Geodesic
Heat conduction problem analytical solution at time dependent heat transfer coefficients
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 171-184

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With the help of thermal balance integrated method and on the basis of introduction of temperature indignation front the analytical decision of a problem of non-stationary heat conductivity is obtained under boundary conditions of the third kind with variable in time factor of heat return. Graphs of isotherms distribution and velocity of their movement are constructed. In order to provide for the accuracy of the solution the additional boundary conditions defined from initial differential equation and basic boundary conditions, including the data obtained at the front of temperature indignation are entered.
Keywords: integral methods, analytical solutions, front of temperature perturbation, additional boundary conditions, isotherms, speeds of movement of isotherms. 
@article{VSGTU_2008_2_a18,
     author = {E. V. Stefanyuk and V. A. Kudinov},
     title = {Heat conduction problem analytical solution at time dependent heat transfer coefficients},
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     pages = {171--184},
     publisher = {mathdoc},
     number = {2},
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E. V. Stefanyuk; V. A. Kudinov. Heat conduction problem analytical solution at time dependent heat transfer coefficients. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 171-184. http://geodesic.mathdoc.fr/item/VSGTU_2008_2_a18/