Construction of Short-Time Heat Conduction Solutions in One-Dimensional Finite Rectangular Bodies

Abstract

The concept of both penetration and deviation times for rectangular coordinates along with the principle of superposition for linear problems allows short-time solutions to be constructed for a one-dimensional (1D) rectangular finite body from the well-known solutions of a semi-infinite medium. Some adequate physical considerations due to thermal symmetries with respect to the middle plane of a slab to simulate homogeneous boundary conditions of the first and second kinds are also needed. These solutions can be applied at the level of accuracy desired (one part in 10A, with A = 2, 3, …, 15) with respect to the maximum temperature variation (that always occurs at the active surface and at the time of evaluation) in place of the exact analytical solution to the problem of interest consisting of an infinite number of terms and, hence, unapplicable.