem is used to calculate temperature field under fully periodic boundary condition. For confirmation of accurate solution, we can compare the result for a harmonic vibration and those reported by others. Also, solutions for a hollow sphere were compared with other present references. At last we can obtain thermal stresses which is caused by temperature field in the hollow sphere.
UR  - http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=112
DO  - 10.18517/ijaseit.1.5.112

RefWorks

RT Journal Article
ID 112
A1 Mehrizi, Mehdi Mahmudi
T1 A Temperature Total Fourier Series Solution For a Hollow Sphere
JF International Journal on Advanced Science, Engineering and Information Technology
VO 1
IS 5
YR 2011
SP 554
OP 559
SN 2088-5334
PB INSIGHT - Indonesian Society for Knowledge and Human Development
K1 Hollow Sphere; Fourier Series; conduction
AB In the following pages, we exhibit an analytical solution of a two-dimensional temperature field in a hollow sphere under total periodic boundary condition. The material is assumed to be homogeneous and isotropic with time-independent thermal properties. Till now periodic boundary condition was derived with a harmonic vibration, whereas there is a noticeable difference in the practical conditions with harmonic vibration. In this essay, by means of Fourier analysis, we imagine the outside total periodic boundary condition, as aggregate of harmonic vibrations . To solve the problem, first we imagine the boundary condition as constant values and with separation of variables; we can obtain temperature distribution in the  sphere. Then Duhamel's theorem is used to calculate temperature field under fully periodic boundary condition. For confirmation of accurate solution, we can compare the result for a harmonic vibration and those reported by others. Also, solutions for a hollow sphere were compared with other present references. At last we can obtain thermal stresses which is caused by temperature field in the hollow sphere.
LK http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=112
DO  - 10.18517/ijaseit.1.5.112