The calculation of variable heat flow in solids

Abstract In many contexts, in laboratory work, in industrial processes and in engineering practice, situations arise in which it is required to determine the flow of heat in bodies under nonsteady conditions. In some cases this can be done by direct experiment, and a few cases are sufficiently simple for formal analytical solutions of the appropriate equations to be obtained and evaluated. But direct experiment is often difficult or impossible, especially under practical conditions of manufacture or operation; and often the conditions of the problem, such as inhomogeneity or the shape of the material, or variation of its thermal properties with temperature, either make the formal solution so complicated that its numerical evaluation is impracticable, or put a formal solution out of the question altogether.