2017 年 4 巻 3 号 p. 17-00096
A new simple analytical method for solving the problem of one-dimensional transient heat conduction in a slab of finite thickness is proposed, in which the initial temperature is assumed zero or constant and the boundary surfaces are assumed to be at constant temperature, constant heat flux, or insulated. In this method, the solution is expressed by an infinite series representation, each term of which is the temperature solution of the corresponding initial-boundary value problem for the semi-infinite solid. Each semi-infinite solid extends to infinity in the positive or negative direction of the x axis and the surface is located at various positions along the x axis. Each term and the partial sum in the infinite series automatically satisfy the heat conduction equation and the initial condition. The solution is easily constructed so that the boundary values of the partial sum converge to those of the heat conduction problem as the number of terms N increases to infinity. The basic concept of the solution method for the problem of one-dimensional transient heat conduction in a slab is described. The solution method is applied to various initial-boundary value problems. The formulas of the typical solutions by this method are found to be the same as those of the solutions obtained by other literature using the method of Laplace transformation, which supports the validity of the new solution method proposed in this paper. The usefulness of this method is also examined.
