Methods of Solution of Equations of Heat Conduction with Constant Thermal Parameters and Without Reaction

Abstract

Solutions of the heat conduction equation are obtained for a variety of initial and boundary conditions when the thermal parameters — thermal conductivity λ, density ρ, specific heat C, and thus thermal diffusivity α — are constant. Usually solutions have one or two standard forms. One is in the form of a series of error functions or related integrals, which is most suitable for calculation in the early stages of heat conduction, as it converges rather quickly. The other is expressed in terms of a trigonometrical and exponential series, which is of interest for large values of time, because it converges very quickly under these conditions.