Three-dimensional transient heat conduction in a multilayer medium

Transient three-dimensional heat conduction calculations are required in many aerospace applications. The computer codes available have several drawbacks. The explicit codes require a small time step to avoid numerical instability, while the implicit codes require an inversion of large matrices. If large numbers of nodes are used, both methods can become quite expensive. By using implicit finite difference techniques, such as the alternating direction implicit method (ADI), it is possible to achieve numerical stability in two-dimensional situations. However, when extended to three-dimensional configurations, ADI methods become unstable. The present investigation is concerned with a computational procedure which is unconditionally stable for three-dimensional situations. The method is demonstrated with the aid of an example, taking into account the pinwheel radiator base of the thermal control system of an earth satellite.