Geodesic
Heating process simulation for a body subjected to an intensive thermal effect on its surface
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2010), pp. 44-54

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An approximate method of calculating the nonstationary temperature fields for the case of fast and intensive heating of bodies is considered. The fast heating of a body is simulated by various boundary conditions at its heated surface. An approximate method is proposed in a one-dimensional formulation to solve the unsteady heat conduction equation with these boundary conditions. The applicability of this method in practice is confirmed by comparing the approximate temperature fields with the exact solution. An approximate temperature field is constructed for a particular case with consideration of a temperature dependence of thermal parameters, which allows one to describe the heat localization in a heated zone. 
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     author = {M. V. Yumashev and M. A. Yumasheva and P. A. Krasnova},
     title = {Heating process simulation for a body subjected to an intensive thermal effect on its surface},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--54},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a7/}
}
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M. V. Yumashev; M. A. Yumasheva; P. A. Krasnova. Heating process simulation for a body subjected to an intensive thermal effect on its surface. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2010), pp. 44-54. http://geodesic.mathdoc.fr/item/VMUMM_2010_4_a7/