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Analytic solutions of initial-boundary-value problems of transient conduction using symmetries. (English) Zbl 1187.35005
Summary: Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and closed form solutions is carried out for a physical problem of heat conduction in a semi-infinite solid bar made of AISI 304 stainless steel.

35B06Symmetries, invariants, etc. (PDE)
35K20Second order parabolic equations, initial boundary value problems
Full Text: DOI
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