Construction of Short-Time Solutions in Heat Conduction

The concept of both penetration and deviation times for rectangular coordinates along with the principle of superposition for linear problems allow short-time solutions to be constructed for a one-dimensional finite body from the well-known solution of a semi-infinite body. 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 10^A, with A = 2, 3, ..., 15) with respect to the maximum temperature rise (that always occurs at the active surface and at the time of interest) in place of the exact analytical solution to the problem of interest.