variation range use false https://scigraph.springernature.com/explorer/license/ temperature perturbation front degree of accuracy 537-555 velocity balance method simple form motion time distribution conditions degree accuracy introduction heat conduction problem series series of problems transfer algebraic polynomials polynomials exponential algebraic polynomials 2009-05 heat transfer integral heat balance method isothermal lines articles analytical solution solution method isotherms motion of isotherms article boundary conditions With the use of the integral heat balance method based on the introduction of the temperature perturbation field and additional boundary conditions, we consider a method for finding analytical solutions of boundary-value problems of nonstationary heat conduction that permits obtaining, for a series of problems, solutions with a given degree of accuracy throughout the range of variation of the Fourier number. Solutions have a simple form of exponential algebraic polynomials, which makes it possible to investigate the heat transfer in the fields of isothermal lines, as well as analyze the time distributions of velocities of motion of isotherms. analytical solution method additional boundary conditions 2009-05-01 distribution front conduction problem heat conduction https://doi.org/10.1007/s10891-009-0223-8 nonstationary heat conduction temperature perturbation field problem range of variation lines 2022-01-01T18:21 perturbation front heat balance method perturbation field field method solution Analytical solution method for heat conduction problems based on the introduction of the temperature perturbation front and additional boundary conditions conduction Fourier number number en form boundary-value problem Samara State Technical University, 244 Molodogvardeiskaya Str., 443100, Samara, Russia Samara State Technical University, 244 Molodogvardeiskaya Str., 443100, Samara, Russia Kudinov V. A. 82 Mathematical Sciences pub.1047257701 dimensions_id Stefanyuk E. V. Springer Nature 1573-871X 1062-0125 Journal of Engineering Physics and Thermophysics doi 10.1007/s10891-009-0223-8 3 Springer Nature - SN SciGraph project Pure Mathematics